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Cambridge University Press eBooks

Extension to Superfluid Fermi Systems

Giancarlo Calvanese Strinati

Published Feb 6, 2026• 0 citations
Publisher

Abstract

The effects of the coupling to the environment can also manifest itself in a superfluid Fermi system. This chapter explicitly considers this case, by addressing the time-dependent behavior of the gap parameter following a sharp quench of the coupling parameter of the contact interaction. In this case, coupling the system to the environment is important for reaching equilibrium eventually. Several simplifying assumptions are adopted along the way for treating the problem in an as simple as possible way.

DOI
10.1017/9781009411509.037

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The effects of the coupling to the environment can also manifest itself in a superfluid Fermi system. This chapter explicitly considers this case, by addressing the time-dependent behavior of the gap parameter following a sharp quench of the coupling parameter of the contact interaction. In this case, coupling the system to the environment is important for reaching equilibrium eventually. Several simplifying assumptions are adopted along the way for treating the problem in an as simple as possible way.
In summary, in this Chapter we have given a brief overview on the dynamical properties of a trapped Fermi gas, both in the collisionless and in the collisional regime. While in a one-component system interactions are negligible (and nevertheless the system presents a rich spectrum), in the two-component case they can influence in a relevant way the equilibrium state and the dispersion relation. We have described mainly the case of a normal fluid, but we have pointed out that the long-wavelength behavior of a superfluid can be described in terms of the properties of the normal fluid in the collisional regime.
In the preceding chapters we have solved a number of specific problems in which electromagnetic fields interact with charges, atoms, or molecules, and these have been approached in several different ways. For example, for the problem of photoelectric detection, which involves short interaction times, we found it convenient to use a perturbative method, whereas the resonance fluorescence problem was treated by solving the Heisenberg equations of motion. In the following sections we shall encounter a number of general methods for tackling interaction problems that can often simplify the problems substantially when they are applicable. We shall illustrate the utility of these methods by recalculating a number of results that were obtained in a different manner before. The quantum regression theorem It was shown by Lax (1963; see also Louisell, 1973, Sec. 6.6) that, with the help of a certain factorization assumption, it is often possible to express multi-time correlation functions of certain quantum mechanical operators in terms of single-time expectations. The result is now known as the regression theorem . As multi-time correlation functions play a rather important role in quantum optics, the theorem is often of great utility, and it can drastically simplify certain calculations. In the following we largely adopt the procedure given by Lax. We consider two coupled quantum systems, to which, for the sake of convenience, we shall refer as the system ( S ) and the reservoir ( R ).
A new field of research, which gained interest in the past years, is the field of non- equilibrium physics of strongly interacting fermionic systems. In this thesis we present a novel apparatus to study an ultracold strongly interacting superfluid Fermi gas driven out of equilibrium. In more detail, we study the excitation of a collective mode, the Higgs mode, and the dynamics occurring after a rapid quench of the interaction strength. Ultracold gases are ideal candidates to explore the physics of strongly interacting Fermi gases due to their purity and the possibility to continuously change many different system parameters, such as the interaction strength. The novel apparatus enabling the experiments outlined below is built from scratch. The setup is described and characterized in detail. We produce a fermionic superfluid of 4 × 10^6 6Li atoms at a temperature of T/T_F = 0.07 ± 0.02, where T_F is the Fermi temperature. This is achieved within 23 s by a combination of laser cooling, radio frequency evaporation of 23Na and simultaneous sympathetic cooling of 6Li in an optical plugged magnetic trap and subsequent evaporative cooling of 6Li in a dipole trap. In this thesis we provide the first experimental evidence of the Higgs mode in a strongly interacting Fermi gas in the crossover from a BCS superfluid to a molecular Bose-Einstein condensate. We develop a novel excitation method, which directly couples to the amplitude of the order parameter. This is achieved by continuously changing the population of one spin component by driving a radio frequency transition to a previously unoccupied third hyperfine state. This effectively modulates the interaction strength and the amplitude of the order parameter. We spectroscopically observe a resonance behavior at twice the gap frequency. For strong coupling, the peak width broadens and eventually the Higgs mode disappears when the Cooper pairs turn into tightly bound dimers signaling the instability of the Higgs mode. It has been suggested that the Higgs mode frequency is a precise measure of the superconducting gap in the BEC-BCS crossover, where the exact value of the gap is yet unknown and numerical calculations are challenging. Hence, our novel method provides a unique technique to determine the superconducting gap. Moreover, we perform rapid variations of the interaction parameter and vary both the initial interaction strength and the amplitude of the quench. The rapid quenches are performed by rapidly transferring one spin component of a two-component spin mixture into a third state with a different interaction strength by using a radio frequency transition. Using this novel method, we can perform the quenches in half the Fermi time, which is experimentally very close to a sudden change and to date faster than any other research group performing interaction quenches with ultra cold gases. In the experiment, we observe a fast relaxation to a zero order parameter for large quenches, whereas for small quenches we observe, after a sudden drop, a revival of the order parameter and equilibration to a long-term superfluid steady state. Our measurement provides the first evidence of the collapse and subsequent revival of order in a strongly interacting fermionic system.