Thermalization and breakdown of thermalization in photon condensates

The authors acknowledge financial support from EPSRC program “TOPNES” (Grant No. EP/I031014/1) and EPSRC (Grant No. EP/G004714/2). P.G.K. acknowledges support from EPSRC (Grant No. EP/M010910/1).We examine in detail the mechanisms behind thermalization and Bose-Einstein condensation (BEC) of a gas of photons in a dye-filled microcavity. We derive a microscopic quantum model, based on that of a standard laser, and show how this model can reproduce the behavior of recent experiments. Using the rate-equation approximation of this model, we show how a thermal distribution of photons arises. We go on to describe how the nonequilibrium effects in our model can cause thermalization to break down as one moves away from the experimental parameter values. In particular, we examine the effects of changing cavity length, and of altering the vibrational spectrum of the dye molecules. We are able to identify two measures which quantify whether the system is in thermal equilibrium. Using these, we plot “phase diagrams” distinguishing BEC and standard lasing regimes. Going beyond the rate-equation approximation, our quantum model allows us to investigate both the second-order coherence g(2) and the linewidth of the emission from the cavity. We show how the linewidth collapses as the system transitions to a Bose condensed state, and compare the results to the Schawlow-Townes linewidth.Publisher PDFPeer reviewe

Efficient real-time path integrals for non-Markovian spin-boson models

Funders: Strathearn - EPSRC, ID: EP/L505079/1, Lovett - EPSRC, ID: EP/K025562/1, Kirton- EPSRC, ID: EP/M010910/1Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.Publisher PDFPeer reviewe

Designing spin-channel geometries for entanglement distribution

We investigate different geometries of spin-1/2 nitrogen impurity channels for distributing entanglement between pairs of remote nitrogen vacancy centers (NVs) in diamond. To go beyond the system size limits imposed by directly solving the master equation, we implement a matrix product operator method to describe the open system dynamics. In so doing, we provide an early demonstration of how the time-evolving block decimation algorithm can be used for answering a problem related to a real physical system that could not be accessed by other methods. For a fixed NV separation there is an interplay between incoherent impurity spin decay and coherent entanglement transfer: Long-transfer-time, few-spin systems experience strong dephasing that can be overcome by increasing the number of spins in the channel. We examine how missing spins and disorder in the coupling strengths affect the dynamics, finding that in some regimes a spin ladder is a more effective conduit for information than a single-spin chain.Publisher PDFPeer reviewe

Jacqueline Brunet, Grammaire critique de l\u27italien

We consider the orientational alignment of dipoles due to strong matter light coupling, for a non-vanishing density of excitations. We compare various approaches to this problem in the limit of large numbers of emitters, and show that direct Monte Carlo integration, mean-field theory, and large deviation methods match exactly in this limit. All three results show that orientational alignment develops in the presence of a macroscopically occupied polariton mode, and that the dipoles asymptotically approach perfect alignment in the limit of high density or low temperature.Comment: 7 pages, 4 figure

Superradiant and lasing states in driven-dissipative Dicke models

Funding: UK EPSRC (EP/M010910/1) (PK); EPSRC programs TOPNES (EP/I031014/1) and “Hybrid Polaritonics” (EP/M025330/1) (JK).We present the non-equilibrium phase diagram of a model which can demonstrate both Dicke-Hepp-Lieb superradiance and regular lasing by varying the coherent and incoherent driving terms. We find that the regions in the phase diagram corresponding to superradiance and standard lasing are always separated by a normal region. We analyse the behaviour of the system using a combination of exact numerics based on permutation symmetry of the density matrix for small to intermediate numbers of molecules, and second order cumulant equations for large numbers of molecules. We find that the nature of the photon distribution in the superradiant and lasing states are very similar, but the emission spectrum is very different. We also show that in the presence of both coherent and incoherent driving, a period-doubling route to a chaotic state occurs.Publisher PDFPeer reviewe

Efficient non-Markovian quantum dynamics using time-evolving matrix product operators

AS acknowledges a studentship from EPSRC (EP/L505079/1). PK acknowledges support from EPSRC (EP/M010910/1). DK acknowledges support from the EPSRC CM-CDT (EP/L015110/1). JK acknowledges support from EPSRC programs "TOPNES" (EP/I031014/1) and "Hybrid Polaritonics" (EP/M025330/1). BWL acknowledges support from EPSRC (EP/K025562/1).In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings or to special cases where specific numerical techniques become effective. Here we present a general and yet exact numerical approach that efficiently describes the time evolution of a quantum system coupled to a non-Markovian harmonic environment. Our method relies on expressing the system state and its propagator as a matrix product state and operator, respectively, and using a singular value decomposition to compress the description of the state as time evolves. We demonstrate the power and flexibility of our approach by numerically identifying the localisation transition of the Ohmic spin-boson model, and considering a model with widely separated environmental timescales arising for a pair of spins embedded in a common environment.Publisher PDFPeer reviewe

Coherence protection in coupled quantum systems

HMC acknowledges studentship funding from EPSRC under grant no. EP/G03673X/1. PGK acknowledges support from EPSRC (EP/M010910/1). BWL acknowledges support from EPSRC (EP/K025562/1). PRE acknowledges funding from SFI (15/IACA/3402). JK acknowledges financial support from EPSRC programs “TOPNES” (EP/I031014/1) and “Hybrid-Polaritonics” (EP/M025330/1).The interaction of a quantum system with its environment causes decoherence, setting a fundamental limit on its suitability for quantum information processing. However, we show that if the system consists of coupled parts with different internal energy scales then the interaction of one part with a thermal bath need not lead to loss of coherence from the other. Remarkably, we find that the protected part can remain coherent for longer when the coupling to the bath becomes stronger or the temperature is raised. Our theory will enable the design of decoherence-resistant hybrid quantum computers.Publisher PDFPeer reviewe

Non-linear dynamics of a driven nanomechanical single electron transistor

This work was supported by EPSRC [Grant number EP/I017818/1]We analyze the response of a nanomechanical resonator to an external drive when it is also coupled to a single-electron transistor (SET). The interaction between the SET electrons and the mechanical resonator depends on the amplitude of the mechanical motion leading to a strongly non-linear response to the drive which is similar to that of a Duffing oscillator. We show that the average dynamics of the resonator is well-described by a simple effective model which incorporates damping and frequency renormalization terms which are amplitude dependent. We also find that for a certain range of parameters the system displays interesting bistable dynamics in which noise arising from charge fluctuations causes the resonator to switch slowly between different dynamical states.PostprintPeer reviewe

Nonequilibrium Model of Photon Condensation

We develop a nonequilibrium model of condensation and lasing of photons in a dye filled microcavity. We examine in detail the nature of the thermalization process induced by absorption and emission of photons by the dye molecules, and investigate when the photons are able to reach a thermal equilibrium Bose-Einstein distribution. At low temperatures, or large cavity losses, the absorption and emission rates are too small to allow the photons to reach thermal equilibrium and the behavior becomes more like that of a conventional laser.Publisher PDFPeer reviewe