1
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Mao L, Yang F, Zhai H. Symmetry-preserving quadratic Lindbladian and dissipation driven topological transitions in Gaussian states. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:070501. [PMID: 38899363 DOI: 10.1088/1361-6633/ad44d4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2023] [Accepted: 04/29/2024] [Indexed: 06/21/2024]
Abstract
The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian. Since the topological classification of such Hamiltonians depends on their symmetry classes, a primary issue we address is determining the requirement for the Lindbladian operators, under which the modular Hamiltonian can preserve its symmetry class during the dynamical evolution. We solve this problem for the fermionic Gaussian state and for the modular Hamiltonian being a quadratic operator of a set of fermionic operators. When these conditions are satisfied, along with a nontrivial topological classification of the symmetry class of the modular Hamiltonian, a topological transition can occur as time evolves. We present two examples of dissipation-driven topological transitions where the modular Hamiltonian lies in the AIII class withU(1) symmetry and the DIII class withoutU(1) symmetry. By a finite size scaling, we show that this density matrix topology transition occurs at a finite time. We also present the physical signature of this transition.
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Affiliation(s)
- Liang Mao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
| | - Fan Yang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
| | - Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
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2
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Guo Y, Yao H, Dhar S, Pizzino L, Horvath M, Giamarchi T, Landini M, Nägerl HC. Anomalous cooling of bosons by dimensional reduction. SCIENCE ADVANCES 2024; 10:eadk6870. [PMID: 38354241 PMCID: PMC10866542 DOI: 10.1126/sciadv.adk6870] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Accepted: 01/11/2024] [Indexed: 02/16/2024]
Abstract
Cold atomic gases provide a remarkable testbed to study the physics of interacting many-body quantum systems. Temperatures are necessarily nonzero, but cooling to the ultralow temperatures needed for quantum simulation purposes or even simply measuring the temperatures directly on the system can prove to be very challenging tasks. Here, we implement thermometry on strongly interacting two- and one-dimensional Bose gases with high sensitivity in the nanokelvin temperature range. Our method is aided by the fact that the decay of the first-order correlation function is very sensitive to the temperature when interactions are strong. We find that there may be a substantial temperature variation when the three-dimensional quantum gas is cut into two-dimensional slices or into one-dimensional tubes. Notably, the temperature for the one-dimensional case can be much lower than the initial temperature. Our findings show that this decrease results from the interplay of dimensional reduction and strong interactions.
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Affiliation(s)
- Yanliang Guo
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
| | - Hepeng Yao
- DQMP, University of Geneva, 24 Quai Ernest-Ansermet, Geneva CH-1211, Switzerland
| | - Sudipta Dhar
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
| | - Lorenzo Pizzino
- DQMP, University of Geneva, 24 Quai Ernest-Ansermet, Geneva CH-1211, Switzerland
| | - Milena Horvath
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
| | - Thierry Giamarchi
- DQMP, University of Geneva, 24 Quai Ernest-Ansermet, Geneva CH-1211, Switzerland
| | - Manuele Landini
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
| | - Hanns-Christoph Nägerl
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
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3
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Slager RJ, Bouhon A, Ünal FN. Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems. Nat Commun 2024; 15:1144. [PMID: 38326295 PMCID: PMC10850167 DOI: 10.1038/s41467-024-45302-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 01/18/2024] [Indexed: 02/09/2024] Open
Abstract
While a significant fraction of topological materials has been characterized using symmetry requirements1-4, the past two years have witnessed the rise of novel multi-gap dependent topological states5-9, the properties of which go beyond these approaches and are yet to be fully explored. Although already of active interest at equilibrium10-15, we show that the combination of out-of-equilibrium processes and multi-gap topological insights galvanize a new direction within topological phases of matter. We show that periodic driving can induce anomalous multi-gap topological properties that have no static counterpart. In particular, we identify Floquet-induced non-Abelian braiding, which in turn leads to a phase characterized by an anomalous Euler class, being the prime example of a multi-gap topological invariant. Most strikingly, we also retrieve the first example of an 'anomalous Dirac string phase'. This gapped out-of-equilibrium phase features an unconventional Dirac string configuration that physically manifests itself via anomalous edge states on the boundary. Our results not only provide a stepping stone for the exploration of intrinsically dynamical and experimentally viable multi-gap topological phases, but also demonstrate periodic driving as a powerful way to observe these non-Abelian braiding processes notably in quantum simulators.
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Affiliation(s)
- Robert-Jan Slager
- TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.
| | - Adrien Bouhon
- TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom
| | - F Nur Ünal
- TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.
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4
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Chen C, Liu RZ, Wu J, Su ZE, Ding X, Qin J, Wang L, Zhang WW, He Y, Wang XL, Lu CY, Li L, Sanders BC, Liu XJ, Pan JW. Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands. PHYSICAL REVIEW LETTERS 2023; 131:133601. [PMID: 37831993 DOI: 10.1103/physrevlett.131.133601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 08/17/2023] [Indexed: 10/15/2023]
Abstract
Berry curvature is a fundamental element to characterize topological quantum physics, while a full measurement of Berry curvature in momentum space was not reported for topological states. Here we achieve two-dimensional Berry curvature reconstruction in a photonic quantum anomalous Hall system via Hall transport measurement of a momentum-resolved wave packet. Integrating measured Berry curvature over the two-dimensional Brillouin zone, we obtain Chern numbers corresponding to -1 and 0. Further, we identify bulk-boundary correspondence by measuring topology-linked chiral edge states at the boundary. The full topological characterization of photonic Chern bands from Berry curvature, Chern number, and edge transport measurements enables our photonic system to serve as a versatile platform for further in-depth study of novel topological physics.
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Affiliation(s)
- Chao Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Run-Ze Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Jizhou Wu
- Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Zu-En Su
- The Physics Department and the Solid State Institute, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Xing Ding
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Jian Qin
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Lin Wang
- Department of Physics, University of Konstanz, D-78457 Konstanz, Germany
| | - Wei-Wei Zhang
- School of Computer Science, Northwestern Polytechnical University, Xi'an 710129, China
| | - Yu He
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xi-Lin Wang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Li Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Barry C Sanders
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- International Quantum Academy, Shenzhen 518048, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
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5
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Di Colandrea F, Amato L, Schiattarella R, Dauphin A, Cardano F. Retrieving space-dependent polarization transformations via near-optimal quantum process tomography. OPTICS EXPRESS 2023; 31:31698-31717. [PMID: 37858989 DOI: 10.1364/oe.491518] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 07/02/2023] [Indexed: 10/21/2023]
Abstract
An optical waveplate rotating light polarization can be modeled as a single-qubit unitary operator. This analogy can be exploited to experimentally retrieve a polarization transformation within the paradigm of quantum process tomography. Standard approaches to tomographic problems rely on the maximum-likelihood estimation, providing the most likely transformation to yield the same outcomes as a set of experimental projective measurements. The performances of this method strongly depend on the number of input measurements and the numerical minimization routine that is adopted. Here we investigate the application of genetic and machine learning approaches to this problem, finding that both allow for accurate reconstructions and fast operations when processing a set of projective measurements very close to the minimal one. We apply these techniques to the case of space-dependent polarization transformations, providing an experimental characterization of the optical action of spin-orbit metasurfaces having patterned birefringence. Our efforts thus expand the toolbox of methodologies for optical process tomography. In particular, we find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes, including non-unitary gates and operations in higher-dimensional Hilbert spaces.
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6
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Shui H, Lai CK, Yu Z, Tian J, Wu C, Chen X, Zhou X. Optimal lattice depth on lifetime of D-band ultracold atoms in a triangular optical lattice. OPTICS EXPRESS 2023; 31:26599-26609. [PMID: 37710517 DOI: 10.1364/oe.489823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Accepted: 07/15/2023] [Indexed: 09/16/2023]
Abstract
Ultracold atoms in optical lattices are a flexible and effective platform for quantum precision measurement, and the lifetime of high-band atoms is an essential parameter for the performance of quantum sensors. In this work, we investigate the relationship between the lattice depth and the lifetime of D-band atoms in a triangular optical lattice and show that there is an optimal lattice depth for the maximum lifetime. After loading the Bose-Einstein condensate into D band of optical lattice by shortcut method, we observe the atomic distribution in quasi-momentum space for the different evolution time, and measure the atomic lifetime at D band with different lattice depths. The lifetime is maximized at an optimal lattice depth, where the overlaps between the wave function of D band and other bands (mainly S band) are minimized. Additionally, we discuss the influence of atomic temperature on lifetime. These experimental results are in agreement with our numerical simulations. This work paves the way to improve coherence properties of optical lattices, and contributes to the implications for the development of quantum precision measurement, quantum communication, and quantum computing.
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7
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Zeng X, Liao L, Wang M, Wang H. Rare-earth metal-N 6 centers in porous carbon for electrocatalytic CO 2 reduction. Phys Chem Chem Phys 2023. [PMID: 37465923 DOI: 10.1039/d3cp02314a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/20/2023]
Abstract
Single-atom catalysts fabricated using rare earth elements have emerged for electrocatalytic carbon dioxide reduction, but they need to be studied systematically and intensively. Herein, density functional theory was employed to determine the electrocatalytic CO2 reduction activity of rare earth-N6 porous carbon (Re = Ce, Nd, Sm, Eu, Gd, Tb, Er, Tm, Yb, and Lu) single-atom catalysts. The results revealed that the binding energy of the rare-earth atoms to the N6C monolayers in the ten studied Re-N6C monatomic catalysts is much more negative than the cohesion energy of the bulk rare-earth metal, which makes rare-earth atoms stably dispersed in the N6C skeleton. CO is the primary chemical product of electrocatalytic CO2 reduction by Ce, Eu, and Lu. The primary product of the six monatomic species, i.e., Nd, Sm, Tb, Er, Tm, and Yb, is HCOOH. The dominant product of Gd is CH4. The limiting potentials of these catalysts are in the range of 0.31-0.786 V and their overpotentials are in the range of 0.06-0.707 V, all of which are relatively low, showing that they are potential and promising electrocatalysts for CO2 reduction. Subsequently, Eu-N6C was experimentally synthesized and used for electrocatalytic CO2 reduction to obtain CO products, and the overpotential showed good agreement with the theoretically calculated values.
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Affiliation(s)
- Xianshi Zeng
- Institute for Advanced Study, Nanchang University, Nanchang 330031, China.
- School of Physics and Materials Science, Nanchang University, Nanchang 330031, China
| | - Luliang Liao
- Institute for Advanced Study, Nanchang University, Nanchang 330031, China.
| | - Meishan Wang
- School of Integrated Circuits, Ludong University, Yantai city, 264025, China.
| | - Hongming Wang
- Institute for Advanced Study, Nanchang University, Nanchang 330031, China.
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8
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Wang Z, Zeng XT, Biao Y, Yan Z, Yu R. Realization of a Hopf Insulator in Circuit Systems. PHYSICAL REVIEW LETTERS 2023; 130:057201. [PMID: 36800475 DOI: 10.1103/physrevlett.130.057201] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 01/13/2023] [Indexed: 06/18/2023]
Abstract
Three-dimensional (3D) two-band Hopf insulators are a paradigmatic example of topological phases beyond the topological classifications based on powerful methods like K theory and symmetry indicators. Since this class of topological insulating phases was theoretically proposed in 2008, they have attracted significant interest owing to their conceptual novelty, connection to knot theory, and many fascinating physical properties. However, because their realization requires special forms of long-range spin-orbit coupling, they have not been achieved in any 3D system yet. Here, we report the first experimental realization of the long-sought-after Hopf insulator in a 3D circuit system. To implement the Hopf insulator, we construct basic pseudospin modules and connection modules that can realize 2×2-matrix elements and then design the circuit network according to a tight-binding Hopf insulator Hamiltonian constructed by the Hopf map. By simulating the band structure of the designed circuit network and calculating the Hopf invariant, we find that the circuit realizes a Hopf insulator with Hopf invariant equaling 4. Experimentally, we measure the band structure of a printed circuit board and find the observed properties of the bulk bands and topological surface states are in good agreement with the theoretical predictions, verifying the bulk-boundary correspondence of the Hopf insulator. Our scheme brings the experimental study of Hopf insulators to reality and opens the door to the implementation of more unexplored topological phases beyond the known topological classifications.
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Affiliation(s)
- Zhu Wang
- Wuhan Institute of Quantum Technology, Wuhan 430206, China
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Xu-Tao Zeng
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
- School of Physics, Beihang University, Beijing 100191, China
| | - Yuanchuan Biao
- Wuhan Institute of Quantum Technology, Wuhan 430206, China
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Zhongbo Yan
- Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University, Guangzhou 510275, China
| | - Rui Yu
- Wuhan Institute of Quantum Technology, Wuhan 430206, China
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
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9
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Dong X, Wu C, Yu Z, Tian J, Wang Z, Chen X, Jin S, Zhou X. Atomic Ramsey interferometry with S- and D-band in a triangular optical lattice. OPTICS EXPRESS 2022; 30:41437-41446. [PMID: 36366622 DOI: 10.1364/oe.474257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2022] [Accepted: 10/08/2022] [Indexed: 06/16/2023]
Abstract
Ramsey interferometers have wide applications in science and engineering. Compared with the traditional interferometer based on internal states, the interferometer with external quantum states has advantages in some applications for quantum simulation and precision measurement. Here, we develop a Ramsey interferometry with Bloch states in S- and D-band of a triangular optical lattice for the first time. The key to realizing this interferometer in two-dimensionally coupled lattice is that we use the shortcut method to construct π/2 pulse. We observe clear Ramsey fringes and analyze the decoherence mechanism of fringes. Further, we design an echo π pulse between S- and D-band, which significantly improves the coherence time. This Ramsey interferometer in the dimensionally coupled lattice has potential applications in the quantum simulations of topological physics, frustrated effects, and motional qubits manipulation.
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10
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Leng B, Van V. N-band photonic Hopf insulators based on 2D microring lattices. OPTICS LETTERS 2022; 47:5128-5131. [PMID: 36181203 DOI: 10.1364/ol.471454] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 09/08/2022] [Indexed: 06/16/2023]
Abstract
Hopf insulators are topological insulators whose topological behavior arises from the nontrivial mapping from a 3D sphere to a 2D sphere, known as the Hopf map. The Hopf map, typically encountered in the study of spinor and Skyrmion systems, is classified topologically by an integer invariant called the Hopf index. Here we show that, owing to the periodic circulation of light inside each microring, a 2D lattice of microring resonators can emulate an N-band photonic Hopf insulator with nontrivial Hopf index. In particular, we show by numerical computation and direct analytical proof that the N-band Hopf index of the microring lattice is identical to its winding number. The result shows that the Hopf index is an alternative topological invariant for classifying 2D microring photonic lattices and establishes a correspondence between the Hopf insulator phase and the anomalous Floquet insulator phase of the lattice. More generally, our work shows that 2D microring lattices can provide a versatile nanophotonic platform for studying non-Abelian topological photonic systems.
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11
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Pyrialakos GG, Beck J, Heinrich M, Maczewsky LJ, Kantartzis NV, Khajavikhan M, Szameit A, Christodoulides DN. Bimorphic Floquet topological insulators. NATURE MATERIALS 2022; 21:634-639. [PMID: 35484331 DOI: 10.1038/s41563-022-01238-w] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
Topological theories have established a unique set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by specifically tailored discrete coupling protocols or helical lattice motions, we introduce a class of bimorphic Floquet topological insulators that leverage connective chains with periodically modulated on-site potentials to reveal rich topological features in the system. In exploring a 'chain-driven' generalization of the archetypical Floquet honeycomb lattice, we identify a rich phase structure that can host multiple non-trivial topological phases associated simultaneously with both Chern-type and anomalous chiral states. Experiments carried out in photonic waveguide lattices reveal a strongly confined helical edge state that, owing to its origin in bulk flat bands, can be set into motion in a topologically protected fashion, or halted at will, without compromising its adherence to individual lattice sites.
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Affiliation(s)
- Georgios G Pyrialakos
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, USA
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece
| | - Julius Beck
- Institute for Physics, University of Rostock, Rostock, Germany
| | | | | | - Nikolaos V Kantartzis
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece
| | - Mercedeh Khajavikhan
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA
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12
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Zhang L, Jia W, Liu XJ. Universal topological quench dynamics for Z2 topological phases. Sci Bull (Beijing) 2022; 67:1236-1242. [DOI: 10.1016/j.scib.2022.04.019] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2021] [Revised: 03/08/2022] [Accepted: 04/20/2022] [Indexed: 10/18/2022]
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13
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Myerson-Jain NE, Yan S, Weld D, Xu C. Construction of Fractal Order and Phase Transition with Rydberg Atoms. PHYSICAL REVIEW LETTERS 2022; 128:017601. [PMID: 35061455 DOI: 10.1103/physrevlett.128.017601] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Accepted: 12/08/2021] [Indexed: 06/14/2023]
Abstract
We propose the construction of a many-body phase of matter with fractal structure using arrays of Rydberg atoms. The degenerate low energy excited states of this phase form a self-similar fractal structure. This phase is analogous to the so-called "type-II fracton topological states." The main challenge in realizing fractonlike models in standard condensed matter platforms is the creation of multispin interactions, since realistic systems are typically dominated by two-body interactions. In this work, we demonstrate that the van der Waals interaction and experimental tunability of Rydberg-based platforms enable the simulation of exotic phases of matter with fractal structures, and the study of a quantum phase transition involving a fractal ordered phase.
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Affiliation(s)
- Nayan E Myerson-Jain
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Stephen Yan
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - David Weld
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Cenke Xu
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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14
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Wang K, Li T, Xiao L, Han Y, Yi W, Xue P. Detecting Non-Bloch Topological Invariants in Quantum Dynamics. PHYSICAL REVIEW LETTERS 2021; 127:270602. [PMID: 35061422 DOI: 10.1103/physrevlett.127.270602] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Accepted: 12/07/2021] [Indexed: 06/14/2023]
Abstract
Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian topological systems, and are a key concept in the contemporary study of non-Hermitian topology. Here we report the dynamic detection of non-Bloch topological invariants in single-photon quantum walks, revealed through the biorthogonal chiral displacement, and crosschecked with the dynamic spin textures in the generalized quasimomentum-time domain following a quantum quench. Both detection schemes are robust against symmetry-preserving disorders, and yield consistent results with theoretical predictions. Our experiments are performed far away from any boundaries, and therefore underline non-Bloch topological invariants as intrinsic properties of the system that persist in the thermodynamic limit. Our work sheds new light on the experimental investigation of non-Hermitian topology.
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Affiliation(s)
- Kunkun Wang
- Beijing Computational Science Research Center, Beijing 100084, China
- School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, China
| | - Tianyu Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
| | - Lei Xiao
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Yiwen Han
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
| | - Wei Yi
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
| | - Peng Xue
- Beijing Computational Science Research Center, Beijing 100084, China
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15
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Yu J, Zhang RX, Song ZD. Dynamical symmetry indicators for Floquet crystals. Nat Commun 2021; 12:5985. [PMID: 34645782 PMCID: PMC8514516 DOI: 10.1038/s41467-021-26092-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Accepted: 09/15/2021] [Indexed: 11/09/2022] Open
Abstract
Various exotic topological phases of Floquet systems have been shown to arise from crystalline symmetries. Yet, a general theory for Floquet topology that is applicable to all crystalline symmetry groups is still in need. In this work, we propose such a theory for (effectively) non-interacting Floquet crystals. We first introduce quotient winding data to classify the dynamics of the Floquet crystals with equivalent symmetry data, and then construct dynamical symmetry indicators (DSIs) to sufficiently indicate the inherently dynamical Floquet crystals. The DSI and quotient winding data, as well as the symmetry data, are all computationally efficient since they only involve a small number of Bloch momenta. We demonstrate the high efficiency by computing all elementary DSI sets for all spinless and spinful plane groups using the mathematical theory of monoid, and find a large number of different nontrivial classifications, which contain both first-order and higher-order 2+1D anomalous Floquet topological phases. Using the framework, we further find a new 3+1D anomalous Floquet second-order topological insulator (AFSOTI) phase with anomalous chiral hinge modes.
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Affiliation(s)
- Jiabin Yu
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD, USA.
| | - Rui-Xing Zhang
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD, USA
- Joint Quantum Institute, University of Maryland, College Park, MD, USA
| | - Zhi-Da Song
- Department of Physics, Princeton University, Princeton, NJ, USA
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16
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Gluza M, Eisert J. Recovering Quantum Correlations in Optical Lattices from Interaction Quenches. PHYSICAL REVIEW LETTERS 2021; 127:090503. [PMID: 34506183 DOI: 10.1103/physrevlett.127.090503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 03/29/2021] [Accepted: 07/13/2021] [Indexed: 06/13/2023]
Abstract
Quantum simulations with ultracold atoms in optical lattices open up an exciting path toward understanding strongly interacting quantum systems. Atom gas microscopes are crucial for this as they offer single-site density resolution, unparalleled in other quantum many-body systems. However, currently a direct measurement of local coherent currents is out of reach. In this Letter, we show how to achieve that by measuring densities that are altered in response to quenches to noninteracting dynamics, e.g., after tilting the optical lattice. For this, we establish a data analysis method solving the closed set of equations relating tunneling currents and atom number dynamics, allowing us to reliably recover the full covariance matrix, including off-diagonal terms representing coherent currents. The signal processing builds upon semidefinite optimization, providing bona fide covariance matrices optimally matching the observed data. We demonstrate how the obtained information about noncommuting observables allows one to quantify entanglement at finite temperature, which opens up the possibility to study quantum correlations in quantum simulations going beyond classical capabilities.
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Affiliation(s)
- Marek Gluza
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - Jens Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
- Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
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17
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Bandyopadhyay S, Bhattacharjee S, Sen D. Driven quantum many-body systems and out-of-equilibrium topology. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:393001. [PMID: 34225268 DOI: 10.1088/1361-648x/ac1151] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 07/05/2021] [Indexed: 06/13/2023]
Abstract
In this review we present some of the work done in India in the area of driven and out-of-equilibrium systems with topological phases. After presenting some well-known examples of topological systems in one and two dimensions, we discuss the effects of periodic driving in some of them. We discuss the unitary as well as the non-unitary dynamical preparation of topologically non-trivial states in one and two dimensional systems. We then discuss the effects of Majorana end modes on transport through a Kitaev chain and a junction of three Kitaev chains. Following this, transport through the surface states of a three-dimensional topological insulator has also been reviewed. The effects of hybridization between the top and bottom surfaces in such systems and the application of electromagnetic radiation on a strip-like region on the top surface are described. Two unusual topological systems are mentioned briefly, namely, a spin system on a kagome lattice and a Josephson junction of three superconducting wires. We have also included a pedagogical discussion on topology and topological invariants in the appendices, where the connection between topological properties and the intrinsic geometry of many-body quantum states is also elucidated.
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Affiliation(s)
- Souvik Bandyopadhyay
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Sourav Bhattacharjee
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Diptiman Sen
- Center for High Energy Physics and Department of Physics, Indian Institute of Science, Bengaluru 560012, India
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18
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Käming N, Dawid A, Kottmann K, Lewenstein M, Sengstock K, Dauphin A, Weitenberg C. Unsupervised machine learning of topological phase transitions from experimental data. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abffe7] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Abstract
Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries from noisy and imperfect data without the knowledge of the order parameter. Here, we apply different unsupervised machine learning techniques, including anomaly detection and influence functions, to experimental data from ultracold atoms. In this way, we obtain the topological phase diagram of the Haldane model in a completely unbiased fashion. We show that these methods can successfully be applied to experimental data at finite temperatures and to the data of Floquet systems when post-processing the data to a single micromotion phase. Our work provides a benchmark for the unsupervised detection of new exotic phases in complex many-body systems.
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19
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Wang ZY, Cheng XC, Wang BZ, Zhang JY, Lu YH, Yi CR, Niu S, Deng Y, Liu XJ, Chen S, Pan JW. Realization of an ideal Weyl semimetal band in a quantum gas with 3D spin-orbit coupling. Science 2021; 372:271-276. [PMID: 33859030 DOI: 10.1126/science.abc0105] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Accepted: 03/12/2021] [Indexed: 11/02/2022]
Abstract
Weyl semimetals are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band. According to lattice theory, Weyl cones must come in pairs, with the minimum number of cones being two. A semimetal with only two Weyl cones is an ideal Weyl semimetal (IWSM). Here we report the experimental realization of an IWSM band by engineering 3D spin-orbit coupling for ultracold atoms. The topological Weyl points are clearly measured via the virtual slicing imaging technique in equilibrium and are further resolved in the quench dynamics. The realization of an IWSM band opens an avenue to investigate various exotic phenomena that are difficult to access in solids.
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Affiliation(s)
- Zong-Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Science, Shanghai 201315, China
| | - Xiang-Can Cheng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Science, Shanghai 201315, China
| | - Bao-Zong Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.,International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Jin-Yi Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Science, Shanghai 201315, China
| | - Yue-Hui Lu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.,CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Chang-Rui Yi
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Science, Shanghai 201315, China
| | - Sen Niu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.,CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Youjin Deng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Science, Shanghai 201315, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China. .,CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Shuai Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China. .,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Science, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China. .,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Science, Shanghai 201315, China
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20
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Leykam D, Smolina E, Maluckov A, Flach S, Smirnova DA. Probing Band Topology Using Modulational Instability. PHYSICAL REVIEW LETTERS 2021; 126:073901. [PMID: 33666481 DOI: 10.1103/physrevlett.126.073901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations of the nonlinear Bloch waves are sensitive to topological band inversions. At longer timescales, nonlinear wave mixing induces spreading of energy through the entire band and spontaneous creation of wave polarization singularities determined by the band Chern number. Our analytical and numerical results establish modulational instability as a tool to probe bulk topological invariants and create topologically nontrivial wave fields.
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Affiliation(s)
- Daniel Leykam
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Korea
- Basic Science Program, Korea University of Science and Technology, Daejeon 34113, Korea
| | - Ekaterina Smolina
- Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod 603950, Russia
| | - Aleksandra Maluckov
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Korea
- P* Group, Vinča Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia
| | - Sergej Flach
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Korea
- Basic Science Program, Korea University of Science and Technology, Daejeon 34113, Korea
| | - Daria A Smirnova
- Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod 603950, Russia
- Nonlinear Physics Centre, Australian National University, Canberra, Australian Capital Territory 2601, Australia
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21
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Topological features without a lattice in Rashba spin-orbit coupled atoms. Nat Commun 2021; 12:593. [PMID: 33500408 PMCID: PMC7838279 DOI: 10.1038/s41467-020-20762-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 12/18/2020] [Indexed: 11/08/2022] Open
Abstract
Topological order can be found in a wide range of physical systems, from crystalline solids, photonic meta-materials and even atmospheric waves to optomechanic, acoustic and atomic systems. Topological systems are a robust foundation for creating quantized channels for transporting electrical current, light, and atmospheric disturbances. These topological effects are quantified in terms of integer-valued 'invariants', such as the Chern number, applicable to the quantum Hall effect, or the [Formula: see text] invariant suitable for topological insulators. Here, we report the engineering of Rashba spin-orbit coupling for a cold atomic gas giving non-trivial topology, without the underlying crystalline structure that conventionally yields integer Chern numbers. We validated our procedure by spectroscopically measuring both branches of the Rashba dispersion relation which touch at a single Dirac point. We then measured the quantum geometry underlying the dispersion relation using matter-wave interferometry to implement a form of quantum state tomography, giving a Berry's phase with magnitude π. This implies that opening a gap at the Dirac point would give two dispersions (bands) each with half-integer Chern number, potentially implying new forms of topological transport.
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22
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Motruk J, Na I. Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement. PHYSICAL REVIEW LETTERS 2020; 125:236401. [PMID: 33337233 DOI: 10.1103/physrevlett.125.236401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 10/22/2020] [Indexed: 06/12/2023]
Abstract
The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields providing the required topological band structures. However, detecting their occurrence might prove difficult since transport measurements akin to those in solid state systems are challenging to perform in cold atom setups and alternatives have to be found. We show that for a ν=1/2 FCI state realized in the lowest band of a Harper-Hofstadter model of interacting bosons confined by a harmonic trapping potential, the fractionally quantized Hall conductivity σ_{xy} can be accurately determined by the displacement of the atomic cloud under the action of a constant force which provides a suitable experimentally measurable signal for detecting the topological nature of the state. Using matrix-product state algorithms, we show that, in both cylinder and square geometries, the movement of the particle cloud in time under the application of a constant force field on top of the confining potential is proportional to σ_{xy} for an extended range of field strengths.
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Affiliation(s)
- Johannes Motruk
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Ilyoun Na
- Department of Physics, University of California, Berkeley, California 94720, USA
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23
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Di Liberto M, Goldman N, Palumbo G. Non-Abelian Bloch oscillations in higher-order topological insulators. Nat Commun 2020; 11:5942. [PMID: 33230167 PMCID: PMC7684321 DOI: 10.1038/s41467-020-19518-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 10/13/2020] [Indexed: 11/09/2022] Open
Abstract
Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to a force. Observed in a wide range of synthetic systems, BOs are intrinsically related to geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry-phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties through the measurement of Berry phases and center-of-mass displacements.
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Affiliation(s)
- M Di Liberto
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, Brussels, B-1050, Belgium.
| | - N Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, Brussels, B-1050, Belgium
| | - G Palumbo
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, Brussels, B-1050, Belgium
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24
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Sun M, Zhang P, Zhai H. High Temperature Virial Expansion to Universal Quench Dynamics. PHYSICAL REVIEW LETTERS 2020; 125:110404. [PMID: 32975972 DOI: 10.1103/physrevlett.125.110404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2020] [Accepted: 08/21/2020] [Indexed: 06/11/2023]
Abstract
High temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this Letter we generalize the high temperature virial expansion approach to treat far-from-equilibrium quench dynamics. As an application of our framework, we study the dynamics of a Bose gas quenched from noninteracting to unitarity, and we compare our theoretical results with unexplained experimental results by the Cambridge group [Eigen et al., Nature 563, 221 (2018)]. We show that, during the quench dynamics, the momentum distribution decreases for the low-momentum part with k<k^{*}, and increases for high-momentum part with k>k^{*}, where k^{*} is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of k^{*}λ that agrees perfectly with the experiment, with λ being the thermal de Broglie wavelength. We also find a jump of the halfway relaxation time across k^{*}λ and the nonmonotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the longtime steady state thermalizes or not, and we find that this state reaches a partial thermalization, namely, it thermalizes for the low-energy part with kλ≲1 but does not thermalize for the very high momentum tail with kλ≫1. Our framework can also be applied to quench dynamics in other systems.
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Affiliation(s)
- Mingyuan Sun
- State Key Lab of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Peng Zhang
- Department of Physics, Renmin University of China, Beijing 100872, China
- Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China
| | - Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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25
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Ünal FN, Bouhon A, Slager RJ. Topological Euler Class as a Dynamical Observable in Optical Lattices. PHYSICAL REVIEW LETTERS 2020; 125:053601. [PMID: 32794847 DOI: 10.1103/physrevlett.125.053601] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2020] [Revised: 06/21/2020] [Accepted: 07/06/2020] [Indexed: 05/22/2023]
Abstract
The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology-the Euler class-in such a dynamical setting. The enigmatic invariant (ξ) falls outside conventional symmetry-eigenvalue indicated phases and, in simplest incarnation, is described by triples of bands that comprise a gapless pair featuring 2ξ stable band nodes, and a gapped band. These nodes host non-Abelian charges and can be further undone by converting their charge upon intricate braiding mechanisms, revealing that Euler class is a fragile topology. We theoretically demonstrate that quenching with nontrivial Euler Hamiltonian results in stable monopole-antimonopole pairs, which in turn induce a linking of momentum-time trajectories under the first Hopf map, making the invariant experimentally observable. Detailing explicit tomography protocols in a variety of cold-atom setups, our results provide a basis for exploring new topologies and their interplay with crystalline symmetries in optical lattices beyond paradigmatic Chern insulators.
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Affiliation(s)
- F Nur Ünal
- TCM Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Adrien Bouhon
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 21 Uppsala, Sweden
| | - Robert-Jan Slager
- TCM Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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26
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Hu H, Zhao E. Topological Invariants for Quantum Quench Dynamics from Unitary Evolution. PHYSICAL REVIEW LETTERS 2020; 124:160402. [PMID: 32383903 DOI: 10.1103/physrevlett.124.160402] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Accepted: 03/30/2020] [Indexed: 05/22/2023]
Abstract
Recent experiments began to explore the topological properties of quench dynamics, i.e., the time evolution following a sudden change in the Hamiltonian, via tomography of quantum gases in optical lattices. In contrast to the well-established theory for static band insulators or periodically driven systems, at present it is not clear whether, and how, topological invariants can be defined for a general quench of band insulators. Previous work solved a special case of this problem beautifully using Hopf mapping of two-band Hamiltonians in two dimensions. However, it only works for a topologically trivial initial state and is hard to generalize to multiband systems or other dimensions. Here we introduce the concept of loop unitary constructed from the unitary time-evolution operator and show its homotopy invariant fully characterizes the dynamical topology. For two-band systems in two dimensions, we prove that the invariant is precisely equal to the change in the Chern number across the quench, regardless of the initial state. We further show that the nontrivial dynamical topology manifests as hedgehog defects in the loop unitary and also as winding and linking of its eigenvectors along a curve where dynamical quantum phase transition occurs. This opens up a systematic route to classify and characterize quantum quench dynamics.
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Affiliation(s)
- Haiping Hu
- Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, USA
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Erhai Zhao
- Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, USA
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27
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Yu M, Yang P, Gong M, Cao Q, Lu Q, Liu H, Zhang S, Plenio MB, Jelezko F, Ozawa T, Goldman N, Cai J. Experimental measurement of the quantum geometric tensor using coupled qubits in diamond. Natl Sci Rev 2020; 7:254-260. [PMID: 34692040 PMCID: PMC8288884 DOI: 10.1093/nsr/nwz193] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Revised: 11/17/2019] [Accepted: 11/18/2019] [Indexed: 12/03/2022] Open
Abstract
Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring 13C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.
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Affiliation(s)
- Min Yu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Pengcheng Yang
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Musang Gong
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Qingyun Cao
- Institut für Quantenoptik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany.,School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Qiuyu Lu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Haibin Liu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Shaoliang Zhang
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Martin B Plenio
- Institut für Theoretische Physik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Fedor Jelezko
- Institut für Quantenoptik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Tomoki Ozawa
- Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako, Saitama 351-0198, Japan
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, B-1050 Brussels, Belgium
| | - Jianming Cai
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
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28
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Barbarino S, Yu J, Zoller P, Budich JC. Preparing Atomic Topological Quantum Matter by Adiabatic Nonunitary Dynamics. PHYSICAL REVIEW LETTERS 2020; 124:010401. [PMID: 31976708 DOI: 10.1103/physrevlett.124.010401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Indexed: 06/10/2023]
Abstract
Motivated by the outstanding challenge of realizing low-temperature states of quantum matter in synthetic materials, we propose and study an experimentally feasible protocol for preparing topological states such as Chern insulators. By definition, such (nonsymmetry protected) topological phases cannot be attained without going through a phase transition in a closed system, largely preventing their preparation in coherent dynamics. To overcome this fundamental caveat, we propose to couple the target system to a conjugate system, so as to prepare a symmetry protected topological phase in an extended system by intermittently breaking the protecting symmetry. Finally, the decoupled conjugate system is discarded, thus projecting onto the desired topological state in the target system. By construction, this protocol may be immediately generalized to the class of invertible topological phases, characterized by the existence of an inverse topological order. We illustrate our findings with microscopic simulations on an experimentally realistic Chern insulator model of ultracold fermionic atoms in a driven spin-dependent hexagonal optical lattice.
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Affiliation(s)
- S Barbarino
- Institute of Theoretical Physics, Technische Universität Dresden and Würzburg-Dresden Cluster of Excellence ct.qmat, 01062 Dresden, Germany
| | - J Yu
- Center for Quantum Physics, Faculty of Mathematics, Computer Science and Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - P Zoller
- Center for Quantum Physics, Faculty of Mathematics, Computer Science and Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - J C Budich
- Institute of Theoretical Physics, Technische Universität Dresden and Würzburg-Dresden Cluster of Excellence ct.qmat, 01062 Dresden, Germany
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29
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Yi CR, Zhang L, Zhang L, Jiao RH, Cheng XC, Wang ZY, Xu XT, Sun W, Liu XJ, Chen S, Pan JW. Observing Topological Charges and Dynamical Bulk-Surface Correspondence with Ultracold Atoms. PHYSICAL REVIEW LETTERS 2019; 123:190603. [PMID: 31765219 DOI: 10.1103/physrevlett.123.190603] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2019] [Revised: 08/16/2019] [Indexed: 05/22/2023]
Abstract
Quantum dynamics induced in quenching a d-dimensional topological phase across a phase transition may exhibit a nontrivial dynamical topological pattern on the (d-1)D momentum subspace, called band inversion surfaces (BISs), which have a one-to-one correspondence to the bulk topology of the postquench phase. Here we report the experimental observation of such dynamical bulk-surface correspondence through measuring the topological charges in a 2D quantum anomalous Hall model realized in an optical Raman lattice. The system can be quenched with respect to every spin axis by suddenly varying the two-photon detuning or phases of the Raman couplings, in which the topological charges and BISs are measured dynamically by the time-averaged spin textures. We observe that the total charges in the region enclosed by BISs define a dynamical topological invariant, which equals the Chern number of the postquench band and also characterizes the topological pattern of a dynamical field emerging on the BISs, rendering the dynamical bulk-surface correspondence. This study opens a new avenue to explore topological phases dynamically.
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Affiliation(s)
- Chang-Rui Yi
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Long Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Lin Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Rui-Heng Jiao
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Xiang-Can Cheng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Zong-Yao Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Xiao-Tian Xu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Wei Sun
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Beijing Academy of Quantum Information Science, Beijing 100193, China
| | - Shuai Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
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30
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Qiu X, Deng TS, Hu Y, Xue P, Yi W. Fixed Points and Dynamic Topological Phenomena in a Parity-Time-Symmetric Quantum Quench. iScience 2019; 20:392-401. [PMID: 31622880 PMCID: PMC6818370 DOI: 10.1016/j.isci.2019.09.037] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2019] [Revised: 08/23/2019] [Accepted: 09/24/2019] [Indexed: 11/26/2022] Open
Abstract
We identify dynamic topological phenomena such as dynamic Chern numbers and dynamic quantum phase transitions in quantum quenches of the non-Hermitian Su-Schrieffer-Heeger Hamiltonian with parity-time (PT) symmetry. Their occurrences in the non-unitary dynamics are intimately connected with fixed points in the Brillouin zone, where the density matrices do not evolve in time. Based on our theoretical formalism characterizing topological properties of non-unitary dynamics, we prove the existence of fixed points for quenches between distinct static topological phases in the PT-symmetry-preserving regime, thus unveiling the interplay between dynamic topological phenomena and PT symmetry. Interestingly, non-Hermiticity of the driving Hamiltonian gives rise to rich dynamic topological phenomena which are different, either qualitatively or quantitatively, from their counterparts in unitary dynamics. Our work sheds light on dynamic topological phenomena in open systems and is readily accessible in experiments.
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Affiliation(s)
- Xingze Qiu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Tian-Shu Deng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Ying Hu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China.
| | - Peng Xue
- Beijing Computational Science Research Center, Beijing 100084, China; Department of Physics, Southeast University, Nanjing 211189, China; State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China.
| | - Wei Yi
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; CAS Center for Excellence in Quantum Information and Quantum Physics, Hefei 230026, China.
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31
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Titum P, Iosue JT, Garrison JR, Gorshkov AV, Gong ZX. Probing Ground-State Phase Transitions through Quench Dynamics. PHYSICAL REVIEW LETTERS 2019; 123:115701. [PMID: 31573251 DOI: 10.1103/physrevlett.123.115701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Indexed: 06/10/2023]
Abstract
The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
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Affiliation(s)
- Paraj Titum
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Joseph T Iosue
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - James R Garrison
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Zhe-Xuan Gong
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
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32
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Mera B, Sacha K, Omar Y. Topologically Protected Quantization of Work. PHYSICAL REVIEW LETTERS 2019; 123:020601. [PMID: 31386501 DOI: 10.1103/physrevlett.123.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Indexed: 06/10/2023]
Abstract
The transport of a particle in the presence of a potential that changes periodically in space and in time can be characterized by the amount of work needed to shift a particle by a single spatial period of the potential. In general, this amount of work, when averaged over a single temporal period of the potential, can take any value in a continuous fashion. Here, we present a topological effect inducing the quantization of the average work. We find that this work is equal to the first Chern number calculated in a unit cell of a space-time lattice. Hence, this quantization of the average work is topologically protected. We illustrate this phenomenon with the example of an atom whose center of mass motion is coupled to its internal degrees of freedom by electromagnetic waves.
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Affiliation(s)
- Bruno Mera
- Instituto de Telecomunicações, Lisboa and Instituto Superior Tecnico, Universidade de Lisboa, Portugal
| | - Krzysztof Sacha
- Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, ulica Profesora Stanisława Łojasiewicza 11, PL-30-348 Kraków, Poland
| | - Yasser Omar
- Instituto de Telecomunicações, Lisboa and Instituto Superior Tecnico, Universidade de Lisboa, Portugal
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Abstract
Ordinarily, photons do not interact with one another. However, atoms can be used to mediate photonic interactions1,2, raising the prospect of forming synthetic materials3 and quantum information systems4-7 from photons. One promising approach combines highly excited Rydberg atoms8-12 with the enhanced light-matter coupling of an optical cavity to convert photons into strongly interacting polaritons13-15. However, quantum materials made of optical photons have not yet been realized, because the experimental challenge of coupling a suitable atomic sample with a degenerate cavity has constrained cavity polaritons to a single spatial mode that is resonant with an atomic transition. Here we use Floquet engineering16,17-the periodic modulation of a quantum system-to enable strongly interacting polaritons to access multiple spatial modes of an optical cavity. First, we show that periodically modulating an excited state of rubidium splits its spectral weight to generate new lines-beyond those that are ordinarily characteristic of the atom-separated by multiples of the modulation frequency. Second, we use this capability to simultaneously generate spectral lines that are resonant with two chosen spatial modes of a non-degenerate optical cavity, enabling what we name 'Floquet polaritons' to exist in both modes. Because both spectral lines correspond to the same Floquet-engineered atomic state, adding a single-frequency field is sufficient to couple both modes to a Rydberg excitation. We demonstrate that the resulting polaritons interact strongly in both cavity modes simultaneously. The production of Floquet polaritons provides a promising new route to the realization of ordered states of strongly correlated photons, including crystals and topological fluids, as well as quantum information technologies such as multimode photon-by-photon switching.
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Ünal FN, Seradjeh B, Eckardt A. How to Directly Measure Floquet Topological Invariants in Optical Lattices. PHYSICAL REVIEW LETTERS 2019; 122:253601. [PMID: 31347903 DOI: 10.1103/physrevlett.122.253601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Indexed: 06/10/2023]
Abstract
The classification of topological Floquet systems with time-periodic Hamiltonians transcends that of static systems. For example, spinless fermions in periodically driven two-dimensional lattices are not completely characterized by the Chern numbers of the quasienergy bands, but rather by a set of winding numbers associated with the gaps. We propose a feasible scheme for measuring these winding numbers in a periodically driven optical lattice efficiently and directly. It is based on the construction of a one-parameter family of drives, continuously connecting the Floquet system of interest to a trivial reference system. The winding numbers are then determined by the identification and the tomography of the band-touching singularities occurring on the way. As a by-product, we also propose a method for probing spectral properties of time evolution operators via a time analog of crystallography.
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Affiliation(s)
- F Nur Ünal
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
| | - Babak Seradjeh
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
- Department of Physics, Indiana University, 727 E Third Street, Bloomington, Indiana 47405, USA
| | - André Eckardt
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
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35
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Wang K, Qiu X, Xiao L, Zhan X, Bian Z, Sanders BC, Yi W, Xue P. Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics. Nat Commun 2019; 10:2293. [PMID: 31123259 PMCID: PMC6533298 DOI: 10.1038/s41467-019-10252-7] [Citation(s) in RCA: 67] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2018] [Accepted: 04/30/2019] [Indexed: 11/09/2022] Open
Abstract
Topology in quench dynamics gives rise to intriguing dynamic topological phenomena, which are intimately connected to the topology of static Hamiltonians yet challenging to probe experimentally. Here we theoretically characterize and experimentally detect momentum-time skyrmions in parity-time [Formula: see text]-symmetric non-unitary quench dynamics in single-photon discrete-time quantum walks. The emergent skyrmion structures are protected by dynamic Chern numbers defined for the emergent two-dimensional momentum-time submanifolds, and are revealed through our experimental scheme enabling the construction of time-dependent non-Hermitian density matrices via direct measurements in position space. Our work experimentally reveals the interplay of [Formula: see text] symmetry and quench dynamics in inducing emergent topological structures, and highlights the application of discrete-time quantum walks for the study of dynamic topological phenomena.
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Affiliation(s)
- Kunkun Wang
- Beijing Computational Science Research Center, 100084, Beijing, China
- Department of Physics, Southeast University, 211189, Nanjing, China
| | - Xingze Qiu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei, 230026, China
| | - Lei Xiao
- Beijing Computational Science Research Center, 100084, Beijing, China
- Department of Physics, Southeast University, 211189, Nanjing, China
| | - Xiang Zhan
- Beijing Computational Science Research Center, 100084, Beijing, China
- Department of Physics, Southeast University, 211189, Nanjing, China
| | - Zhihao Bian
- Beijing Computational Science Research Center, 100084, Beijing, China
- Department of Physics, Southeast University, 211189, Nanjing, China
| | - Barry C Sanders
- Institute for Quantum Science and Technology, University of Calgary, Alberta, T2N 1N4, Canada
- Program in Quantum Information Science, Canadian Institute for Advanced Research, Toronto, Ontario, M5G 1Z8, Canada
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, 201315, Shanghai, China
| | - Wei Yi
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei, 230026, China.
| | - Peng Xue
- Beijing Computational Science Research Center, 100084, Beijing, China.
- Department of Physics, Southeast University, 211189, Nanjing, China.
- State Key Laboratory of Precision Spectroscopy, East China Normal University, 200062, Shanghai, China.
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36
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Genkina D, Aycock LM, Lu HI, Lu M, Pineiro AM, Spielman IB. Imaging topology of Hofstadter ribbons. NEW JOURNAL OF PHYSICS 2019; 21:https://doi.org/10.1088/1367-2630/ab165b. [PMID: 32855619 PMCID: PMC7448228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Physical systems with non-trivial topological order find direct applications in metrology (Klitzing et al 1980 Phys. Rev. Lett. 45 494-7) and promise future applications in quantum computing (Freedman 2001 Found. Comput. Math. 1 183-204; Kitaev 2003 Ann. Phys. 303 2-30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system's topology (Laughlin 1981 Phys. Rev. B 23 5632-33). At magnetic fields beyond the reach of current condensed matter experiment, around 104 T, this conductance remains precisely quantized with values based on the topological order (Thouless et al 1982 Phys. Rev. Lett. 49 405-8). Hitherto, quantized conductance has only been measured in extended 2D systems. Here, we experimentally studied narrow 2D ribbons, just 3 or 5 sites wide along one direction, using ultracold neutral atoms where such large magnetic fields can be engineered (Jaksch and Zoller 2003 New J. Phys. 5 56; Miyake et al 2013 Phys. Rev. Lett. 111 185302; Aidelsburger et al 2013 Phys. Rev. Lett. 111 185301; Celi et al 2014 Phys. Rev. Lett. 112 043001; Stuhl etal 2015 Science 349 1514; Mancini et al 2015 Science 349 1510; An et al 2017 Sci. Adv. 3). We microscopically imaged the transverse spatial motion underlying the quantized Hall effect. Our measurements identify the topological Chern numbers with typical uncertainty of 5%, and show that although band topology is only properly defined in infinite systems, its signatures are striking even in nearly vanishingly thin systems.
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Affiliation(s)
- Dina Genkina
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
| | - Lauren M Aycock
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
| | - Hsin-I Lu
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
- Currently Modern Electron, Bellevue, WA 98007, United States of America
| | - Mingwu Lu
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
| | - Alina M Pineiro
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
| | - I B Spielman
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, United States of America
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