Keldysh field theory for nonequilibrium condensation in a parametrically pumped polariton system

Abstract

We develop a quantum field theory for parametrically pumped polaritons using Keldysh Green's function techniques with which the occupations of the excitation spectra can be calculated. By considering the mean field and Gaussian fluctuations, we find that the highly nonequilibrium phase transition to the optical parametric oscillator regime is in some ways similar to equilibrium condensation. In particular, we show that this phase transition can be associated with an effective chemical potential, at which the system's bosonic distribution function diverges, and an effective temperature for low energy modes. As in equilibrium systems, the transition is achieved by tuning this effective chemical potential to the energy of the lowest normal mode. Since the nonequilibrium occupations of the modes are available, we determine experimentally observable properties such as the luminescence and absorption spectra.

Cavity Higgs polaritons

“…Condensation could be potentially realized by the now standard optical parametric oscillation technique, wherein the non-linearity of of the lower polariton branch allows pairs of excitations near the inflection point of the dispersion to decay into a higher energy idler excitation and a near zero momentum signal excitation, as has been used to great effect in the experimental realization of exciton-polariton condensation [35,36]. Thus, sufficiently strong driving of the modes near the inflection point should allow for incoherent population of the small momentum states at the minimum of the dispersion, giving the opportunity for condensation without externally imposed coherence.…”

Emergent finite frequency criticality of driven-dissipative correlated lattice bosons

“…(10). In particular, as we show in the top panel of figure 4, the critical frequency is set by the local occupancy, rather than by the strenght of the order parameter as for the oscillations of weakly interacting non-equilibrium superfluids 37 , a fact which highlights the quantum nature of the incoherent phase becoming unstable at Ω * .…”

Tuning across Universalities with a Driven Open Condensate

“…1. The Keldysh part of the inverse Green's function, [D −1 0 ] K j = i2γ j , stems from integrating out the bosonic decay bath fields in the Markovian approximation [35]. X j ≡ X(k j ) is the excitonic Hopfield coefficient of the mode j with momentum k j [29], and g X is the strength of the exciton-exciton interaction.…”