Spatial dynamics, thermalization, and gain clamping in a photon condensate

Keeling, Jonathan; Kirton, Peter

doi:10.1103/physreva.93.013829

Cited by 39 publications

(66 citation statements)

References 70 publications

(129 reference statements)

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“…In response to observations of the breakdown of thermalization due to inhomogeneous pumping, in both stationary [34] and time-resolved experiments [35], they modified their model to include spatial distributions of pumping and molecular excitation [43]. The results match the salient points of the experimental data.…”

Section: A Nonequilibrium Model Of Photon Condensationsupporting

confidence: 63%

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

Nyman

Walker

2017

Journal of Modern Optics

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Photons can come to thermal equilibrium at room temperature by scattering multiple times from a fluorescent dye. By confining the light and dye in a microcavity, a minimum energy is set and the photons can then show Bose-Einstein condensation. We present here the physical principles underlying photon thermalization and condensation, and review the literature on the subject. We then explore the 'small' regime where very few photons are needed for condensation. We compare thermal equilibrium results to a rate-equation model of microlasers, which includes spontaneous emission into the cavity, and we note that small systems result in ambiguity in the definition of threshold. FOREWORDThis article is written in memory of Danny Segal, who was a colleague of one of us (Rob Nyman) in the Quantum Optics and Laser Science group at Imperial College for many years. The topic of this article touches on the subject of dye lasers, the stuff of nightmares for any AMO physicist of his generation, but a stronger connection to Danny is that he was very supportive of my application for the fellowship that pushed my career forward, and funded this research. One of Danny's quirks was a strong dislike of flying. As a consequence, I had the pleasure of joining him on a 24 hour, four-train journey from London to Italy to a conference. That's a lot of time for story telling and forging memories for life. Danny was one of the good guys, and I sorely miss his good humour and advice.This article presents a gentle introduction to thermalization and Bose-Einstein condensation (BEC) of photons in dye-filled microcavities, followed by a review of the state of the art. We then note the similarity to microlasers, particularly when there are very few photons involved. We compare a simple non-equilibrium model for microlasers with an even simpler thermal equilibrium model for BEC and show that the models coincide for similar values of a 'smallness' parameter.

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Section: A Nonequilibrium Model Of Photon Condensationsupporting

confidence: 63%

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

Nyman

Walker

2017

Journal of Modern Optics

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“…The pump spot is elliptical with an aspect ratio near unity and a minor axis of typically 50-60μm diameter. These parameters are known to produce near thermal-equilibrium conditions [23]. The pump pulses last 500ns, which is much longer than any thermalisation (about 300 ps) or cavity loss (about 1 ns) time scale in the system.…”

Section: Experimental Systemmentioning

confidence: 99%

Spatiotemporal coherence of non-equilibrium multimode photon condensates

et al. 2016

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We report on the observation of quantum coherence of Bose-Einstein condensed photons in an optically pumped, dye-filled microcavity. We find that coherence is long-range in space and time above condensation threshold, but short-range below threshold, compatible with thermalequilibrium theory. Far above threshold, the condensate is no longer at thermal equilibrium and is fragmented over non-degenerate, spatially overlapping modes. A microscopic theory including cavity loss, molecular structure and relaxation shows that this multimode condensation is similar to multimode lasing induced by imperfect gain clamping. BEC means that interferometry is one of the most urgent measurements to be made with a condensate [4,5]. Where thermal equilibrium is not completely reached, coherence is the defining characteristic of non-BEC quantum condensation, e.g for semiconductor exciton-polaritons [6-9] and organic polaritons [10,11]. In nonideal Bose gases, such as ultracold atoms, interactions tend to reduce but not destroy the coherence [12][13][14].The long range coherence behaviour of two-dimensional (2D) microcavity condensates is currently an open question. The coherence of interacting, equilibrium 2D Bose gases decays with a power law at large distances. The exponent is no greater than 1/4, which is reached at the threshold for the Berezinskii-Kosterlitz-Thouless transition [15]. It is known that the equation of motion for the local phase of a non-equilibrium drivendissipative 2D condensate is in the universality class of the Kardar-Parisi-Zhang (KPZ) equation [16], and nonpower-law decays are possible. Since the long-range coherence only shows non-equilibrium behaviour for systems which are very large compared to interaction length scales (such as the healing length), it has proven difficult to observe the true long-range behaviour, mainly due to unavoidable pumping inhomogeneities [17].Photon condensates in dye-filled microcavities are weakly interacting [18][19][20][21], inhomogeneous [22, 23], dissipative Bose gases close to thermal equilibrium at room temperature [24][25][26][27][28]. It is worth noting that the physical system has some similarities to a dye laser, with the decisive difference being that lasing is necessarily a non-equilibrium effect whereas photons can also undergo BEC in thermal equilibrium. Consequently BEC implies macroscopic occupation of the ground state independently of the loss and gain properties, whereas a laser is characterised by a large occupation of exactly the mode that has the most gain [29].Unique among physical realisations of BEC, in dye-microcavity photon BEC the particles thermalise only with a bath and not directly among themselves. This implies that the establishment of phase coherence in the OPEN ACCESS RECEIVED

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“…In reality, the coupling between TLS and some cavity mode will also depend on the spatial mode function. A tractable model that incorporates the spatial dynamics was devised by Keeling and Kirton [40]. It has led to the successful understanding of the recent experiments [6,17].…”

Section: Modelmentioning

confidence: 99%

“…The first microscopic model of a photon condensate was developed by Kirton and Keeling [38,39], which has recently been further extended by the same authors [40,41]. They considered a dye-filled cavity with multiple optical modes together with additional incoherent pump and loss channels and derived a Markovian quantum master equation of the Lindblad type [42,43].…”

Section: Introductionmentioning

confidence: 99%

Interplay of coherent and dissipative dynamics in condensates of light

et al. 2018

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Based on the Lindblad master equation approach we obtain a detailed microscopic model of photons in a dye-filled cavity, which features condensation of light. To this end we generalise a recent nonequilibrium approach of Kirton and Keeling such that the dye-mediated contribution to the photonphoton interaction in the light condensate is accessible due to an interplay of coherent and dissipative dynamics. We describe the steady-state properties of the system by analysing the resulting equations of motion of both photonic and matter degrees of freedom. In particular, we discuss the existence of two limiting cases for steady states: photon Bose-Einstein condensate and laser-like. In the former case, we determine the corresponding dimensionless photon-photon interaction strength by relying on realistic experimental data and find a good agreement with previous theoretical estimates. Furthermore, we investigate how the dimensionless interaction strength depends on the respective system parameters.

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Spatial dynamics, thermalization, and gain clamping in a photon condensate

Cited by 39 publications

References 70 publications

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

Spatiotemporal coherence of non-equilibrium multimode photon condensates

Interplay of coherent and dissipative dynamics in condensates of light

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