Thermal blurring of a coherent Fermi gas

It is generally assumed that a condensate of paired fermions at equilibrium is characterized by a macroscopic wavefunction with a well-defined, immutable phase. In reality, all systems have a finite size and are prepared at non-zero temperature; the condensate has then a finite coherence time, even when the system is isolated in its evolution and the particle number $N$ is fixed. The loss of phase memory is due to interactions of the condensate with the excited modes that constitute a dephasing environment. This fundamental effect, crucial for applications using the condensate of pairs macroscopic coherence, was scarcely studied. We link the coherence time to the condensate phase dynamics, and we show with a microscopic theory that the time derivative of the condensate phase operator $hat{theta}_0$ is proportional to a chemical potential operator that we construct including both the pair-breaking and pair-motion excitation branches. In a single realization of energy $E$, $hat{theta}_0$ evolves at long times as $-2mu_{rm mc}(E)t/hbar$ where $mu_{rm mc}(E)$ is the microcanonical chemical potential; energy fluctuations from one realization to the other then lead to a ballistic spreading of the phase and to a Gaussian decay of the temporal coherence function with a characteristic time $propto N^{1/2}$. In the absence of energy fluctuations, the coherence time scales as $N$ due to the diffusive motion of $hat{theta}_0$. We propose a method to measure the coherence time with ultracold atoms, which we predict to be tens of milliseconds for the canonical ensemble unitary Fermi gas.

Energy, decay rate, and effective masses for a moving polaron in a Fermi sea: Explicit results in the weakly attractive limit

We study the properties of an impurity of mass $M$ moving through a spatially homogeneous three-dimensional fully polarized Fermi gas of particles of mass $m$. In the weakly attractive limit, where the effective coupling constant $gto0^-$ and perturbation theory can be used, both for a broad and a narrow Feshbach resonance, we obtain an explicit analytical expression for the complex energy $Delta E(KK)$ of the moving impurity up to order two included in $g$. This also gives access to its longitudinal and transverse effective masses $m_parallel^*(KK)$, $m_perp^*(KK)$, as functions of the impurity wave vector $KK$. Depending on the modulus of $KK$ and on the impurity-to-fermion mass ratio $M/m$ we identify four regions separated by singularities in derivatives with respect to $KK$ of the second-order term of $Delta E(KK)$, and we discuss the physical origin of these regions. Remarkably, the second-order term of $m_parallel^*(KK)$ presents points of non-differentiability, replaced by a logarithmic divergence for $M=m$, when $KK$ is on the Fermi surface of the fermions. We also discuss the third-order contribution and relevance for cold atom experiments.

Photonic band-gap in a realistic atomic diamond lattice: penetration depth, finite-size and vacancy effects

We study the effects of finite size and of vacancies on the photonic band gap recently predicted for an atomic diamond lattice. Close to a $J_g=0to J_e=1$ atomic transition, and for atomic lattices containing up to $Napprox 3times10^4$ atoms, we show how the density of states can be affected by both the shape of the system and the possible presence of a fraction of unoccupied lattice sites. We numerically predict and theoretically explain the presence of shape-induced border states and of vacancy-induced localized states appearing in the gap. We also investigate the penetration depth of the electromagnetic field which we compare to the case of an infinite system.

Trimers in the resonant 2+1 fermionic problem on a narrow Feshbach resonance : Crossover from Efimovian to Hydrogenoid spectrum

We study the quantum three-body free space problem of two same-spin-state fermions of mass $m$ interacting with a different particle of mass $M$, on an infinitely narrow Feshbach resonance with infinite s-wave scattering length. This problem is made interesting by the existence of a tunable parameter, the mass ratio $alpha=m/M$. By a combination of analytical and numerical techniques, we obtain a detailed picture of the spectrum of three-body bound states, within {sl each} sector of fixed total angular momentum $l$. For $alpha$ increasing from 0, we find that the trimer states first appear at the $l$-dependent Efimovian threshold $alpha_c^{(l)}$, where the Efimov exponent $s$ vanishes, and that the {sl entire} trimer spectrum (starting from the ground trimer state) is geometric for $alpha$ tending to $alpha_c^{(l)}$ from above, with a global energy scale that has a finite and non-zero limit. For further increasing values of $alpha$, the least bound trimer states still form a geometric spectrum, with an energy ratio $exp(2pi/|s|)$ that becomes closer and closer to unity, but the most bound trimer states deviate more and more from that geometric spectrum and eventually form a hydrogenoid spectrum.