Equilibrium to Nonequilibrium Condensation in Driven-Dissipative Semiconductor Systems

Abstract

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 quasibosonic 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.

Generating functional approach for spontaneous coherence in semiconductor electron-hole-photon systems

“…This means that the dynamics of certain physical quantities is captured on a rotating frame with a frequency µ for time-dependent problems, while a grand canonical ensemble can be considered with a chemical potential µ if the system is identified as being in (quasi-)equilibrium phases. 94 As a result,…”

“…In the mean-field approximation, certain operatorsÔ i (i = 1, 2, · · · ) are described byÔ i = Ô i + δÔ i and the quadratic terms δÔ i δÔ j are neglected in the Hamiltonians. By takingÔ i ∈ {â k ,ĉ † 2,kĉ 1,k ,ĉ † 1,kĉ 1,k ,ĉ † 2,kĉ 2,k }, with definitions â k ≡ δ k,0 a 0 , ĉ † 2,kĉ 1,k ≡ δ k,k p k , and ĉ † α,kĉ α,k ≡ δ k,k n α,k , we obtain the mean-field Hamil- Here, ∆ k ≡ g * a 0 + k U k −k p k is the generalized Rabi frequency describing the effect of forming the e-h pairs 65,94,101 andξ α,k ≡ ξ α,k + Σ BGR α,k denotes the singleparticle energy renormalized by the Coulomb interaction Σ BGR α,k ≡ − k U k −k n α,k , which includes the bandgap renormalization (BGR) in semiconductor physics. In Eq.…”

“…Although we will postpone our theoretical treatment and derivation to Sections V and VI for clarity, we alternatively show here that our formalism is appropriate to discuss the cooperative phenomena, such as the BEC, BCS, LASER, SR and SF, in a unified way. Then, as important examples, we study the BEC-BCS-LASER crossover in the excitonpolariton systems [56][57][58][59][60][61][62][63][64][65]77,94 and the connections between the Fermi-edge SF 33 and the e-h BCS phase with several numerical calculations.…”

“…57,59,[62][63][64] However, we note that the e-h pair breaking energy is reduced by the crossover into the lasing phase, as shown in Figure 5(f); dotted and solid lines. Such a "lasing gap" has not been observed experimentally but, at least in principle, can be measured in the optical gain spectrum because it is strongly affected by the renormalized band structure in general; 65,94 the details will be discussed later (Section IV).…”

“…Here, we will give detailed insights to the BEC-BCS-LASER crossover. 65,77,94 We then discuss the connections between the Fermi-edge SF and the e-h BCS phases, the theoretical study of which has been impossible before. In Section IV, we shortly explain our formalism to calculate the emission spectrum and the gain-absorption spectrum, and then, present several numerical results.…”