We show that the Bardeen-Cooper-Schrieffer state (BCS) and the Bose-Einstein condensation (BEC) sides of the BCS-BEC crossover can be rigorously distinguished from each other by the extrema of the spectrum of the fermionic excitations. Moreover, we demonstrate that this formal distinction is realized as a non-equilibrium phase transition under radio frequency radiation. The BEC phase remains translationally invariant, whereas the BCS phase transforms into the supersolid phase. For a two-dimensional system this effect occurs at arbitrary small amplitude of the radiation field.
Strictly speaking the laws of the conventional Statistical Physics, based on the Equipartition Postulate and Ergodicity Hypothesis, apply only in the presence of a heat bath. Until recently this restriction was not important for real physical systems: a weak coupling with the bath was believed to be sufficient. However, the progress in both quantum gases and solid state coherent quantum devices demonstrates that the coupling to the bath can be reduced dramatically. To describe such systems properly one should revisit the very foundations of the Statistical Mechanics. We examine this general problem for the case of the Josephson junction chain and show that it displays a novel high temperature non-ergodic phase with finite resistance. With further increase of the temperature the system undergoes a transition to the fully localized state characterized by infinite resistance and exponentially long relaxation.
We predict the spontaneous modulated emission from a pair of exciton-polariton condensates due to coherent (Josephson) and dissipative coupling. We show that strong polariton-polariton inter- action generates complex dynamics in the weak-lasing domain way beyond Hopf bifurcations. As a result, the exciton-polariton condensates exhibit self-induced oscillations and emit an equidistant frequency comb light spectrum. A plethora of possible emission spectra with asymmetric peak dis- tributions appears due to spontaneously broken time-reversal symmetry. The lasing dynamics is affected by the shot noise arising from the influx of polaritons. That results in a complex inhomo- geneous line broadening.
We investigate the stability of spatially uniform solutions for the collisionless dynamics of a fermionic superfluid. We demonstrate that, if the system size is larger than the superfluid coherence length, the solution characterized by a periodic in time order parameter is unstable with respect to spatial fluctuations. The instability is due to the parametric excitations of pairing modes with opposite momenta. The growth of spatial modulations is suppressed by nonlinear effects resulting in a state characterized by a random superposition of wave packets of the superfluid order parameter. We suggest that this state can be probed by spectroscopic noise measurements.
We determine the radio-frequency (RF) spectra for non-stationary states of a fermionic condensate produced by a rapid switch of the scattering length. The RF spectrum of the nonequilibrium state with constant BCS order parameter has two features in contrast to equilibrium where there is a single peak. The additional feature reflects the presence of excited pairs in the steady state. In the state characterized by periodically oscillating order parameter RF-absorption spectrum contains two sequences of peaks spaced by the frequency of oscillations. Satellite peaks appear due to a process where an RF photon in addition to breaking a pair emits/absorbs oscillation quanta.
