1
|
Wang B, Aidelsburger M, Dalibard J, Eckardt A, Goldman N. Cold-Atom Elevator: From Edge-State Injection to the Preparation of Fractional Chern Insulators. PHYSICAL REVIEW LETTERS 2024; 132:163402. [PMID: 38701474 DOI: 10.1103/physrevlett.132.163402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 03/12/2024] [Indexed: 05/05/2024]
Abstract
Optical box traps offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activating energy-selective chiral edge currents, but also to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly correlated and topological phases.
Collapse
Affiliation(s)
- Botao Wang
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Monika Aidelsburger
- Faculty of Physics, Ludwig-Maximilians-Universität München, Schellingstr. 4, D-80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 Munich, Germany
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - André Eckardt
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Nathan Goldman
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| |
Collapse
|
2
|
Ji X, Yang X. Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:243001. [PMID: 38387101 DOI: 10.1088/1361-648x/ad2c73] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2023] [Accepted: 02/22/2024] [Indexed: 02/24/2024]
Abstract
We present a pedagogical review of the periodically driven non-Hermitian systems, particularly on the rich interplay between the non-Hermitian skin effect and the topology. We start by reviewing the non-Bloch band theory of the static non-Hermitian systems and discuss the establishment of its generalized bulk-boundary correspondence (BBC). Ultimately, we focus on the non-Bloch band theory of two typical periodically driven non-Hermitian systems: harmonically driven non-Hermitian system and periodically quenched non-Hermitian system. The non-Bloch topological invariants were defined on the generalized Brillouin zone and the real space wave functions to characterize the Floquet non-Hermtian topological phases. Then, the generalized BBC was established for the two typical periodically driven non-Hermitian systems. Additionally, we review novel phenomena in the higher-dimensional periodically driven non-Hermitian systems, including Floquet non-Hermitian higher-order topological phases and Floquet hybrid skin-topological modes. The experimental realizations and recent advances have also been surveyed. Finally, we end with a summarization and hope this pedagogical review can motivate further research on Floquet non-Hermtian topological physics.
Collapse
Affiliation(s)
- Xiang Ji
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| | - Xiaosen Yang
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| |
Collapse
|
3
|
Iurov A, Zhemchuzhna L, Gumbs G, Huang D, Tse WK, Blaise K, Ejiogu C. Floquet engineering of tilted and gapped Dirac bandstructure in 1T[Formula: see text]-MoS[Formula: see text]. Sci Rep 2022; 12:21348. [PMID: 36494457 PMCID: PMC9734163 DOI: 10.1038/s41598-022-25898-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Accepted: 12/06/2022] [Indexed: 12/13/2022] Open
Abstract
We have developed a rigorous theoretical formalism for Floquet engineering, investigating, and subsequently tailoring most crucial electronic properties of 1T[Formula: see text]-MoS[Formula: see text] by applying an external high-frequency dressing field within the off-resonance regime. It was recently demonstrated that monolayer semiconducting 1T[Formula: see text]-MoS[Formula: see text] exhibits tunable and gapped spin- and valley-polarized tilted Dirac bands. The electron-photon dressed states depend strongly on the polarization of the applied irradiation and reflect a full complexity of the low-energy Hamiltonian for non-irradiated material. We have calculated and analyzed the properties of the electron dressed states corresponding to linear and circular polarization of a dressing field by focusing on their symmetry, anisotropy, tilting, direct and indirect band gaps. Circularly polarized dressing field is known for transition into a new electronic state with broken time-reversal symmetry and a non-zero Chern number, and therefore, the combination of these topologically non-trivial phases and transitions between them could reveal some truly unique and previously unknown phenomena and applications. We have also computed and discussed the density of states for various types of 1T[Formula: see text]-MoS[Formula: see text] materials and its modification in the presence of a dressing field.
Collapse
Affiliation(s)
- Andrii Iurov
- Department of Physics and Computer Science, Medgar Evers College of City University of New York, Brooklyn, NY 11225 USA
| | - Liubov Zhemchuzhna
- Department of Physics and Computer Science, Medgar Evers College of City University of New York, Brooklyn, NY 11225 USA
- Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York, 10065 USA
| | - Godfrey Gumbs
- Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York, 10065 USA
- Donostia International Physics Center (DIPC), P de Manuel Lardizabal, 4, 20018 San Sebastian, Basque Country Spain
| | - Danhong Huang
- US Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, New Mexico, 87117 USA
| | - Wang-Kong Tse
- Department of Physics and Astronomy, The University of Alabama, Tuscaloosa, AL 35487 USA
| | - Kathy Blaise
- Department of Physics and Computer Science, Medgar Evers College of City University of New York, Brooklyn, NY 11225 USA
| | - Chinedu Ejiogu
- Department of Physics and Computer Science, Medgar Evers College of City University of New York, Brooklyn, NY 11225 USA
| |
Collapse
|
4
|
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: 24] [Impact Index Per Article: 6.0] [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.
Collapse
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
| |
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
Repellin C, Goldman N. Detecting Fractional Chern Insulators through Circular Dichroism. PHYSICAL REVIEW LETTERS 2019; 122:166801. [PMID: 31075039 DOI: 10.1103/physrevlett.122.166801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 06/09/2023]
Abstract
Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. Recent achievements in this direction, together with the possibility of tuning interparticle interactions, suggest that strongly correlated states reminiscent of fractional quantum Hall (FQH) liquids could soon be generated in these systems. In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. Here, we demonstrate that the fractional nature of the quantized Hall conductance, a fundamental characteristic of FQH states, could be detected in ultracold gases through a circular-dichroic measurement, namely, by monitoring the energy absorbed by the atomic cloud upon a circular drive. We validate this approach by comparing the circular-dichroic signal to the many-body Chern number and discuss how such measurements could be performed to distinguish FQH-type states from competing states. Our scheme offers a practical tool for the detection of topologically ordered states in quantum-engineered systems, with potential applications in solid state.
Collapse
Affiliation(s)
- C Repellin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - N Goldman
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| |
Collapse
|
7
|
Lee CH, Ho WW, Yang B, Gong J, Papić Z. Floquet Mechanism for Non-Abelian Fractional Quantum Hall States. PHYSICAL REVIEW LETTERS 2018; 121:237401. [PMID: 30576179 DOI: 10.1103/physrevlett.121.237401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2018] [Revised: 09/17/2018] [Indexed: 06/09/2023]
Abstract
Three-body correlations, which arise between spin-polarized electrons in the first excited Landau level, are believed to play a key role in the emergence of enigmatic non-Abelian fractional quantum Hall (FQH) effects. Inspired by recent advances in Floquet engineering, we investigate periodic driving of anisotropic two-body interactions as a route for controllably creating and tuning effective three-body interactions in the FQH regime. We develop an analytic formalism to describe this Floquet-FQH protocol, which is distinct from previous approaches that instead focus on band structure engineering via modulation of single-particle hopping terms. By systematically analyzing the resulting interactions using generalized pseudopotentials, we show that our Floquet-FQH approach leads to repulsive as well as attractive three-body interactions that are highly tunable and support a variety of non-Abelian multicomponent FQH states. Finally, we propose an implementation of the protocol in optically dressed ultracold polar molecules with modulated Rabi frequencies.
Collapse
Affiliation(s)
- Ching Hua Lee
- Institute of High Performance Computing, A*STAR, Singapore, 138632
- Department of Physics, National University of Singapore, Singapore, 117542
| | - Wen Wei Ho
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Bo Yang
- Institute of High Performance Computing, A*STAR, Singapore, 138632
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore, 637371
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore, 117542
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| |
Collapse
|