Equilibrium to nonequilibrium condensation in driven-dissipative semiconductor systems

Semiconductor microcavity systems strongly coupled to quantum wells are now receiving a great deal of attention because of their ability to efficiently generate coherent light by the Bose-Einstein condensation (BEC) of an exciton-polariton gas. Since the exciton polaritons are composite quasi-bosonic particles, many fundamental features arise from their original constituents, i.e., electrons, holes and photons. As a result, not only equilibrium phases typified by the BEC but also nonequilibrium lasing phases can be achieved. In this contribution, we describe a framework which can treat such equilibrium and nonequilibrium phases in a unified way.Comment: 19 pages, 7 figures; prepared for the Springer Lecture Notes in Physics "Quantum Computing, Quantum Communication and Quantum Metrology" edited by Yoshihisa Yamamoto and Kouichi Semba. Several typing errors are correcte

Stability of polarizable materials against superradiant phase transition

The possibility of the superradiant phase transition in polarizable materials described by the minimal-coupling Hamiltonian with the longitudinal dipole-dipole interaction is examined. We try to reduce the Hamiltonian into the Dicke one in homogeneous and infinite case, and discuss the stability of normal ground state by the formalism of Green function in spatially inhomogeneous case. The presence of the longitudinal dipole-dipole interaction does not enable the superradiant phase transition, if the transverse and longitudinal fields are decoupled. Although the full dipole-dipole interaction can be eliminated in the electric-dipole gauge in the absence of overlap between individual atomic dipoles, we cannot reduce the Hamiltonian to the Dicke one, because the elimination is justified only if all the transverse and longitudinal fields remain. Even if the transverse and longitudinal fields are mixed in spatially inhomogeneous systems, the normal ground state is still stable if the system does not show the superradiant phase transition in the homogeneous case.Comment: 9 pages, no figur

A recipe for Hamiltonian of system-environment coupling applicable to ultrastrong light-matter interaction regime

When the light interacts with matters in a lossy cavity, in the standard cavity quantum electrodynamics, the dissipation of cavity fields is characterized simply by the strengths of the two couplings: the light-matter interaction and the system-environment coupling through the cavity mirror. However, in the ultrastrong light-matter interaction regime, the dissipation depends also on whether the two couplings are mediated by the electric field or the magnetic one (capacitive or inductive in superconducting circuits). Even if we know correctly the microscopic mechanism (Lagrangian) of the system-environment coupling, the coupling Hamiltonian itself is in principle modified due to the ultrastrong interaction in the cavity. In this paper, we show a recipe for deriving a general expression of the Hamiltonian of the system-environment coupling, which is applicable even in the ultrastrong light-matter interaction regime in the good-cavity and independent-transition limit.Comment: 20 pages, 4 figure

System-environment coupling derived by Maxwell's boundary conditions from weak to ultrastrong light-matter coupling regime

In the standard theory of cavity quantum electrodynamics (QED), coupling between photons inside and outside a cavity (cavity system and photonic reservoir) is given conserving the total number of photons. However, when the cavity photons (ultra)strongly interact with atoms or excitations in matters, the system-reservoir coupling must be determined from a more fundamental viewpoint. Based on the Maxwell's boundary conditions in the QED theory for dielectric media, we derive the quantum Langevin equation and input-output relation, in which the total number of polaritons (not photons) inside the cavity and photons outside is conserved.Comment: 14 pages, 2 figure

Reply to Comment on "System-environment coupling derived by Maxwell's boundary conditions from the weak to the ultrastrong light-matter-coupling regime"

As mentioned by Simone De Liberato [arXiv:1307.5615], when we suppose the metallic thin mirror and perform the renormalization additionally to the approach starting from the frequently-used system-environment coupling Hamiltonian, we can certainly resolve the discrepancy of its result from that obtained by the reliable approach in the main discussion of our paper [Phys. Rev. A 88, 013814 (2013), arXiv:1301.3960]. Although the suggested approach is currently applicable to the specific situation after checking its validity by our reliable but cumbersome approach, we instead propose to start from the system-environment coupling Hamiltonian determined properly by the mechanism of the confinement and loss of the cavity fields. This approach is applicable to any cavity structures in principle, and we do not face the renormalization problem appearing in the comment.Comment: Reply to arXiv:1307.5615 by Simone De Liberato on Phys. Rev. A 88, 013814 (2013) [arXiv:1301.3960

What Determines the Wave Function of Electron-Hole Pairs in Polariton Condensates?

The ground state of a microcavity polariton Bose-Einstein condensate is determined by considering experimentally tunable parameters such as excitation density, detuning, and ultraviolet cutoff. During a change in the ground state of Bose-Einstein condensate from excitonic to photonic, which occurs as increasing the excitation density, the origin of the binding force of electron-hole pairs changes from Coulomb to photon-mediated interactions. The change in the origin gives rise to the strongly bound pairs with a small radius, like Frenkel excitons, in the photonic regime. The change in the ground state can be a crossover or a first-order transition, depending on the above-mentionsed parameters, and is outlined by a phase diagram. Our result provides valuable information that can be used to build theoretical models for each regime.Comment: 4 pages, 4 figure

Markovian Quantum Master Equation beyond Adiabatic Regime

By introducing a temporal change timescale $\tau_{\text{A}}(t)$ for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if $\tau_{\text{A}}(t)$ is faster than the decay timescale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.Comment: 12+4 pages, 4 figure

First-order superfluid-Mott-insulator transition for quantum optical switching in cavity QED arrays with two cavity modes

We theoretically investigated the ground states of coupled arrays of cavity quantum electrodynamical (cavity QED) systems in presence of two photon modes. Within the Gutzwiller-type variational approach, we found the first-order quantum phase transition between Mott insulating and superfluid phases as well as the conventional second-order one. The first-order phase transition was found only for specific types of emitter models, and its physical origin is clarified based on the analytic arguments which are allowed in the perturbative and semiclassical limits. The first-order transition of the correlated photons is accompanied with discontinuous change in the emitter states, not only with the appearance of inter-cavity coherence in the superfluid phase. We also discuss the condition for the first-order transition to occur, which can lead to a strategy for future design of quantum optical switching devices with cavity QED arrays.Comment: 11 pages, 11 figures (corrected typos, added references, added discussions in section 2, results unchanged.

Cavity-loss induced plateau in coupled cavity QED array

Nonequilibrium steady states are investigated in a coupled cavity QED array system which is pumped by a thermal bath and dissipated through cavity loss. In the coherent (non-zero photon amplitude) phase, plateau regions appear, where the steady states become unchanged against the variation of the chemical potential of the thermal bath. The cavity loss plays a crucial role for the plateaus: the plateaus appear only if the cavity loss exists, and the photon leakage current, which is induced by the loss, is essential to the mechanism of the plateaus.Comment: 5+1 pages, 3+1 figure

Laser under ultrastrong electromagnetic interaction with matter

The conventional picture of the light amplification by stimulated emission of radiation (laser) is broken under the ultrastrong interaction between the electromagnetic fields and matter, and distinct dynamics of the electric field and of the magnetic one make the "laser" qualitatively different from the conventional laser, which has been described simply without the distinction. The "laser" in the ultrastrong regime can show a rich variety of behaviors with spontaneous appearance of coherence. We found that the "laser" generally accompanies odd-order harmonics of the electromagnetic fields both inside and outside the cavity and a synchronization with an oscillation of atomic population. A bistability is also demonstrated in a simple model under two-level and single-mode approximations.Comment: 12 pages, 7 figure