We consider a weakly interacting two-component Fermi gas of dipolar particles (magnetic atoms or polar molecules) in the two-dimensional geometry. The dipole-dipole interaction (together with the short-range interaction at Feshbach resonances) for di
poles perpendicular to the plane of translational motion may provide a superfluid transition. The dipole-dipole scattering amplitude is momentum dependent, which violates the Anderson theorem claiming the independence of the transition temperature on the presence of weak disorder. We have shown that the disorder can strongly increase the critical temperature (up to 10 nK at realistic densities). This opens wide possibilities for the studies of the superfluid regime in weakly interacting Fermi gases, which was not observed so far.
We report the results of the numerical study of the non-dissipative quantum Josephson junction chain with the focus on the statistics of many-body wave functions and local energy spectra. The disorder in this chain is due to the random offset charges
. This chain is one of the simplest physical systems to study many-body localization. We show that the system may exhibit three distinct regimes: insulating, characterized by the full localization of many-body wavefunctions, fully delocalized (metallic) one characterized by the wavefunctions that take all the available phase volume and the intermediate regime in which the volume taken by the wavefunction scales as a non-trivial power of the full Hilbert space volume. In the intermediate, non-ergodic regime the Thouless conductance (generalized to many-body problem) does not change as a function of the chain length indicating a failure of the conventional single-parameter scaling theory of localization transition. The local spectra in this regime display the fractal structure in the energy space which is related with the fractal structure of wave functions in the Hilbert space. A simple theory of fractality of local spectra is proposed and a new scaling relationship between fractal dimensions in the Hilbert and energy space is suggested and numerically tested.
We consider disordered tight-binding models which Greens functions obey the self-consistent cavity equations . Based on these equations and the replica representation, we derive an analytical expression for the fractal dimension D_{1} that distinguis
hes between the extended ergodic, D_{1}=1, and extended non-ergodic (multifractal), 0<D_{1}<1 states. The latter corresponds to the solution with broken replica symmetry, while the former corresponds to the replica-symmetric solution. We prove the existence of the extended non-ergodic phase in a broad range of disorder strength and energy as well as existence of transition between the two extended phases. The results are applied to the systems with local tree structure (Bethe lattices) and to the systems with infinite connectivity (Rosenzweig-Poter random matrix theory). We obtain the phase diagram in the disorder-energy plain for the Bethe lattice and identify two insulating phases classified by the (one-step) replica symmetry breaking parameter. Finally we express the line of the Anderson localization transition, the stability limit of the non-ergodic extended phase and the line of the first order transitions between the two extended phases in terms of the Lyapunov exponents.
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 d
emonstrate 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 domai
n 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 c
ontrast 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.
Recent experiments by F. Yoshihara et al. [Phys. Rev. Lett. 97, 167001 (2006)] and by K. Kakuyanagi et al. (cond-mat/0609564) provided information on decoherence of the echo signal in Josephson-junction flux qubits at various bias conditions. These r
esults were interpreted assuming a Gaussian model for the decoherence due to 1/f noise. Here we revisit this problem on the basis of the exactly solvable spin-fluctuator model reproducing detailed properties of the 1/f noise interacting with a qubit. We consider the time dependence of the echo signal and conclude that the results based on the Gaussian assumption need essential reconsideration.
We obtained the analog of the Luttinger relation for a commensurate spin-density-wave state. We show that while the relation between the area of the occupied states and the density of particles gets modified in a simple and predictable way when the s
ystem becomes ordered, a perturbative consideration of the Luttinger theorem does not work due to the presence of an anomaly similar to the chiral anomaly in quantum electrodynamics.
