1
|
Sazhin A, Gladilin VN, Erglis A, Hellmann G, Vewinger F, Weitz M, Wouters M, Schmitt J. Observation of nonlinear response and Onsager regression in a photon Bose-Einstein condensate. Nat Commun 2024; 15:4730. [PMID: 38830905 PMCID: PMC11148057 DOI: 10.1038/s41467-024-49064-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 05/22/2024] [Indexed: 06/05/2024] Open
Abstract
The quantum regression theorem states that the correlations of a system at two different times are governed by the same equations of motion as the single-time averages. This provides a powerful framework for the investigation of the intrinsic microscopic behaviour of physical systems by studying their macroscopic response to a controlled external perturbation. Here we experimentally demonstrate that the two-time particle number correlations in a photon Bose-Einstein condensate inside a dye-filled microcavity exhibit the same dynamics as the response of the condensate to a sudden perturbation of the dye molecule bath. This confirms the regression theorem for a quantum gas, and, moreover, demonstrates it in an unconventional form where the perturbation acts on the bath and only the condensate response is monitored. For strong perturbations, we observe nonlinear relaxation dynamics which our microscopic theory relates to the equilibrium fluctuations, thereby extending the regression theorem beyond the regime of linear response.
Collapse
Affiliation(s)
| | | | - Andris Erglis
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany
| | - Göran Hellmann
- Institut für Angewandte Physik, Universität Bonn, Bonn, Germany
- Leibniz Institute of Photonic Technology, Jena, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Bonn, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Bonn, Germany
| | | | - Julian Schmitt
- Institut für Angewandte Physik, Universität Bonn, Bonn, Germany.
| |
Collapse
|
2
|
Sun Y, Hou X, Wan T, Wang F, Zhu S, Ruan Z, Yang Z. Photonic Floquet Skin-Topological Effect. PHYSICAL REVIEW LETTERS 2024; 132:063804. [PMID: 38394569 DOI: 10.1103/physrevlett.132.063804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 01/18/2024] [Indexed: 02/25/2024]
Abstract
Non-Hermitian skin effect and photonic topological edge states are of great interest in non-Hermitian physics and optics. However, the interplay between them is largely unexplored. Here, we propose and demonstrate experimentally the non-Hermitian skin effect constructed from the nonreciprocal flow of Floquet topological edge states, which can be dubbed "Floquet skin-topological effect." We first show the non-Hermitian skin effect can be induced by structured loss when the one-dimensional (1D) system is periodically driven. Next, based on a two-dimensional (2D) Floquet topological photonic lattice with structured loss, we investigate the interaction between the non-Hermiticity and the topological edge states. We observe that all the one-way edge states are imposed onto specific corners, featuring both the non-Hermitian skin effect and topological edge states. Furthermore, a topological switch for the skin-topological effect is presented by utilizing the phase-transition mechanism. Our experiment paves the way for realizing non-Hermitian topological effects in nonlinear and quantum regimes.
Collapse
Affiliation(s)
- Yeyang Sun
- School of Physics and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, Zhejiang Province, China
| | - Xiangrui Hou
- School of Physics and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, Zhejiang Province, China
| | - Tuo Wan
- School of Physics and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, Zhejiang Province, China
| | - Fangyu Wang
- School of Physics and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, Zhejiang Province, China
| | - Shiyao Zhu
- School of Physics and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, Zhejiang Province, China
- State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang University, Hangzhou 310027, China
| | - Zhichao Ruan
- School of Physics and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, Zhejiang Province, China
- State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang University, Hangzhou 310027, China
| | - Zhaoju Yang
- School of Physics and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, Zhejiang Province, China
| |
Collapse
|
3
|
Han PR, Wu F, Huang XJ, Wu HZ, Zou CL, Yi W, Zhang M, Li H, Xu K, Zheng D, Fan H, Wen J, Yang ZB, Zheng SB. Exceptional Entanglement Phenomena: Non-Hermiticity Meeting Nonclassicality. PHYSICAL REVIEW LETTERS 2023; 131:260201. [PMID: 38215365 DOI: 10.1103/physrevlett.131.260201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 11/15/2023] [Indexed: 01/14/2024]
Abstract
Non-Hermitian (NH) extension of quantum-mechanical Hamiltonians represents one of the most significant advancements in physics. During the past two decades, numerous captivating NH phenomena have been revealed and demonstrated, but all of which can appear in both quantum and classical systems. This leads to the fundamental question: what NH signature presents a radical departure from classical physics? The solution of this problem is indispensable for exploring genuine NH quantum mechanics, but remains experimentally untouched so far. Here, we resolve this basic issue by unveiling distinct exceptional entanglement phenomena, exemplified by an entanglement transition, occurring at the exceptional point of NH interacting quantum systems. We illustrate and demonstrate such purely quantum-mechanical NH effects with a naturally dissipative light-matter system, engineered in a circuit quantum electrodynamics architecture. Our results lay the foundation for studies of genuinely quantum-mechanical NH physics, signified by exceptional-point-enabled entanglement behaviors.
Collapse
Affiliation(s)
- Pei-Rong Han
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Fan Wu
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Xin-Jie Huang
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Huai-Zhi Wu
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Chang-Ling Zou
- 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, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, Hefei 230088, 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, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, Hefei 230088, China
| | - Mengzhen Zhang
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Hekang Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Kai Xu
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Hefei National Laboratory, Hefei 230088, China
| | - Dongning Zheng
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Hefei National Laboratory, Hefei 230088, China
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Hefei National Laboratory, Hefei 230088, China
| | - Jianming Wen
- Department of Physics, Kennesaw State University, Marietta, Georgia 30060, USA
| | - Zhen-Biao Yang
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
- Hefei National Laboratory, Hefei 230088, China
| | - Shi-Biao Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
- Hefei National Laboratory, Hefei 230088, China
| |
Collapse
|
4
|
Behrle T, Nguyen TL, Reiter F, Baur D, de Neeve B, Stadler M, Marinelli M, Lancellotti F, Yelin SF, Home JP. Phonon Laser in the Quantum Regime. PHYSICAL REVIEW LETTERS 2023; 131:043605. [PMID: 37566845 DOI: 10.1103/physrevlett.131.043605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 05/30/2023] [Indexed: 08/13/2023]
Abstract
We demonstrate a trapped-ion system with two competing dissipation channels, implemented independently on two ion species cotrapped in a Paul trap. By controlling coherent spin-oscillator couplings and optical pumping rates we explore the phase diagram of this system, which exhibits a regime analogous to that of a (phonon) laser but operates close to the quantum ground state with an average phonon number of n[over ¯]<10. We demonstrate phase locking of the oscillator to an additional resonant drive, and also observe the phase diffusion of the resulting state under dissipation by reconstructing the quantum state from a measurement of the characteristic function.
Collapse
Affiliation(s)
- T Behrle
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - T L Nguyen
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - F Reiter
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
- Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
| | - D Baur
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - B de Neeve
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - M Stadler
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - M Marinelli
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - F Lancellotti
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - S F Yelin
- Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
| | - J P Home
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
- Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| |
Collapse
|
5
|
Li A, Wei H, Cotrufo M, Chen W, Mann S, Ni X, Xu B, Chen J, Wang J, Fan S, Qiu CW, Alù A, Chen L. Exceptional points and non-Hermitian photonics at the nanoscale. NATURE NANOTECHNOLOGY 2023; 18:706-720. [PMID: 37386141 DOI: 10.1038/s41565-023-01408-0] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Accepted: 04/25/2023] [Indexed: 07/01/2023]
Abstract
Exceptional points (EPs) arising in non-Hermitian systems have led to a variety of intriguing wave phenomena, and have been attracting increased interest in various physical platforms. In this Review, we highlight the latest fundamental advances in the context of EPs in various nanoscale systems, and overview the theoretical progress related to EPs, including higher-order EPs, bulk Fermi arcs and Weyl exceptional rings. We peek into EP-associated emerging technologies, in particular focusing on the influence of noise for sensing near EPs, improving the efficiency in asymmetric transmission based on EPs, optical isolators in nonlinear EP systems and novel concepts to implement EPs in topological photonics. We also discuss the constraints and limitations of the applications relying on EPs, and offer parting thoughts about promising ways to tackle them for advanced nanophotonic applications.
Collapse
Affiliation(s)
- Aodong Li
- Wuhan National Laboratory for Optoelectronics and School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, China
| | - Heng Wei
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Michele Cotrufo
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, USA
| | - Weijin Chen
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Sander Mann
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, USA
| | - Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, USA
| | - Bingcong Xu
- Wuhan National Laboratory for Optoelectronics and School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, China
| | - Jianfeng Chen
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Jian Wang
- Wuhan National Laboratory for Optoelectronics and School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, China
| | - Shanhui Fan
- Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, CA, USA
- Department of Applied Physics, Stanford University, Stanford, CA, USA
| | - Cheng-Wei Qiu
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore.
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, USA.
- Physics Program, Graduate Center, City University of New York, New York, NY, USA.
| | - Lin Chen
- Wuhan National Laboratory for Optoelectronics and School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, China.
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China.
| |
Collapse
|
6
|
Wan LL, Lü XY. Quantum-Squeezing-Induced Point-Gap Topology and Skin Effect. PHYSICAL REVIEW LETTERS 2023; 130:203605. [PMID: 37267552 DOI: 10.1103/physrevlett.130.203605] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Accepted: 04/21/2023] [Indexed: 06/04/2023]
Abstract
We theoretically predict the squeezing-induced point-gap topology together with a symmetry-protected Z_{2} "skin effect" in a one-dimensional (1D) quadratic-bosonic system. Protected by a time-reversal symmetry, such a topology is associated with a novel Z_{2} invariant (similar to quantum spin-Hall insulators), which is fully capable of characterizing the occurrence of the Z_{2} skin effect. Focusing on zero energy, the parameter regime of this skin effect in the phase diagram just corresponds to a "real- and point-gap coexisting topological phase." Moreover, this phase associated with the symmetry-protected Z_{2} skin effect is experimentally observable by detecting the steady-state power spectral density. Our Letter is of fundamental interest in enriching non-Bloch topological physics by introducing quantum squeezing and has potential applications for the engineering of symmetry-protected sensors based on the Z_{2} skin effect.
Collapse
Affiliation(s)
- Liang-Liang Wan
- School of Physics and Institute for Quantum Science and Engineering, Huzhong University of Science and Technology, Wuhan 430074, China and Wuhan Institute of Quantum Technology, Wuhan 430074, China
| | - Xin-You Lü
- School of Physics and Institute for Quantum Science and Engineering, Huzhong University of Science and Technology, Wuhan 430074, China and Wuhan Institute of Quantum Technology, Wuhan 430074, China
| |
Collapse
|
7
|
Öztürk FE, Vewinger F, Weitz M, Schmitt J. Fluctuation-Dissipation Relation for a Bose-Einstein Condensate of Photons. PHYSICAL REVIEW LETTERS 2023; 130:033602. [PMID: 36763390 DOI: 10.1103/physrevlett.130.033602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Revised: 07/28/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
For equilibrium systems, the magnitude of thermal fluctuations is closely linked to the dissipative response to external perturbations. This fluctuation-dissipation relation has been described for material particles in a wide range of fields. Here, we experimentally probe the relation between the number fluctuations and the response function for a Bose-Einstein condensate of photons coupled to a dye reservoir, demonstrating the fluctuation-dissipation relation for a quantum gas of light. The observed agreement of the scale factor with the environment temperature both directly confirms the thermal nature of the optical condensate and demonstrates the validity of the fluctuation-dissipation theorem for a Bose-Einstein condensate.
Collapse
Affiliation(s)
- Fahri Emre Öztürk
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Julian Schmitt
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| |
Collapse
|
8
|
Li Y, Cao Y, Chen Y, Yang X. Universal characteristics of one-dimensional non-Hermitian superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:055401. [PMID: 36410037 DOI: 10.1088/1361-648x/aca4b4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Accepted: 11/21/2022] [Indexed: 06/16/2023]
Abstract
We establish a non-Bloch band theory for one-dimensional(1D) non-Hermitian topological superconductors. The universal physical properties of non-Hermitian topological superconductors are revealed based on the theory. According to the particle-hole symmetry, there exist reciprocal particle and hole loops of generalized Brillouin zone. The critical point of quantum phase transition, where the energy gap closes, appears when the particle and hole loops intersect at Bloch points. If the non-Hermitian system has non-Hermitian skin effects, the non-Hermitian skin effect should be theZ2skin effect: the corresponding eigenstates of particle and hole localize at opposite ends of an open chain, respectively. The non-Bloch band theory is applied to two examples, non-Hermitianp- ands-wave topological superconductors. In terms of Majorana Pfaffian, aZ2non-Bloch topological invariant is defined to establish the non-Hermitian bulk-boundary correspondence for the non-Hermitian topological superconductors.
Collapse
Affiliation(s)
- Yang Li
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| | - Yang Cao
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| | - Yuanping Chen
- 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
|
9
|
Król M, Septembre I, Oliwa P, Kędziora M, Łempicka-Mirek K, Muszyński M, Mazur R, Morawiak P, Piecek W, Kula P, Bardyszewski W, Lagoudakis PG, Solnyshkov DD, Malpuech G, Piętka B, Szczytko J. Annihilation of exceptional points from different Dirac valleys in a 2D photonic system. Nat Commun 2022; 13:5340. [PMID: 36096889 PMCID: PMC9468178 DOI: 10.1038/s41467-022-33001-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Accepted: 08/26/2022] [Indexed: 12/03/2022] Open
Abstract
Topological physics relies on Hamiltonian’s eigenstate singularities carrying topological charges, such as Dirac points, and – in non-Hermitian systems – exceptional points (EPs), lines or surfaces. So far, the reported non-Hermitian topological transitions were related to the creation of a pair of EPs connected by a Fermi arc out of a single Dirac point by increasing non-Hermiticity. Such EPs can annihilate by reducing non-Hermiticity. Here, we demonstrate experimentally that an increase of non-Hermiticity can lead to the annihilation of EPs issued from different Dirac points (valleys). The studied platform is a liquid crystal microcavity with voltage-controlled birefringence and TE-TM photonic spin-orbit-coupling. Non-Hermiticity is provided by polarization-dependent losses. By increasing the non-Hermiticity degree, we control the position of the EPs. After the intervalley annihilation, the system becomes free of any band singularity. Our results open the field of non-Hermitian valley-physics and illustrate connections between Hermitian topology and non-Hermitian phase transitions. The authors study a liquid crystal microcavity with polarization-dependent absorption, a source of non-Hermiticity. The transition in the Hermitian topology of the spin-orbit coupling makes possible the annihilation of exceptional points.
Collapse
|
10
|
Li Y, Liang C, Wang C, Lu C, Liu YC. Gain-Loss-Induced Hybrid Skin-Topological Effect. PHYSICAL REVIEW LETTERS 2022; 128:223903. [PMID: 35714249 DOI: 10.1103/physrevlett.128.223903] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Accepted: 05/13/2022] [Indexed: 06/15/2023]
Abstract
Non-Hermitian topological effects are of crucial importance both in fundamental physics and applications. Here we discover the gain-loss-induced hybrid second-order skin-topological effect and the PT phase transition in skin-topological modes. By studying a non-Hermitian Haldane model, we find that the topological edge modes are localized on a special type of corner, while the bulk modes remain extended. Such an effect originates from the interplay between gain, loss, and the chiral edge currents induced by the nonlocal flux, which can be characterized by considering the properties of the edge sites as a one-dimensional chain. We establish a relation between the skin-topological effect and the PT symmetries belonging to different edges. Moreover, we discover the PT phase transition with the emergence of exceptional points between pairs of skin-topological modes. Our results pave the way for the investigation of non-Hermitian topological physics and PT phase transition in higher-dimensional systems.
Collapse
Affiliation(s)
- Yaohua Li
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Chao Liang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Chenyang Wang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Cuicui Lu
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
- Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China
| | - Yong-Chun Liu
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Frontier Science Center for Quantum Information, Beijing 100084, People's Republic of China
| |
Collapse
|
11
|
Pal A, Modak S, Shukla A, Panigrahi PK. PT-symmetry and supersymmetry: interconnection of broken and unbroken phases. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0494] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The broken and unbroken phases of
P
T
and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from unbroken to the broken phases of
P
T
-symmetry, with the merger of eigenfunctions near the exceptional point is found to arise from two distinct realizations of the potential, originating from the underlying supersymmetry. Interestingly, in
P
T
-symmetric phase, spontaneous breaking of supersymmetry occurs in a parametric domain, possessing non-trivial shape invariances, under reparametrization to yield the corresponding energy spectra. One also observes a parametric bifurcation behaviour in this domain. Unlike the real Scraf potential, in
P
T
-symmetric phase, a connection between complex isospecrtal superpotentials and modified Korteweg-de Vries equation occurs, only with certain restrictive parametric conditions. In the broken
P
T
-symmetry phase, supersymmetry is found to be intact in the entire parameter domain yielding the complex energy spectra, with zero-width resonance occurring at integral values of a potential parameter.
Collapse
Affiliation(s)
- Adipta Pal
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Subhrajit Modak
- Indian Institute of Science Education and Research Mohali, Punjab 140306, India
| | - Aradhya Shukla
- Indian Institute of Science Education and Research Kolkata, Mohanpur, West Bengal 741246, India
| | - Prasanta K. Panigrahi
- Indian Institute of Science Education and Research Kolkata, Mohanpur, West Bengal 741246, India
| |
Collapse
|
12
|
Vretenar M, Toebes C, Klaers J. Modified Bose-Einstein condensation in an optical quantum gas. Nat Commun 2021; 12:5749. [PMID: 34593808 PMCID: PMC8484613 DOI: 10.1038/s41467-021-26087-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 09/14/2021] [Indexed: 11/21/2022] Open
Abstract
Open quantum systems can be systematically controlled by making changes to their environment. A well-known example is the spontaneous radiative decay of an electronically excited emitter, such as an atom or a molecule, which is significantly influenced by the feedback from the emitter's environment, for example, by the presence of reflecting surfaces. A prerequisite for a deliberate control of an open quantum system is to reveal the physical mechanisms that determine its state. Here, we investigate the Bose-Einstein condensation of a photonic Bose gas in an environment with controlled dissipation and feedback. Our measurements offer a highly systematic picture of Bose-Einstein condensation under non-equilibrium conditions. We show that by adjusting their frequency Bose-Einstein condensates naturally try to avoid particle loss and destructive interference in their environment. In this way our experiments reveal physical mechanisms involved in the formation of a Bose-Einstein condensate, which typically remain hidden when the system is close to thermal equilibrium.
Collapse
Affiliation(s)
- Mario Vretenar
- Adaptive Quantum Optics (AQO), MESA+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE, Enschede, The Netherlands
| | - Chris Toebes
- Adaptive Quantum Optics (AQO), MESA+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE, Enschede, The Netherlands
| | - Jan Klaers
- Adaptive Quantum Optics (AQO), MESA+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE, Enschede, The Netherlands.
| |
Collapse
|
13
|
Öztürk FE, Lappe T, Hellmann G, Schmitt J, Klaers J, Vewinger F, Kroha J, Weitz M. Observation of a non-Hermitian phase transition in an optical quantum gas. Science 2021; 372:88-91. [PMID: 33795457 DOI: 10.1126/science.abe9869] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2020] [Accepted: 02/23/2021] [Indexed: 12/24/2022]
Abstract
Quantum gases of light, such as photon or polariton condensates in optical microcavities, are collective quantum systems enabling a tailoring of dissipation from, for example, cavity loss. This characteristic makes them a tool to study dissipative phases, an emerging subject in quantum many-body physics. We experimentally demonstrate a non-Hermitian phase transition of a photon Bose-Einstein condensate to a dissipative phase characterized by a biexponential decay of the condensate's second-order coherence. The phase transition occurs because of the emergence of an exceptional point in the quantum gas. Although Bose-Einstein condensation is usually connected to lasing by a smooth crossover, the observed phase transition separates the biexponential phase from both lasing and an intermediate, oscillatory condensate regime. Our approach can be used to study a wide class of dissipative quantum phases in topological or lattice systems.
Collapse
Affiliation(s)
- Fahri Emre Öztürk
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Tim Lappe
- Physikalisches Institut, Universität Bonn, Nussallee 12, 53115 Bonn, Germany
| | - Göran Hellmann
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Julian Schmitt
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany.
| | - Jan Klaers
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Johann Kroha
- Physikalisches Institut, Universität Bonn, Nussallee 12, 53115 Bonn, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany.
| |
Collapse
|