Non-equilibrium Berezinskii-Kosterlitz-Thouless Transition in a Driven Open Quantum System

The Berezinskii-Kosterlitz-Thouless mechanism, in which a phase transition is mediated by the proliferation of topological defects, governs the critical behaviour of a wide range of equilibrium two-dimensional systems with a continuous symmetry, ranging from superconducting thin films to two-dimensional Bose fluids, such as liquid helium and ultracold atoms. We show here that this phenomenon is not restricted to thermal equilibrium, rather it survives more generally in a dissipative highly non-equilibrium system driven into a steady-state. By considering a light-matter superfluid of polaritons, in the so-called optical parametric oscillator regime, we demonstrate that it indeed undergoes a vortex binding-unbinding phase transition. Yet, the exponent of the power-law decay of the first order correlation function in the (algebraically) ordered phase can exceed the equilibrium upper limit -- a surprising occurrence, which has also been observed in a recent experiment. Thus we demonstrate that the ordered phase is somehow more robust against the quantum fluctuations of driven systems than thermal ones in equilibrium.Comment: 11 pages, 9 figure

Kibble-Zurek mechanism in driven-dissipative systems crossing a non-equilibrium phase transition

The Kibble-Zurek mechanism constitutes one of the most fascinating and universal phenomena in the physics of critical systems. It describes the formation of domains and the spontaneous nucleation of topological defects when a system is driven across a phase transition exhibiting spontaneous symmetry breaking. While a characteristic dependence of the defect density on the speed at which the transition is crossed was observed in a vast range of equilibrium condensed matter systems, its extension to intrinsically driven-dissipative systems is a matter of ongoing research. In this work we numerically confirm the Kibble-Zurek mechanism in a paradigmatic family of driven-dissipative quantum systems, namely exciton-polaritons in microcavities. Our findings show how the concepts of universality and critical dynamics extend to driven-dissipative systems that do not conserve energy or particle number nor satisfy a detailed balance condition

Critical slowing down in circuit quantum electrodynamics

Critical slowing down of the time it takes a system to reach equilibrium is a key signature of bistability in dissipative first-order phase transitions. Understanding and characterizing this process can shed light on the underlying many-body dynamics that occur close to such a transition. Here, we explore the rich quantum activation dynamics and the appearance of critical slowing down in an engineered superconducting quantum circuit. Specifically, we investigate the intermediate bistable regime of the generalized Jaynes-Cummings Hamiltonian (GJC), realized by a circuit quantum electrodynamics (cQED) system consisting of a transmon qubit coupled to a microwave cavity. We find a previously unidentified regime of quantum activation in which the critical slowing down reaches saturation and, by comparing our experimental results with a range of models, we shed light on the fundamental role played by the qubit in this regime

Excitons in T-shaped quantum wires

We calculate energies, oscillator strengths for radiative recombination, and two-particle wave functions for the ground state exciton and around 100 excited states in a T-shaped quantum wire. We include the single-particle potential and the Coulomb interaction between the electron and hole on an equal footing, and perform exact diagonalisation of the two-particle problem within a finite basis set. We calculate spectra for all of the experimentally studied cases of T-shaped wires including symmetric and asymmetric GaAs/Al$_{x}$Ga$_{1-x}$As and In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As structures. We study in detail the shape of the wave functions to gain insight into the nature of the various states for selected symmetric and asymmetric wires in which laser emission has been experimentally observed. We also calculate the binding energy of the ground state exciton and the confinement energy of the 1D quantum-wire-exciton state with respect to the 2D quantum-well exciton for a wide range of structures, varying the well width and the Al molar fraction $x$. We find that the largest binding energy of any wire constructed to date is 16.5 meV. We also notice that in asymmetric structures, the confinement energy is enhanced with respect to the symmetric forms with comparable parameters but the binding energy of the exciton is then lower than in the symmetric structures. For GaAs/Al$_{x}$Ga$_{1-x}$As wires we obtain an upper limit for the binding energy of around 25 meV in a 10 {\AA} wide GaAs/AlAs structure which suggests that other materials must be explored in order to achieve room temperature applications. There are some indications that In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As might be a good candidate.Comment: 20 pages, 10 figures, uses RevTeX and psfig, submitted to Physical Review

Properties of the signal mode in the polariton optical parametric oscillator regime

Theoretical analyses of the polariton optical parametric oscillator (OPO) regime often rely on a mean-field approach based on the complex Gross-Pitaevskii equations in a three-mode approximation, where only three momentum states, the signal, pump, and idler, are assumed to be significantly occupied. This approximation, however, lacks a constraint to uniquely determine the signal and idler momenta. In contrast, multimode numerical simulations and experiments show a unique momentum structure for the OPO states. In this work we show that an estimate for the signal momentum chosen by the system can be found from a simple analysis of the pump-only configuration. We use this estimate to investigate how the chosen signal momentum depends on the properties of the drive

Semiconductor nanostructures engineering: Pyramidal quantum dots

Pyramidal quantum dots (QDs) grown in inverted recesses have demonstrated over the years an extraordinary uniformity, high spectral purity and strong design versatility. We discuss recent results, also in view of the Stranski-Krastanow competition and give evidence for strong perspectives in quantum information applications for this system. We examine the possibility of generating entangled and indistinguishable photons, together with the need for the implementation of a, regrettably still missing, strategy for electrical control

Many-body physics of a quantum fluid of exciton-polaritons in a semiconductor microcavity

Some recent results concerning nonlinear optics in semiconductor microcavities are reviewed from the point of view of the many-body physics of an interacting photon gas. Analogies with systems of cold atoms at thermal equilibrium are drawn, and the peculiar behaviours due to the non-equilibrium regime pointed out. The richness of the predicted behaviours shows the potentialities of optical systems for the study of the physics of quantum fluids.Comment: Proceedings of QFS2006 conference to appear on JLT

Dynamical Critical Exponents in Driven-Dissipative Quantum Systems

We study the phase ordering of parametrically and incoherently driven microcavity polaritons after an infinitely rapid quench across the critical region. We confirm that the system, despite its driven-dissipative nature, satisfies the dynamical scaling hypothesis for both driving schemes by exhibiting self-similar patterns for the two-point correlator at late times of the phase ordering. We show that polaritons are characterized by the dynamical critical exponent z ≈ 2 with topological defects playing a fundamental role in the dynamics, giving logarithmic corrections both to the power-law decay of the number of vortices and to the associated growth of the characteristic length scale

Keldysh Green's function approach to coherence in a non-equilibrium steady state: connecting Bose-Einstein condensation and lasing

Solid state quantum condensates often differ from previous examples of condensates (such as Helium, ultra-cold atomic gases, and superconductors) in that the quasiparticles condensing have relatively short lifetimes, and so as for lasers, external pumping is required to maintain a steady state. On the other hand, compared to lasers, the quasiparticles are generally more strongly interacting, and therefore better able to thermalise. This leads to questions of how to describe such non-equilibrium condensates, and their relation to equilibrium condensates and lasers. This chapter discusses in detail how the non-equilibrium Green's function approach can be applied to the description of such a non-equilibrium condensate, in particular, a system of microcavity polaritons, driven out of equilibrium by coupling to multiple baths. By considering the steady states, and fluctuations about them, it is possible to provide a description that relates both to equilibrium condensation and to lasing, while at the same time, making clear the differences from simple lasers