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SciPost Physics

Quenching a Fermi superfluid across the BEC-BCS crossover

Moritz Breyer, D. Eberz, A. Kell, Michael Köhl

Published Feb 14, 2025• 1 citation
Publisher

Abstract

We study the response of a Fermi superfluid to a rapid change of the interaction strength. For a broad range of quench parameters, the order parameter exhibits damped oscillations, however, we also identify quench regimes in which these oscillations are absent. By comparing our data to a numerical model we find that the damping time constants are explainable by a dephasing in a local density approximation, however, the oscillation frequencies, while being comparable to the superconducting order parameter, display in detail significant differences to the integrable BCS (Bardeen-Cooper-Schrieffer) model.

DOI
10.21468/scipostphys.18.2.053

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We study the response of a Fermi superfluid to a rapid change of the interaction strength. For a broad range of quench parameters, the order parameter exhibits damped oscillations, however, we also identify quench regimes in which these oscillations are absent. By comparing our data to a numerical model we find that the damping time constants are explainable by a dephasing in a local density approximation, however, the oscillation frequencies, while being comparable to the superconducting order parameter, display in detail significant differences to the integrable BCS (Bardeen-Cooper-Schrieffer) model.
In quantum many-body systems with spontaneous breaking of continuous symmetries, Higgs modes emerge as collective amplitude oscillations of order parameters. Recently, Higgs mode has been observed in the ultracold Fermi gas. In the present paper, we use the time-dependent Bogoliubov-de Gennes equations to investigate Higgs amplitude oscillations of the superfluid order parameter in a Fermi gas induced by a rapid change of the s{\it s}s-wave scattering length. In particular, we investigate the Higgs mode with different values of the initial scattering length. We find that the energy of the Higgs mode coincides with the threshold energy of the pair-breaking excitation, and exponent of the power-low decay of the Higgs mode γγγ continuously changes between γ=−1/2γ=-1/2γ=−1/2 and γ=−3/2γ=-3/2γ=−3/2 through the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. Moreover, we propose the optimal ramp speed of the scattering length for observing the clearest Higgs oscillations.
The Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover problem is solved for stationary gray solitons via the Boguliubov–de Gennes equations at zero temperature. These crossover solitons exhibit a localized notch in the gap and a characteristic phase difference across the notch for all interaction strengths, from BEC to BCS regimes. However, they do not follow the well-known Josephson-like sinusoidal relationship between velocity and phase difference except in the far BEC limit: at unitarity, the velocity has a nearly linear dependence on phase difference over an extended range. For a fixed phase difference, the soliton is of nearly constant depth from the BEC limit to unitarity and then grows progressively shallower into the BCS limit, and on the BCS side, Friedel oscillations are apparent in both gap amplitude and phase. The crossover soliton appears fundamentally in the gap; we show, however, that the density closely follows the gap, and the soliton is therefore observable. We develop an approximate power-law relationship to express this fact: the density of gray crossover solitons varies as the square of the gap amplitude in the BEC limit and as a power of about 1.5 at unitarity.
We present a study for the collective dipole oscillations of a mixture of Bose and Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in the ENS experimental setup (Ferrier-Barbut et al 2014 Science 345 1035). The dynamics of the double superfluidity is described by coupled time-dependent order-parameter equations, which are Gross–Pitaevskii equations for the Bose superfluid, coupled to the order-parameter equation including the equation of state fitting from the experimental data for the Fermi superfluid in the BCS–BEC crossover. The numerical simulations show that due to the boson–fermion interaction, the frequencies of the dipole oscillations of the Bose and Fermi superfluids are both downshifted and the frequency shifts increase monotonically from the BCS side to BEC side, which are in agreement with the experiment. We further study the dependencies of the frequency shifts on the oscillation amplitudes and the nonlinear effects, in which the Bose and Fermi superfliuds show different features. The frequency shifts of the Bose superfluid increase linearly as the oscillation amplitudes increase, while the frequency shifts of the Fermi superfluid show a quadratical increase. It is found that the intrinsic dipole oscillations of the Bose (Fermi) superfluid can be triggered by only boosting the Fermi (Bose) superfluid.
The Higgs amplitude mode of the order parameter of an ultracold confined Fermi gas in the BCS regime after a quench of the coupling constant is analyzed theoretically. Characteristic features are a damped oscillation which at a certain transition time changes into a rather irregular dynamics. We compare the numerical solution of the full set of nonlinear equations of motion for the normal and anomalous Bogoliubov quasiparticle excitations with a linearized approximation. In doing so the transition time as well as the difference between resonant systems, i.e., systems where the Fermi energy is close to a subband minimum, and off-resonant systems can be well understood and traced back to the system and geometry parameters.
Abstract Motivated by the first experimental realization by the Ecole Normale Supérieure (ENS) group of a mixture of a Bose–Einstein condensate with a Fermi superfluid continuously changing from a Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC) (Ferrier-Barbut et al 2014 Science 345 1035 ), we analytically study the dipole modes of the superfluid Bose–Fermi mixture in the BCS-BEC crossover. The analytical approach can explicitly reveal relationships between the frequencies of the dipole modes and the microscopic properties of the novel system. We start from coupled hydrodynamic equations, where the equation of state for the Fermi superfluid in the crossover is an analytical fitting formula based on experimental data, and by using a scaling approach we analytically study eigenfrequencies of the dipole modes for the coupled system in the ENS experimental parameters. Without the boson–fermion interaction in the equilibrium density profiles, our theoretical results can be reduced to the mean-field model and is consistent with the experimental data. However, by further taking into account the boson–fermion interaction numerically and analytically, we find that the results disagree with the experiment, especially in the parameter regime where the boson interaction is smaller than the boson–fermion interaction.
We investigate dipole oscillations of ultracold Fermi gases along the BEC-BCS crossover through disordered potentials. We observe a disorder-induced damping of oscillations as well as a change of the fundamental Kohn-mode frequency. The measurement results are compared to numerical density matrix renormalization group calculations as well as to a three-dimensional simulation of noninteracting fermions. Experimentally, we find a disorder-dependent damping, which grows approximately with the second power of the disorder strength. Moreover, we observe experimentally a change of oscillation frequency which deviates from the expected behavior of a damped harmonic oscillator on a percent level. While this behavior is qualitatively expected from the theoretical models used, quantitatively the experimental observations show a significantly stronger effect than predicted by theory. Furthermore, while the frequency shift seems to scale differently with interaction strength in the BEC versus BCS regime, the damping coefficient apparently decreases with the strength of interaction, but not with the sign, which changes for BEC- and BCS-type Fermi gases. This is surprising, as the dominant damping mechanisms are expected to be different in the two regimes.