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

We study theoretically the effects of pump-spot size and location on photon condensates. By exploring the inhomogeneous molecular excitation fraction, we make clear the relation between spatial equilibration, gain clamping and thermalization in a photon condensate. This provides a simple understanding of several recent experimental results. We find that as thermalization breaks down, gain clamping is imperfect, leading to "transverse spatial hole burning" and multimode condensation. This opens the possibility of engineering the gain profile to control the condensate structure.Comment: Further extended, including new figures. Now 10 figure

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

Suppressing and restoring the Dicke superradiance transition by dephasing and decay

We show that dephasing of individual atoms destroys the superradiance transition of the Dicke model, but that adding individual decay toward the spin down state can restore this transition. To demonstrate this, we present a method to give an exact solution for the N atom problem with individual dephasing which scales polynomially with N. By comparing finite size scaling of our exact solution to a cumulant expansion, we confirm the destruction and restoration of the superradiance transition holds in the thermodynamic limit.PostprintPeer reviewe

Thermalization and breakdown of thermalization in photon condensates

We examine in detail the mechanisms behind thermalization and Bose-Einstein condensation 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 non-equilibrium 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.Comment: 17 pages, 12 figure

Excitonic spectral features in strongly-coupled organic polaritons

Starting from a microscopic model, we investigate the optical spectra of molecules in strongly-coupled organic microcavities examining how they might self-consistently adapt their coupling to light. We consider both rotational and vibrational degrees of freedom, focusing on features which can be seen in the peak in the center of the spectrum at the bare excitonic frequency. In both cases we find that the matter-light coupling can lead to a self-consistent change of the molecular states, with consequent temperature-dependent signatures in the absorption spectrum. However, for typical parameters, these effects are much too weak to explain recent measurements. We show that another mechanism which naturally arises from our model of vibrationally dressed polaritons has the right magnitude and temperature dependence to be at the origin of the observed data.Comment: 14 pages, 6 figur

Superradiant and lasing states in driven-dissipative Dicke models

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

Nonequilibrium magnetic phases in spin lattices with gain and loss

We study the magnetic phases of a nonequilibrium spin chain, where coherent interactions between neighboring lattice sites compete with alternating gain and loss processes. This competition between coherent and incoherent dynamics induces transitions between magnetically aligned and highly mixed phases, across which the system changes from a low to an infinite temperature state. We show that the origin of these transitions can be traced back to the dynamical effect of parity–time-reversal symmetry breaking, which has no counterpart in the theory of equilibrium phase transitions. This mechanism also results in very atypical features and we find first-order transitions without phase coexistence and mixed-order transitions which do not break the underlying U(1) symmetry, even in the appropriate thermodynamic limit. Thus, despite its simplicity, the current model considerably extends the phenomenology of nonequilibrium phase transitions beyond that commonly assumed for driven-dissipative spins and related systems

Super-correlated radiance in nonlinear photonic waveguides

We study the collective decay of two-level emitters coupled to a nonlinear waveguide, for example, a nanophotonic lattice or a superconducting resonator array with strong photon-photon interactions. Under these conditions, a new decay channel into bound photon pairs emerges, through which spatial correlations between emitters are established by regular interference as well as interactions between the photons. We derive an effective Markovian theory to model the resulting decay dynamics of an arbitrary distribution of emitters and identify collective effects beyond the usual phenomena of super- and subradiance. Specifically, in the limit of many close-by emitters, we find that the system undergoes a supercorrelated decay process where all the emitters are either in the excited state or in the ground state but not in any of the intermediate states. The predicted effects can be probed in state-of-the-art waveguide QED experiments and provide a striking example of how the dynamics of open quantum systems can be modified by many-body effects in a nonharmonic environment

Emergence of PT-symmetry breaking in open quantum systems

The effect of PT -symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. However, it is still an unsolved problem how to generalize the concept of PT symmetry to the quantum domain, where the conventional definition in terms of non-Hermitian Hamiltonians is not applicable. Here we introduce a symmetry relation for Liouville operators that describe the dissipative evolution of arbitrary open quantum systems. Specifically, we show that the invariance of the Liouvillian under this symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected PT -symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe PT -symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes

Fluctuations and noise in nanoelectrical and nanomechanical systems

In this thesis we present a study of the fluctuations and noise which occur in a particular nanoelectrical device, the single electron transistor (SET). Electrical transport through the SET occurs through a combination of stochastic, incoherent tunnelling and coherent quantum oscillations, giving rise to a rich variety of transport processes. In the first section of the thesis, we look at the fluctuations in the electrical properties of a SET. We describe the SET as an open quantum system, and use this model to develop Born-Markov master equation descriptions of the dynamics close to three resonant transport processes: the Josephson quasiparticle resonance, the double Josephson quasiparticle resonance and the Cooper-pair resonances. We use these models to examine the noise properties of both the charge on the SET island and the current flowing through the SET. Quantum coherent oscillations of Cooper-pairs in the SET give rise to noise spectra which can be highly asymmetric in frequency. We give an explicit calculation of how an oscillator capacitively coupled to the SET island can be used to infer the quantum noise properties close to the Cooper-pair resonances. To calculate the current noise we develop a new technique, based on classical full counting statistics. We are able to use this technique to calculate the effect of the current fluctuations on an oscillator coupled to the current through the SET, the results of which are in good agreement with recent measurements. In the final part of the thesis we explore the coupled dynamics of a normal state SET capacitively coupled to a resonator in the presence of an external drive. The coupling between the electrical and mechanical degrees of freedom leads to interesting non-linear behaviour in the resonator. We are able to find regions where the resonator has two possible stable amplitudes of oscillation, which can lead to a bistability in the dynamics. We also look at the fluctuations in the energy of the system. We use numerical methods to simulate the dynamics of the system, and to obtain the probability distribution for the work done, whose form can be interpreted by the appropriate fluctuation relation