1
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Tang Y, Dhar HS, Oulton RF, Nyman RA, Mintert F. Breakdown of Temporal Coherence in Photon Condensates. PHYSICAL REVIEW LETTERS 2024; 132:173601. [PMID: 38728729 DOI: 10.1103/physrevlett.132.173601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 03/20/2024] [Indexed: 05/12/2024]
Abstract
The temporal coherence of an ideal Bose gas increases as the system approaches the Bose-Einstein condensation threshold from below, with coherence time diverging at the critical point. However, counterexamples have been observed for condensates of photons formed in an externally pumped, dye-filled microcavity, wherein the coherence time decreases rapidly for increasing particle number above threshold. This Letter establishes intermode correlations as the central explanation for the experimentally observed dramatic decrease in the coherence time beyond critical pump power.
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Affiliation(s)
- Yijun Tang
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
| | - Himadri S Dhar
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Rupert F Oulton
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
| | - Robert A Nyman
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
| | - Florian Mintert
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany
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2
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Figueiredo JL, Mendonça JT, Terças H. Bose-Einstein condensation of photons in microcavity plasmas. Phys Rev E 2023; 108:L013201. [PMID: 37583182 DOI: 10.1103/physreve.108.l013201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 06/21/2023] [Indexed: 08/17/2023]
Abstract
Bose-Einstein condensation of a finite number of photons propagating inside a plasma-filled microcavity is investigated. The nonzero chemical potential is provided by the electrons, which induces a finite photon mass and allows condensation to occur. We derive an equation that models the evolution of the photon-mode occupancies, with Compton scattering taken into account as the mechanism of thermalization. The kinetic evolution of the photon spectrum is solved numerically, and we find evidence of condensation down to nanosecond timescales for typical microplasma conditions, n_{e}∼10^{14}-10^{15}cm^{-3}. The critical temperature scales almost linearly with the number of photons, and we find high condensate fractions at microcavity-plasma temperatures, for experimentally achievable cavity lengths (100-500µm) and photon numbers (10^{10}-10^{12}).
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Affiliation(s)
- J L Figueiredo
- GoLP - Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
| | - J T Mendonça
- GoLP - Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
| | - H Terças
- GoLP - Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
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3
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Dalla Torre EG, Reagor MJ. Simulating the Interplay of Particle Conservation and Long-Range Coherence. PHYSICAL REVIEW LETTERS 2023; 130:060403. [PMID: 36827580 DOI: 10.1103/physrevlett.130.060403] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Revised: 12/13/2022] [Accepted: 01/04/2023] [Indexed: 06/18/2023]
Abstract
Lasers and Bose-Einstein condensates (BECs) exhibit macroscopic quantum coherence in seemingly unrelated ways. Lasers possess a well-defined global phase while the number of photons fluctuates. In BECs of atoms, instead, the number of particles is conserved and the global phase is undefined. Here, we use gate-based quantum circuits to create a unified framework that connects lasers and BEC states. Our approach relies on a scalable circuit that measures the total number of particles without destroying long-range coherence. We introduce two complementary probes of global and relative phase coherence, study how they are affected by measurements of the particle number, and implement them on a superconducting quantum computer by Rigetti. We find that particle conservation enhances long-range phase coherence, highlighting a mechanism used by superfluids and superconductors to gain phase stiffness.
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Affiliation(s)
- Emanuele G Dalla Torre
- Department of Physics and Center for Quantum Entanglement Science and Technology, Bar-Ilan University, 52900 Ramat Gan, Israel
- Superconducting Quantum Materials and Systems Center (SQMS), Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Matthew J Reagor
- Superconducting Quantum Materials and Systems Center (SQMS), Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
- Rigetti Computing, 775 Heinz Avenue, Berkeley, California 94710, USA
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4
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Shishkov VY, Andrianov ES. Negative compressibility of a nonequilibrium nonideal Bose-Einstein condensate. Phys Rev E 2022; 106:064108. [PMID: 36671074 DOI: 10.1103/physreve.106.064108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 11/18/2022] [Indexed: 06/17/2023]
Abstract
An ideal equilibrium Bose-Einstein condensate (BEC) is usually considered in the grand canonical (μVT) ensemble, which implies the presence of the chemical equilibrium with the environment. However, in most experimental scenarios, the total amount of particles in BEC is determined either by the initial conditions or by the balance between dissipation and pumping. As a result, BEC may possess the thermal equilibrium but almost never the chemical equilibrium. In addition, many experimentally achievable BECs are non-ideal due to interaction between particles. In the recent work [Shiskov et al., Phys. Rev. Lett. 128, 065301 (2022)0031-900710.1103/PhysRevLett.128.065301], it has been shown that invariant subspaces in the system Hilbert space appear in non-equilibrium BEC in the fast thermalization limit. In each of these subspaces, Gibbs distribution is established with a certain number of particles that makes it possible to investigate properties of non-ideal non-equilibrium BEC independently in each invariant subspace. In this work, we analyze the BEC stability due to change in dispersion curve caused by non-linearity in BEC. Generally, non-linearity leads to the redshift or blueshift of the dispersion curve and to the change in the effective mass of the particles. We show that the redshift of the dispersion curve can lead to the negative compressibility of BEC and onset of instability, whereas the change in the effective mass always makes BEC more stable. We find the explicit condition for the particle density in BEC, at which the negative compressibility appears. We show that the appearance of BEC instability is followed by the formation of stable and spatially inhomogeneous BEC.
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Affiliation(s)
- Vladislav Yu Shishkov
- Dukhov Research Institute of Automatics (VNIIA), 22 Sushchevskaya, Moscow 127055, Russia; Moscow Institute of Physics and Technology, 9 Institutskiy pereulok, Dolgoprudny 141700, Moscow region, Russia; Center for Photonics and Quantum Materials, Skolkovo Institute of Science and Technology, Moscow, Russia; and Laboratories for Hybrid Photonics, Skolkovo Institute of Science and Technology, Moscow, Russia
| | - Evgeny S Andrianov
- Dukhov Research Institute of Automatics (VNIIA), 22 Sushchevskaya, Moscow 127055, Russia; Moscow Institute of Physics and Technology, 9 Institutskiy pereulok, Dolgoprudny 141700, Moscow region, Russia; Center for Photonics and Quantum Materials, Skolkovo Institute of Science and Technology, Moscow, Russia; and Laboratories for Hybrid Photonics, Skolkovo Institute of Science and Technology, Moscow, Russia
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5
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Sánchez-Barquilla M, Fernández-Domínguez AI, Feist J, García-Vidal FJ. A Theoretical Perspective on Molecular Polaritonics. ACS PHOTONICS 2022; 9:1830-1841. [PMID: 35726239 PMCID: PMC9204811 DOI: 10.1021/acsphotonics.2c00048] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/08/2022] [Revised: 05/20/2022] [Accepted: 05/20/2022] [Indexed: 06/15/2023]
Abstract
In the past decade, much theoretical research has focused on studying the strong coupling between organic molecules (or quantum emitters, in general) and light modes. The description and prediction of polaritonic phenomena emerging in this light-matter interaction regime have proven to be difficult tasks. The challenge originates from the enormous number of degrees of freedom that need to be taken into account, both in the organic molecules and in their photonic environment. On one hand, the accurate treatment of the vibrational spectrum of the former is key, and simplified quantum models are not valid in many cases. On the other hand, most photonic setups have complex geometric and material characteristics, with the result that photon fields corresponding to more than just a single electromagnetic mode contribute to the light-matter interaction in these platforms. Moreover, loss and dissipation, in the form of absorption or radiation, must also be included in the theoretical description of polaritons. Here, we review and offer our own perspective on some of the work recently done in the modeling of interacting molecular and optical states with increasing complexity.
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Affiliation(s)
- Mónica Sánchez-Barquilla
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Antonio I. Fernández-Domínguez
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Johannes Feist
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Francisco J. García-Vidal
- Departamento
de Física Teórica de la Materia Condensada and Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
- Institute
of High Performance Computing, Agency for
Science, Technology, and Research (A*STAR), Connexis, Singapore, 138632 Singapore
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6
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Abstract
In this work we suggest a novel paradigm of social laser (solaser), which can explain such Internet inspired social phenomena as echo chambers, reinforcement and growth of information cascades, enhancement of social actions under strong mass media operation. The solaser is based on a well-known in quantum physics laser model of coherent amplification of the optical field. Social networks are at the core of the solaser model; we define them by means of a network model possessing power–law degree distribution. In the solaser the network environment plays the same role as the gain medium has in a physical laser device. We consider social atoms as decision making agents (humans or even chat bots), which possess two (mental) states and occupy the nodes of a network. The solaser establishes communication between the agents as absorption and spontaneous or stimulated emission of socially actual information within echo chambers, which mimic an optical resonator of a convenient (physical) laser. We have demonstrated that social lasing represents the second order nonequilibrium phase transition, which evokes the release of coherent socially stimulated information field represented with the order parameter. The solaser implies the formation of macroscopic social polarization and results in a huge social impact, which is realized by viral information cascades occurring in the presence of population imbalance (social bias). We have shown that decision making agents follow an adiabatically time dependent mass media pump, which acts in the network community reproducing various reliable scenarios for information cascade evolution. We have also shown that in contrast to physical lasers, due to node degree peculiarities, the coupling strength of decision making agents with the network may be enhanced \documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{\langle k\rangle }$$\end{document}⟨k⟩ times. It leads to a large increase of speed, at which a viral message spreads through a social media. In this case, the mass media pump supports additional reinforcement and acceleration of cascade growth. We have revealed that the solaser model in some approximations possesses clear links with familiar Ising and SIS (susceptible-infected-susceptible) models typically used for evaluating a social impact and information growth, respectively. However, the solaser paradigm can serve as a new platform for modelling temporal social events, which originate from “microscopic” (quantum-like) processes occurring in the society. Our findings open new perspectives for interdisciplinary studies of distributed intelligence agents behavior associated with information exchange and social impact.
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7
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Shishkov VY, Andrianov ES, Zasedatelev AV, Lagoudakis PG, Lozovik YE. Exact Analytical Solution for the Density Matrix of a Nonequilibrium Polariton Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2022; 128:065301. [PMID: 35213178 DOI: 10.1103/physrevlett.128.065301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
In this Letter, we give an analytical quantum description of a nonequilibrium polariton Bose-Einstein condensate (BEC) based on the solution of the master equation for the full polariton density matrix in the limit of fast thermalization. We find the density matrix of a nonequilibrium BEC, that takes into account quantum correlations between all polariton states. We show that the formation of BEC is accompanied by the build-up of cross-correlations between the ground state and the excited states reaching their highest values at the condensation threshold. Despite the nonequilibrium nature of polariton systems, we show the average population of polariton states exhibits the Bose-Einstein distribution with an almost zero effective chemical potential above the condensation threshold similar to an equilibrium BEC. We demonstrate that above threshold the effective temperature of polaritons drops below the reservoir temperature.
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Affiliation(s)
- Vladislav Yu Shishkov
- Dukhov Research Institute of Automatics (VNIIA), 22 Sushchevskaya, Moscow 127055, Russia; Moscow Institute of Physics and Technology, 9 Institutskiy pereulok, Dolgoprudny 141700, Moscow region, Russia; and Hybrid Photonics Laboratory, Skolkovo Institute of Science and Technology, Territory of Innovation Center Skolkovo, Bolshoy Boulevard 30, building 1, 121205 Moscow, Russia
| | - Evgeny S Andrianov
- Dukhov Research Institute of Automatics (VNIIA), 22 Sushchevskaya, Moscow 127055, Russia; Moscow Institute of Physics and Technology, 9 Institutskiy pereulok, Dolgoprudny 141700, Moscow region, Russia; and Hybrid Photonics Laboratory, Skolkovo Institute of Science and Technology, Territory of Innovation Center Skolkovo, Bolshoy Boulevard 30, building 1, 121205 Moscow, Russia
| | - Anton V Zasedatelev
- Hybrid Photonics Laboratory, Skolkovo Institute of Science and Technology, Territory of Innovation Center Skolkovo, Bolshoy Boulevard 30, building 1, 121205 Moscow, Russia
| | - Pavlos G Lagoudakis
- Hybrid Photonics Laboratory, Skolkovo Institute of Science and Technology, Territory of Innovation Center Skolkovo, Bolshoy Boulevard 30, building 1, 121205 Moscow, Russia and Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Yurii E Lozovik
- Institute for Spectroscopy RAS, 5 Fizicheskaya, Troitsk 142190, Russia; Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, 101000 Moscow, Russia; Hybrid Photonics Laboratory, Skolkovo Institute of Science and Technology, Territory of Innovation Center Skolkovo, Bolshoy Boulevard 30, building 1, 121205 Moscow, Russia; and Dukhov Research Institute of Automatics (VNIIA), 22 Sushchevskaya, Moscow 127055, Russia
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8
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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.
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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.
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9
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Otlaadisa P, Tabi CB, Kofané TC. Modulation instability in helicoidal spin-orbit coupled open Bose-Einstein condensates. Phys Rev E 2021; 103:052206. [PMID: 34134292 DOI: 10.1103/physreve.103.052206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2020] [Accepted: 04/08/2021] [Indexed: 06/12/2023]
Abstract
We introduce a vector form of the cubic complex Ginzburg-Landau equation describing the dynamics of dissipative solitons in the two-component helicoidal spin-orbit coupled open Bose-Einstein condensates (BECs), where the addition of dissipative interactions is done through coupled rate equations. Furthermore, the standard linear stability analysis is used to investigate theoretically the stability of continuous-wave (cw) solutions and to obtain an expression for the modulational instability gain spectrum. Using direct simulations of the Fourier space, we numerically investigate the dynamics of the modulational instability in the presence of helicoidal spin-orbit coupling. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold for amplitude perturbations.
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Affiliation(s)
- Phelo Otlaadisa
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
| | - Conrad Bertrand Tabi
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
| | - Timoléon Crépin Kofané
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
- Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaoundé I, Yaoundé, Cameroon
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10
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Rodrigues JD, Dhar HS, Walker BT, Smith JM, Oulton RF, Mintert F, Nyman RA. Learning the Fuzzy Phases of Small Photonic Condensates. PHYSICAL REVIEW LETTERS 2021; 126:150602. [PMID: 33929251 DOI: 10.1103/physrevlett.126.150602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 03/18/2021] [Indexed: 06/12/2023]
Abstract
Phase transitions, being the ultimate manifestation of collective behavior, are typically features of many-particle systems only. Here, we describe the experimental observation of collective behavior in small photonic condensates made up of only a few photons. Moreover, a wide range of both equilibrium and nonequilibrium regimes, including Bose-Einstein condensation or laserlike emission are identified. However, the small photon number and the presence of large relative fluctuations places major difficulties in identifying different phases and phase transitions. We overcome this limitation by employing unsupervised learning and fuzzy clustering algorithms to systematically construct the fuzzy phase diagram of our small photonic condensate. Our results thus demonstrate the rich and complex phase structure of even small collections of photons, making them an ideal platform to investigate equilibrium and nonequilibrium physics at the few particle level.
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Affiliation(s)
- João D Rodrigues
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
| | - Himadri S Dhar
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
| | - Benjamin T Walker
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
- Centre for Doctoral Training in Controlled Quantum Dynamics, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
| | - Jason M Smith
- Department of Materials, University of Oxford, Oxford OX2 6NN, United Kingdom
| | - Rupert F Oulton
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
| | - Florian Mintert
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
| | - Robert A Nyman
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ, United Kingdom
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11
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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.
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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.
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12
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Barland S, Azam P, Lippi GL, Nyman RA, Kaiser R. Photon thermalization and a condensation phase transition in an electrically pumped semiconductor microresonator. OPTICS EXPRESS 2021; 29:8368-8375. [PMID: 33820285 DOI: 10.1364/oe.409344] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 02/13/2021] [Indexed: 06/12/2023]
Abstract
We report on an experimental study of photon thermalization and condensation in a semiconductor microresonator in the weak-coupling regime. We measure the dispersion relation of light and the photon mass in a single-wavelength, broad-area resonator. The observed luminescence spectrum is compatible with a room-temperature, thermal-equilibrium distribution. A phase transition, identified by a saturation of the population at high energies and a superlinear increase of the occupation at low energy, takes place when the phase-space density is of order unity. We explain our observations by Bose-Einstein condensation of photons in equilibrium with a particle reservoir and discuss the relation with laser emission.
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13
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Gladilin VN, Wouters M. Vortices in Nonequilibrium Photon Condensates. PHYSICAL REVIEW LETTERS 2020; 125:215301. [PMID: 33274963 DOI: 10.1103/physrevlett.125.215301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 10/09/2020] [Indexed: 06/12/2023]
Abstract
We present a theoretical study of vortices in arrays of photon condensates. Even when interactions are negligible, as is the case in current experiments, pumping and losses can lead to a finite vortex core size. While some properties of photon condensate vortices, such as their self-acceleration and the generation of vortex pairs by a moving vortex resemble those in lasers and interacting polariton condensates far from equilibrium, in several aspects they differ from previously studied systems: the vortex core size is determined by the balance between pumping and tunneling, the core appears oblate in the direction of its motion, and new vortex pairs can spontaneously nucleate in the core region.
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Affiliation(s)
- Vladimir N Gladilin
- TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium
| | - Michiel Wouters
- TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium
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14
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Sub-picosecond thermalization dynamics in condensation of strongly coupled lattice plasmons. Nat Commun 2020; 11:3139. [PMID: 32561728 PMCID: PMC7305221 DOI: 10.1038/s41467-020-16906-1] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Accepted: 05/18/2020] [Indexed: 01/08/2023] Open
Abstract
Bosonic condensates offer exciting prospects for studies of non-equilibrium quantum dynamics. Understanding the dynamics is particularly challenging in the sub-picosecond timescales typical for room temperature luminous driven-dissipative condensates. Here we combine a lattice of plasmonic nanoparticles with dye molecule solution at the strong coupling regime, and pump the molecules optically. The emitted light reveals three distinct regimes: one-dimensional lasing, incomplete stimulated thermalization, and two-dimensional multimode condensation. The condensate is achieved by matching the thermalization rate with the lattice size and occurs only for pump pulse durations below a critical value. Our results give access to control and monitoring of thermalization processes and condensate formation at sub-picosecond timescale.
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15
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Silva REF, Pino JD, García-Vidal FJ, Feist J. Polaritonic molecular clock for all-optical ultrafast imaging of wavepacket dynamics without probe pulses. Nat Commun 2020; 11:1423. [PMID: 32184408 PMCID: PMC7078293 DOI: 10.1038/s41467-020-15196-x] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2019] [Accepted: 02/21/2020] [Indexed: 11/29/2022] Open
Abstract
Conventional approaches to probing ultrafast molecular dynamics rely on the use of synchronized laser pulses with a well-defined time delay. Typically, a pump pulse excites a molecular wavepacket. A subsequent probe pulse can then dissociate or ionize the molecule, and measurement of the molecular fragments provides information about where the wavepacket was for each time delay. Here, we propose to exploit the ultrafast nuclear-position-dependent emission obtained due to large light-matter coupling in plasmonic nanocavities to image wavepacket dynamics using only a single pump pulse. We show that the time-resolved emission from the cavity provides information about when the wavepacket passes a given region in nuclear configuration space. This approach can image both cavity-modified dynamics on polaritonic (hybrid light-matter) potentials in the strong light-matter coupling regime and bare-molecule dynamics in the intermediate coupling regime of large Purcell enhancements, and provides a route towards ultrafast molecular spectroscopy with plasmonic nanocavities.
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Affiliation(s)
- R E F Silva
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049, Madrid, Spain.
| | - Javier Del Pino
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG, Amsterdam, The Netherlands
| | - Francisco J García-Vidal
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049, Madrid, Spain
- Donostia International Physics Center (DIPC), E-20018, Donostia/San Sebastián, Spain
| | - Johannes Feist
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049, Madrid, Spain.
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16
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Walker BT, Rodrigues JD, Dhar HS, Oulton RF, Mintert F, Nyman RA. Non-stationary statistics and formation jitter in transient photon condensation. Nat Commun 2020; 11:1390. [PMID: 32170081 PMCID: PMC7070038 DOI: 10.1038/s41467-020-15154-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Accepted: 02/17/2020] [Indexed: 11/26/2022] Open
Abstract
While equilibrium phase transitions are easily described by order parameters and free-energy landscapes, for their non-stationary counterparts these quantities are usually ill-defined. Here, we probe transient non-equilibrium dynamics of an optically pumped, dye-filled microcavity. We quench the system to a far-from-equilibrium state and find delayed condensation close to a critical excitation energy, a transient equivalent of critical slowing down. Besides number fluctuations near the critical excitation energy, we show that transient phase transitions exhibit timing jitter in the condensate formation. This jitter is a manifestation of the randomness associated with spontaneous emission, showing that condensation is a stochastic, rather than deterministic process. Despite the non-equilibrium character of this phase transition, we construct an effective free-energy landscape that describes the formation jitter and allows, in principle, its generalization to a wider class of processes. Description of non-equilibrium phase transitions is problematic, due to the absence of suitable free energy landscapes. Here, the authors experimentally show delayed photon condensation and timing jitter in a dye-filled microcavity, modelled by a non-equilibrium extension of the free-energy landscape.
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Affiliation(s)
- Benjamin T Walker
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK.,Centre for Doctoral Training in Controlled Quantum Dynamics, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK
| | - João D Rodrigues
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK.
| | - Himadri S Dhar
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK
| | - Rupert F Oulton
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK
| | - Florian Mintert
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK
| | - Robert A Nyman
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK
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17
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Kurtscheid C, Dung D, Busley E, Vewinger F, Rosch A, Weitz M. Thermally condensing photons into a coherently split state of light. Science 2019; 366:894-897. [PMID: 31727840 DOI: 10.1126/science.aay1334] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2019] [Revised: 09/23/2019] [Accepted: 10/23/2019] [Indexed: 11/02/2022]
Abstract
The quantum state of light plays a crucial role in a wide range of fields, from quantum information science to precision measurements. Whereas complex quantum states can be created for electrons in solid-state materials through mere cooling, optical manipulation and control builds on nonthermodynamic methods. Using an optical dye microcavity, we show that photon wave packets can be split through thermalization within a potential with two minima subject to tunnel coupling. At room temperature, photons condense into a quantum-coherent bifurcated ground state. Fringe signals upon recombination show the relative coherence between the two wells, demonstrating a working interferometer with the nonunitary thermodynamic beam splitter. Our energetically driven optical-state preparation method provides a route for exploring correlated and entangled optical many-body states.
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Affiliation(s)
- Christian Kurtscheid
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany.
| | - David Dung
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Erik Busley
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Achim Rosch
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Cologne, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany.
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18
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Strashko A, Kirton P, Keeling J. Organic Polariton Lasing and the Weak to Strong Coupling Crossover. PHYSICAL REVIEW LETTERS 2018; 121:193601. [PMID: 30468582 DOI: 10.1103/physrevlett.121.193601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2018] [Indexed: 06/09/2023]
Abstract
Following experimental realizations of room temperature polariton lasing with organic molecules, we present a microscopic model that allows us to explore the crossover from weak to strong matter-light coupling. We consider a nonequilibrium Dicke-Holstein model, including both strong coupling to vibrational modes and strong matter-light coupling, providing the phase diagram of this model in the thermodynamic limit. We discuss the mechanism of polariton lasing, uncovering a process of self-tuning, and identify the relation and distinction between regular dye lasers and organic polariton lasers.
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Affiliation(s)
- Artem Strashko
- SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, United Kingdom
| | - Peter Kirton
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1040 Vienna, Austria
| | - Jonathan Keeling
- SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, United Kingdom
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19
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Schnell A, Ketzmerick R, Eckardt A. On the number of Bose-selected modes in driven-dissipative ideal Bose gases. Phys Rev E 2018; 97:032136. [PMID: 29776161 DOI: 10.1103/physreve.97.032136] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2018] [Indexed: 06/08/2023]
Abstract
In an ideal Bose gas that is driven into a steady state far from thermal equilibrium, a generalized form of Bose condensation can occur. Namely, the single-particle states unambiguously separate into two groups: the group of Bose-selected states, whose occupations increase linearly with the total particle number, and the group of all other states whose occupations saturate [Phys. Rev. Lett. 111, 240405 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.240405]. However, so far very little is known about how the number of Bose-selected states depends on the properties of the system and its coupling to the environment. The answer to this question is crucial since systems hosting a single, a few, or an extensive number of Bose-selected states will show rather different behavior. While in the former two scenarios each selected mode acquires a macroscopic occupation, corresponding to (fragmented) Bose condensation, the latter case rather bears resemblance to a high-temperature state of matter. In this paper, we systematically investigate the number of Bose-selected states, considering different classes of the rate matrices that characterize the driven-dissipative ideal Bose gases in the limit of weak system-bath coupling. These include rate matrices with continuum limit, rate matrices of chaotic driven systems, random rate matrices, and rate matrices resulting from thermal baths that couple to a few observables only.
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Affiliation(s)
- Alexander Schnell
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Roland Ketzmerick
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
| | - André Eckardt
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
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20
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Caputo D, Ballarini D, Dagvadorj G, Sánchez Muñoz C, De Giorgi M, Dominici L, West K, Pfeiffer LN, Gigli G, Laussy FP, Szymańska MH, Sanvitto D. Topological order and thermal equilibrium in polariton condensates. NATURE MATERIALS 2018; 17:145-151. [PMID: 29200196 DOI: 10.1038/nmat5039] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2016] [Accepted: 10/24/2017] [Indexed: 06/07/2023]
Abstract
The Berezinskii-Kosterlitz-Thouless phase transition from a disordered to a quasi-ordered state, mediated by the proliferation of topological defects in two dimensions, governs seemingly remote physical systems ranging from liquid helium, ultracold atoms and superconducting thin films to ensembles of spins. Here we observe such a transition in a short-lived gas of exciton-polaritons, bosonic light-matter particles in semiconductor microcavities. The observed quasi-ordered phase, characteristic for an equilibrium two-dimensional bosonic gas, with a decay of coherence in both spatial and temporal domains with the same algebraic exponent, is reproduced with numerical solutions of stochastic dynamics, proving that the mechanism of pairing of the topological defects (vortices) is responsible for the transition to the algebraic order. This is made possible thanks to long polariton lifetimes in high-quality samples and in a reservoir-free region. Our results show that the joint measurement of coherence both in space and time is required to characterize driven-dissipative phase transitions and enable the investigation of topological ordering in open systems.
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Affiliation(s)
- Davide Caputo
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
- University of Salento, Via Arnesano, 73100 Lecce, Italy
| | - Dario Ballarini
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Galbadrakh Dagvadorj
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
- Department of Physics, University of Warwick, Coventry CV4 7AL, UK
| | | | - Milena De Giorgi
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Lorenzo Dominici
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Kenneth West
- PRISM, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08540, USA
| | - Loren N Pfeiffer
- PRISM, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08540, USA
| | - Giuseppe Gigli
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
- University of Salento, Via Arnesano, 73100 Lecce, Italy
| | - Fabrice P Laussy
- Faculty of Science and Engineering, University of Wolverhampton, Wulfruna Street, WV1 1LY, UK
- Russian Quantum Center, Novaya 100, 143025 Skolkovo, Moscow Region, Russia
| | - Marzena H Szymańska
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
| | - Daniele Sanvitto
- CNR NANOTEC-Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
- INFN sezione di Lecce, 73100 Lecce, Italy
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21
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Hesten HJ, Nyman RA, Mintert F. Decondensation in Nonequilibrium Photonic Condensates: When Less Is More. PHYSICAL REVIEW LETTERS 2018; 120:040601. [PMID: 29437424 DOI: 10.1103/physrevlett.120.040601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Indexed: 06/08/2023]
Abstract
We investigate the steady state of a system of photons in a pumped dye-filled microcavity. By varying pump and thermalization the system can be tuned between Bose-Einstein condensation, multimode condensation, and lasing. We present a rich nonequilibrium phase diagram which exhibits transitions between these phases, including decondensation of individual modes under conditions that would typically favor condensation.
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Affiliation(s)
- Henry J Hesten
- Quantum Optics and Laser Science Group, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom
| | - Robert A Nyman
- Quantum Optics and Laser Science Group, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom
| | - Florian Mintert
- Quantum Optics and Laser Science Group, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom
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22
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Schnell A, Vorberg D, Ketzmerick R, Eckardt A. High-Temperature Nonequilibrium Bose Condensation Induced by a Hot Needle. PHYSICAL REVIEW LETTERS 2017; 119:140602. [PMID: 29053292 DOI: 10.1103/physrevlett.119.140602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2017] [Indexed: 06/07/2023]
Abstract
We investigate theoretically a one-dimensional ideal Bose gas that is driven into a steady state far from equilibrium via the coupling to two heat baths: a global bath of temperature T and a "hot needle," a bath of temperature T_{h}≫T with localized coupling to the system. Remarkably, this system features a crossover to finite-size Bose condensation at temperatures T that are orders of magnitude larger than the equilibrium condensation temperature. This counterintuitive effect is explained by a suppression of long-wavelength excitations resulting from the competition between both baths. Moreover, for sufficiently large needle temperatures ground-state condensation is superseded by condensation into an excited state, which is favored by its weaker coupling to the hot needle. Our results suggest a general strategy for the preparation of quantum degenerate nonequilibrium steady states with unconventional properties and at large temperatures.
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Affiliation(s)
- Alexander Schnell
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Daniel Vorberg
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Roland Ketzmerick
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany
| | - André Eckardt
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
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23
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Weill R, Bekker A, Levit B, Zhurahov M, Fischer B. Thermalization of one-dimensional photon gas and thermal lasers in erbium-doped fibers. OPTICS EXPRESS 2017; 25:18963-18973. [PMID: 29041087 DOI: 10.1364/oe.25.018963] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Accepted: 07/18/2017] [Indexed: 06/07/2023]
Abstract
We demonstrate thermalization and Bose-Einstein (BE) distribution of photons in standard erbium-doped fibers (edf) in a broad spectral range up to ~200nm at the 1550nm wavelength regime. Our measurements were done at a room temperature ~300K and 77K. It is a special demonstration of thermalization of photons in fiber cavities and even in open fibers. They are one-dimensional (1D), meters-long, with low finesse, high loss and small capture fraction of the spontaneous emission. Moreover, we find in the edf cavities coexistence of thermal-equilibrium (TE) and thermal lasing without an overall inversion (T-LWI). The experimental results are supported by a theoretical analysis based on the rate equations.
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24
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Damm T, Dung D, Vewinger F, Weitz M, Schmitt J. First-order spatial coherence measurements in a thermalized two-dimensional photonic quantum gas. Nat Commun 2017; 8:158. [PMID: 28761123 PMCID: PMC5537358 DOI: 10.1038/s41467-017-00270-8] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Accepted: 06/16/2017] [Indexed: 11/21/2022] Open
Abstract
Phase transitions between different states of matter can profoundly modify the order in physical systems, with the emergence of ferromagnetic or topological order constituting important examples. Correlations allow the quantification of the degree of order and the classification of different phases. Here we report measurements of first-order spatial correlations in a harmonically trapped two-dimensional photon gas below, at and above the critical particle number for Bose–Einstein condensation, using interferometric measurements of the emission of a dye-filled optical microcavity. For the uncondensed gas, the transverse coherence decays on a length scale determined by the thermal de Broglie wavelength of the photons, which shows the expected scaling with temperature. At the onset of Bose–Einstein condensation, true long-range order emerges, and we observe quantum statistical effects as the thermal wave packets overlap. The excellent agreement with equilibrium Bose gas theory prompts microcavity photons as promising candidates for studies of critical scaling and universality in optical quantum gases. Phase transitions in quantum matter are related to correlation effects and they can change the ordering of material. Here the authors measure the first-order spatial correlation and the de Broglie wavelength for both thermal and condensed form of a photonic Bose gas in a dye-filled optical microcavity.
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Affiliation(s)
- Tobias Damm
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany
| | - David Dung
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany.
| | - Julian Schmitt
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany.
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25
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Weiss C, Tempere J. Grand-canonical condensate fluctuations in weakly interacting Bose-Einstein condensates of light. Phys Rev E 2016; 94:042124. [PMID: 27841546 DOI: 10.1103/physreve.94.042124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2015] [Indexed: 06/06/2023]
Abstract
Grand-canonical fluctuations of Bose-Einstein condensates of light are accessible to state-of-the-art experiments [J. Schmitt et al., Phys. Rev. Lett. 112, 030401 (2014).PRLTAO0031-900710.1103/PhysRevLett.112.030401]. We phenomenologically describe these fluctuations by using the grand-canonical ensemble for a weakly interacting Bose gas at thermal equilibrium. For a two-dimensional harmonic trap, we use two models for which the canonical partition functions of the weakly interacting Bose gas are given by exact recurrence relations. We find that the grand-canonical condensate fluctuations for weakly interacting Bose gases vanish at zero temperature, thus behaving qualitatively similarly to an ideal gas in the canonical ensemble (or microcanonical ensemble) rather than the grand-canonical ensemble. For low but finite temperatures, the fluctuations remain considerably higher than for the canonical ensemble, as predicted by the ideal gas in the grand-canonical ensemble, thus clearly showing that we are not in a regime in which the ensembles are equivalent.
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Affiliation(s)
- Christoph Weiss
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - Jacques Tempere
- TQC-Theory of Quantum and Complex Systems, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium
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26
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Schütz S, Jäger SB, Morigi G. Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles. PHYSICAL REVIEW LETTERS 2016; 117:083001. [PMID: 27588853 DOI: 10.1103/physrevlett.117.083001] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2015] [Indexed: 06/06/2023]
Abstract
We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behavior which is first dominated by coherent long-range forces and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the self-organized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.
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Affiliation(s)
- Stefan Schütz
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - Simon B Jäger
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - Giovanna Morigi
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
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27
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Damm T, Schmitt J, Liang Q, Dung D, Vewinger F, Weitz M, Klaers J. Calorimetry of a Bose-Einstein-condensed photon gas. Nat Commun 2016; 7:11340. [PMID: 27090978 PMCID: PMC4838885 DOI: 10.1038/ncomms11340] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2015] [Accepted: 03/16/2016] [Indexed: 11/09/2022] Open
Abstract
Phase transitions, as the condensation of a gas to a liquid, are often revealed by a discontinuous behaviour of thermodynamic quantities. For liquid helium, for example, a divergence of the specific heat signals the transition from the normal fluid to the superfluid state. Apart from liquid helium, determining the specific heat of a Bose gas has proven to be a challenging task, for example, for ultracold atomic Bose gases. Here we examine the thermodynamic behaviour of a trapped two-dimensional photon gas, a system that allows us to spectroscopically determine the specific heat and the entropy of a nearly ideal Bose gas from the classical high temperature to the Bose-condensed quantum regime. The critical behaviour at the phase transition is clearly revealed by a cusp singularity of the specific heat. Regarded as a test of quantum statistical mechanics, our results demonstrate a quantitative agreement with its predictions at the microscopic level.
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Affiliation(s)
- Tobias Damm
- Institut für Angewandte Physik, Atominstitut, Institute of Quantum Electronics, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Julian Schmitt
- Institut für Angewandte Physik, Atominstitut, Institute of Quantum Electronics, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Qi Liang
- Institut für Angewandte Physik, Atominstitut, Institute of Quantum Electronics, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - David Dung
- Institut für Angewandte Physik, Atominstitut, Institute of Quantum Electronics, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Atominstitut, Institute of Quantum Electronics, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Atominstitut, Institute of Quantum Electronics, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Jan Klaers
- Institut für Angewandte Physik, Atominstitut, Institute of Quantum Electronics, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
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28
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Schmitt J, Damm T, Dung D, Wahl C, Vewinger F, Klaers J, Weitz M. Spontaneous Symmetry Breaking and Phase Coherence of a Photon Bose-Einstein Condensate Coupled to a Reservoir. PHYSICAL REVIEW LETTERS 2016; 116:033604. [PMID: 26849597 DOI: 10.1103/physrevlett.116.033604] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2015] [Indexed: 06/05/2023]
Abstract
We examine the phase evolution of a Bose-Einstein condensate of photons generated in a dye microcavity by temporal interference with a phase reference. The photoexcitable dye molecules constitute a reservoir of variable size for the condensate particles, allowing for grand canonical statistics with photon bunching, as in a lamp-type source. We directly observe phase jumps of the condensate associated with the large statistical number fluctuations and find a separation of correlation time scales. For large systems, our data reveal phase coherence and a spontaneously broken symmetry, despite the statistical fluctuations.
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Affiliation(s)
- Julian Schmitt
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Tobias Damm
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - David Dung
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Christian Wahl
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Jan Klaers
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
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29
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Wilson RM, Mahmud KW, Hu A, Gorshkov AV, Hafezi M, Foss-Feig M. Collective phases of strongly interacting cavity photons. PHYSICAL REVIEW. A 2016; 94:10.1103/PhysRevA.94.033801. [PMID: 31098434 PMCID: PMC6515917 DOI: 10.1103/physreva.94.033801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin- 1 2 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady-state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectory simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics and establish a simple relationship between the switching times and properties of the quantum Liouvillian.
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Affiliation(s)
- Ryan M Wilson
- Department of Physics, The United States Naval Academy, Annapolis, Maryland 21402, USA
- Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, USA
| | - Khan W Mahmud
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Anzi Hu
- Department of Physics, American University, Washington, DC 20016, USA
| | - Alexey V Gorshkov
- Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, USA
- 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
| | - Mohammad Hafezi
- Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical Engineering and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Michael Foss-Feig
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
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Schmitt J, Damm T, Dung D, Vewinger F, Klaers J, Weitz M. Observation of grand-canonical number statistics in a photon Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2014; 112:030401. [PMID: 24484122 DOI: 10.1103/physrevlett.112.030401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2013] [Indexed: 06/03/2023]
Abstract
We report measurements of particle number correlations and fluctuations of a photon Bose-Einstein condensate in a dye microcavity using a Hanbury Brown-Twiss experiment. The photon gas is coupled to a reservoir of molecular excitations, which serve as both heat bath and particle reservoir to realize grand-canonical conditions. For large reservoirs, we observe strong number fluctuations of the order of the total particle number extending deep into the condensed phase. Our results demonstrate that Bose-Einstein condensation under grand-canonical ensemble conditions does not imply second-order coherence.
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Affiliation(s)
- Julian Schmitt
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Tobias Damm
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - David Dung
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Jan Klaers
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
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