Piselli, Verdiana (2022) Static and Dynamic coherence Effects in Fermionic Superfluids at finite Temperature. [Tesi di dottorato]

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Subjects of my PhD project are the static and dynamic coherence effects in fermionic superfluids at finite temperature. The most famous example in superconductivity of a coherence effect is probably the DC Josephson effect: The occurrence of a supercurrent through a system composed of two fermionic superfluids coupled via a weak link with no voltage applied. In order to perform a systematic study of the main features of this effect, we have considered a rectangular (or a Gaussian) barrier embedded in an otherwise homogeneous superfluid extending to infinity, with the fermionic coupling kept unmodified under the barrier (SS’S junction). This arrangement is similar to the actual system encountered experimentally with ultra-cold Femi gases and allow us to consider both high and small transparency barriers. We have solved numerically the non-linear differential LPDA (Local Phase Density Approximation) equation for the spatially dependent gap parameter Δ(r) and obtained the Josephson current-vs-phase characteristics in different physical systems, by varying the inter-particle coupling, the height and width of the potential barrier, and the temperature at which the system is kept. The main results of our simulations include, among others, the appearance of a novel kind of Josephson-induced proximity effect for increasing barrier width, the extension of the Landau criterion for superfluidity to finite temperature, and a favorable comparison with the experimental results currently available for ultra-cold Fermi gases. To the extent that the LPDA equation (obtained by a coarse-graining procedure on the BdG equations) represents essentially a mean-field approach to the inhomogeneous problem that we are considering, we are currently going beyond the LPDA approach and developing a procedure that enables us to include pairing fluctuations over and above an inhomogeneous mean-field background. Preliminary results along these lines produce a better agreement with the available experimental data. We have also considered an SNS junction, for which the inter-particle coupling varies from the S to the N region. In this context, our aim was to reproduce the measurements of the critical current for a condensed-matter system (specifically, for a high-Tc superconductor) and to find an analogy between the condensed-matter (SNS) and cold-atoms (SS’S) Josephson junctions. Dynamic perturbations of superconducting systems have become a flourishing research field in recent years. Indeed, the possibility of enhancing superconductivity below the critical temperature Tc, or even inducing it above Tc for a limited amount of time, promises to endless technological applications. Pulse-and-probe experiments, which employ mid- or far-infrared optical pulses to excite high-Tc superconductors by generating transient or meta-stable superconductivity above Tc, have shown that the decay time of the obtained light-induced superconducting state is deeply affected by the pulse duration. Non-equilibrium phenomena have been addressed also in atomic quantum gases, where following a quench of the interaction a crossing of the normal to superfluid phase has been observed. In this context, we are currently solving the time-dependent BdG equations to study the dynamics of a two-component (even imbalanced) Fermi gas in a 1D box following a dynamical perturbation, in order to provide a closer-to-reality perspective of the occurring phenomena with respect to the toy models utilized in the literature thus far. Specifically, we are considering three different scenarios: • We initially separate the two spin-components by means of spin-dependent external potentials and then release them in a given time tR. In this way, we are able to evaluate the equilibration time of the system, provided that equilibration can occur, and the effective temperature at which the system ends up which may be higher than Tc. • We perturb an initially homogeneous system by means of a spin-independent external potential, in order to mimic the pump-and-probe experiments, and observe that the dynamic of the system is deeply affected by the value of the interaction strength of the fermions. • Starting from the equilibrated state provided by one of the previous protocols, we perform a quench of the interaction strength and study the subsequent dynamic. In this scenario (whose implementation is currently under way), we expect to obtain results qualitatively similar to those recently attained experimentally in cold-atom systems.

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