Abstract
We study the signatures of the collective modes of a superfluid Fermi gas in its linear response functions for the order-parameter and density fluctuations in the Random Phase Approximation (RPA). We show that a resonance associated to the Popov-Andrianov (or sometimes “Higgs”) mode is visible inside the pair-breaking continuum at all values of the wavevector q, not only in the (order-parameter) modulus-modulus response function but also in the modulus-density and density-density responses. At nonzero temperature, the resonance survives in the presence of thermally broken pairs even until the vicinity of the critical temperature Tc, and coexists with both the Anderson-Bogoliubov modes at temperatures comparable to the gap Δ and with the low-velocity phononic mode predicted by RPA near Tc. The existence of a Popov-Andrianov-“Higgs” resonance is thus a robust, generic feature of the high-energy phenomenology of pair-condensed Fermi gases, and should be accessible to state-of-the-art cold atom experiments.
Highlights
A primary way to probe the collective mode spectrum of a many-body system is by measuring the response functions of its macroscopic observables such as its density, or, in the case of a condensed system, its order parameter
There are two major obstacles24,28,35 to the observation of the Popov-Andrianov-“Higgs” resonance in a conventional fermionic condensate. (i) So far the resonance has been clearly identified only in the modulus-modulus response function, whereas experiments usually excite or measure the density of the fermions. (ii) In a conventional fermionic condensate, where the resonance energy is above 2Δ and the resonance broadened by its coupling to the pair-breaking continuum, it is generally not known whether a quality factor and spectral weight large enough to allow for an observation can be reached
At nonzero temperature, where the Random Phase Approximation (RPA) captures the thermal population of the fermionic quasiparticle branches and describes the collective modes in the collisionless approximation, we show that the Popov-Andrianov resonance is not destroyed by the presence of thermally excited fermionic quasiparticles
Summary
A primary way to probe the collective mode spectrum of a many-body system is by measuring the response functions of its macroscopic observables such as its density, or, in the case of a condensed system, its order parameter. In the long wavelength limit (q 2mΔ ) the solutions of the collective mode Eq [40] and the behavior of the response functions can be studied analytically.
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