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arXiv:1502.00431 · Physical Review A

Evolution of the Higgs mode in a fermion superfluid with tunable interactions

Boyang Liu, Hui Zhai, Shizhong Zhang

Published Mar 23, 2016• 22 citations
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Abstract

In this work we present a coherent picture for the evolution of Higgs mode in neutral $s$-wave fermion superfluids. As the strength of attractive interaction between fermions increases from the BCS to the Bose-Einstein condensate (BEC) regime we find that the Higgs mode in the fermionic superfluids is pushed to higher energy while at the same time, gradually loses its spectral weight, which is because the system is tuned away from Lorentz invariance. Furthermore, when damping is taken into account, the spectral weight of the Higgs mode is significantly broadened due to coupling to phase mode in the whole BEC-BCS crossover.

DOI
10.1103/physreva.93.033641

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In this work we present a coherent picture for the evolution of Higgs mode in neutral sss-wave fermion superfluids. As the strength of attractive interaction between fermions increases from the BCS to the Bose-Einstein condensate (BEC) regime we find that the Higgs mode in the fermionic superfluids is pushed to higher energy while at the same time, gradually loses its spectral weight, which is because the system is tuned away from Lorentz invariance. Furthermore, when damping is taken into account, the spectral weight of the Higgs mode is significantly broadened due to coupling to phase mode in the whole BEC-BCS crossover.
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.
We study the observability of the Higgs mode in BEC-BCS crossover. The observability of the Higgs mode is investigated by calculating the spectral weight functions of the amplitude fluctuation below the critical transition temperature. At zero temperature, we find that there are two sharp peaks on the spectral function of the amplitude fluctuation attributed to Goldstone and Higgs modes, respectively. As the system goes from the BCS to Bose-Einstein condensate (BEC) side, there is strong enhancement of spectral weight transfer from the Higgs to Goldstone mode. However, even at the unitary regime where the Lorentz invariance is lost, the sharp feature of the Higgs mode still exists. We specifically calculate the finite-temperature spectral function of the amplitude fluctuation at the unitary regime and show that the Higgs mode is observable at the temperature that present experiments can reach.
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 the dynamical behavior of large-amplitude collective modes in a superfluid Fermi gas in the crossover from Bardeen--Cooper--Schrieffer (BCS) superfluid to Bose--Einstein condensate (BEC) based on a hydrodynamic approach. We first solve the superfluid hydrodynamic equations that describe the time evolution of fermionic condensates in the BCS-BEC crossover and calculate explicitly the frequency shifts of the collective modes induced by nonlinear effects using the Lindstedt--Poincar\'e method. The result shows that the frequency shifts display different features in different superfluid regimes. We then study the second-harmonic generation of the collective modes under a phase-matching condition, which can be fulfilled by choosing appropriate parameters of the system. The analytical results obtained are checked by numerical simulations and good agreement is found.
Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the amplitude (Higgs) susceptibility in the lower half plane of complex frequency. We analyze the behavior of the Higgs mode in a two-dimensional neutral fermionic superfluid at T=0T=0T=0 throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. This occurs when the dressed chemical potential $\ensuremath{\mu}$ changes sign from positive to negative. For $\ensuremath{\mu}>0$, we find a pole in the Higgs susceptibility in the lower half plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For $\ensuremath{\mu}<0$, the pole still exists but is ``hidden,'' not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.
We propose that the evolution of superfluidity from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime can be realized using ultracold Fermi gas coupled to a single-mode cavity. By the functional integral formalism, we derive an effective atom-only action, which mimics the two-component Fermi gas with tunable two-body interaction. First, we address the features of the cavity-mediated interaction. We find that the matter-light coupling creates an effective sss-wave scattering whose sign and amplitude are controlled by parameters of the cavity. Second, we discuss the fermionic superfluidity on the mean-field level, including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, and dissociation temperature. It is shown that by varying the atom-cavity detuning, a BCS to BEC crossover occurs. In addition, the influences of the atomic collaborative effect and external pumping field on the pairing correlation are also studied.