1
|
Redmann A, Kurtscheid C, Wolf N, Vewinger F, Schmitt J, Weitz M. Bose-Einstein Condensation of Photons in a Four-Site Quantum Ring. PHYSICAL REVIEW LETTERS 2024; 133:093602. [PMID: 39270190 DOI: 10.1103/physrevlett.133.093602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Accepted: 07/29/2024] [Indexed: 09/15/2024]
Abstract
Thermalization of radiation by contact to matter is a well-known concept, but the application of thermodynamic methods to complex quantum states of light remains a challenge. Here, we observe Bose-Einstein condensation of photons into the hybridized ground state of a coupled four-site ring potential. In our experiment, the periodically closed ring lattice superimposed by a weak harmonic trap for photons is realized inside a spatially structured dye-filled microcavity. Photons thermalize to room temperature, and above a critical photon number macroscopically occupy the symmetric linear combination of the site eigenstates with zero phase winding, which constitutes the ground state of the system. The mutual phase coherence of photons at different lattice sites is verified by optical interferometry.
Collapse
|
2
|
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
|
3
|
Busley E, Miranda LE, Redmann A, Kurtscheid C, Umesh KK, Vewinger F, Weitz M, Schmitt J. Compressibility and the equation of state of an optical quantum gas in a box. Science 2022; 375:1403-1406. [PMID: 35324306 DOI: 10.1126/science.abm2543] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The compressibility of a medium, quantifying its response to mechanical perturbations, is a fundamental property determined by the equation of state. For gases of material particles, studies of the mechanical response are well established, in fields from classical thermodynamics to cold atomic quantum gases. We demonstrate a measurement of the compressibility of a two-dimensional quantum gas of light in a box potential and obtain the equation of state for the optical medium. The experiment was carried out in a nanostructured dye-filled optical microcavity. We observed signatures of Bose-Einstein condensation at high phase-space densities in the finite-size system. Upon entering the quantum degenerate regime, the measured density response to an external force sharply increases, hinting at the peculiar prediction of an infinite compressibility of the deeply degenerate Bose gas.
Collapse
Affiliation(s)
- Erik Busley
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Leon Espert Miranda
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Andreas Redmann
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Christian Kurtscheid
- 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
|
4
|
Diessel OK, Diehl S, Chiocchetta A. Emergent Kardar-Parisi-Zhang Phase in Quadratically Driven Condensates. PHYSICAL REVIEW LETTERS 2022; 128:070401. [PMID: 35244410 DOI: 10.1103/physrevlett.128.070401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 12/24/2021] [Indexed: 06/14/2023]
Abstract
In bosonic gases at thermal equilibrium, an external quadratic drive can induce a Bose-Einstein condensation described by the Ising transition, as a consequence of the explicitly broken U(1) phase rotation symmetry down to Z_{2}. However, in physical realizations such as exciton polaritons and nonlinear photonic lattices, thermal equilibrium is lost and the state is rather determined by a balance between losses and external drive. A fundamental question is then how nonequilibrium fluctuations affect this transition. Here, we show that in a two-dimensional driven-dissipative Bose system the Ising phase is suppressed and replaced by a nonequilibrium phase featuring Kardar-Parisi-Zhang (KPZ) physics. Its emergence is rooted in a U(1)-symmetry restoration mechanism enabled by the strong fluctuations in reduced dimensionality. Moreover, we show that the presence of the quadratic drive term enhances the visibility of the KPZ scaling, compared to two-dimensional U(1)-symmetric gases, where it has remained so far elusive.
Collapse
Affiliation(s)
- Oriana K Diessel
- Max-Planck-Institute of Quantum Optics, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
| | - Sebastian Diehl
- Institute for Theoretical Physics, University of Cologne, Zülpicher Strasse 77, 50937 Cologne, Germany
| | - Alessio Chiocchetta
- Institute for Theoretical Physics, University of Cologne, Zülpicher Strasse 77, 50937 Cologne, Germany
| |
Collapse
|
5
|
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
|