56236670
Collective branch in the continuum of BCS superconductors and superfluid Fermi gases
We demonstrate the existence of a collective excitation branch in the pair-breaking continuum of superfluid Fermi gases and BCS superconductors, as suggested by Littlewood and Varma in 1982. We analytically continue the RPA equation on the collective mode energy through its branch cut associated with the continuum, and obtain the full complex dispersion relation, including in the strong coupling regime. For ∆/μ > 1.210 (very close to unitarity in a superfluid Fermi gas), where ∆ is the order parameter and μ the chemical potential, the real part of the branch is wholly within the band gap [0, 2∆]. In the long wavelength limit, the branch varies quadratically with the wave number, with a complex effective mass that we compute analytically. This contradicts the result of Littlewood and Varma that prevailed so far.
7357447
Evolution from BCS superconductivity to Bose condensation: analytic results for the crossover in three dimensions
Abstract:We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution.
117753615
Collective mode of homogeneous superfluid Fermi gases in the BEC-BCS crossover (14 pages)
We perform a detailed study of the collective mode across the whole crossover from the Bose-Einstein condensate (BEC)-to the BCS regime in fermionic gases at zero temperature, covering the whole range of energy beyond the linear regime. This is done on the basis of the dynamical BCS model. We recover first the results of the linear regime in a simple form. Then specific attention is paid to the nonlinear part of the dispersion relation and its interplay with the continuum of single-fermionic excitations. In particular we consider in detail the merging of the collective mode into the continuum of single-fermionic excitations. This occurs not only on the BCS side of the crossover, but also slightly beyond unitarity on the BEC side. Another remarkable feature is the very linear behavior of the dispersion relation in the vicinity of unitarity almost up to merging with the continuum. Finally, while on the BEC side the mode is quite analogous to the Bogoliubov mode, a difference appears at high wave vectors. On the basis of our results we determine the Landau critical velocity in the BEC-BCS crossover which is found to be largest close to unitarity. Our investigation has revealed interesting qualitative features whichmore » deserve experimental exploration as well as further theoretical studies by more sophisticated means.« less
2065522
Measurement of Sound Velocity in a Fermi Gas near a Feshbach Resonance
Sound waves are excited in an optically trapped degenerate Fermi gas of spin-up and spin-down atoms with magnetically tunable interactions. Measurements are made throughout the crossover region, from a weakly interacting Fermi gas through the resonant Fermi superfluid regime to a Bose condensate of dimer molecules. The measured sound velocities test theories of hydrodynamic wave propagation and predictions of the equation of state. At resonance, the sound velocity exhibits universal scaling with the Fermi velocity, to within 1.8% over a factor of 30 in density.
59392755
Goldstone mode and pair-breaking excitations in atomic Fermi superfluids
Bragg spectroscopy shows the evolution of gapless Goldstone modes and single-particle-like excitations in an atomic Fermi superfluid as it crosses from a Bardeen–Cooper–Schrieffer superfluid to the Bose–Einstein condensate regime.
118416648
Amplitude/Higgs Modes in Condensed Matter Physics
The order parameter and its variations in space and time in many different states in condensed matter physics at low temperatures are described by the complex function Ψ(r, t). These states include superfluids, superconductors, and a subclass of antiferromagnets and charge density waves. The collective fluctuations in the ordered state may then be categorized as oscillations of phase and amplitude of Ψ(r, t). The phase oscillations are the Goldstone modes of the broken continuous symmetry. The amplitude modes, even at long wavelengths, are well defined and are decoupled from the phase oscillations only near particle-hole symmetry, where the equations of motion have an effective Lorentz symmetry, as in particle physics and if there are no significant avenues for decay into other excitations. They bear close correspondence with the so-called Higgs modes in particle physics, whose prediction and discovery are very important for the standard model of particle physics. In this review, we discuss the theory and...
122034880
Amplitude collective modes in superconductors and their coupling to charge-density waves
At low temperature the long-wavelength perturbations of the amplitude of the superconducting gap propagate as an undamped collective mode with a finite frequency. The dispersion and damping of this mode are calculated. The phase or the Bogoliubov modes of a superconductor are strongly affected by Coulomb interactions and rendered indistinguishable from plasmons. By contrast, the amplitude modes are shown not to perturb the charge density thus remaining unaffected by the Coulomb interactions. Under certain conditions long-wavelength phonons couple to this mode. This coupling is derived and the observation of the amplitude mode through Raman scattering experiments in the charge-density-wave compound Nb${\mathrm{Se}}_{2}$ are quantitatively explained.
41186207
Nonequilibrium dynamics of weakly and strongly paired superconductors.
We study small oscillations of the order parameter in weakly and strongly paired superconductors driven slightly out of equilibrium, in the collisionless approximation. While it was known for quite some time that the amplitude of the oscillations in a weakly paired superconductor decays as t(-1/2), we show that in a superconductor sufficiently strongly paired so that its fermions form bound states usually referred to as molecules, these oscillations decay as t(-3/2). The transition between these two regimes happens when the chemical potential of the superconductor vanishes; thus, the behavior of the oscillations can be used to distinguish weakly and strongly paired superconductors. Finally, we interpret the result in the strongly paired superconductor as the probability of the molecular decay as a function of time.
16966822
Direct observation of Higgs mode oscillations in the pump-probe photoemission spectra of electron-phonon mediated superconductors
Using the non-equilibrium Keldysh formalism, we solve the equations of motion for electron-phonon superconductivity, including an ultrafast pump field. We present results for time-dependent photoemission spectra out of equilibrium which probes the dynamics of the superconducting gap edge. The partial melting of the order by the pump field leads to oscillations at twice the melted gap frequency, a hallmark of the Higgs or amplitude mode. Thus the Higgs mode can be directly excited through the nonlinear effects of an electromagnetic field and detected without any additional symmetry breaking.
119411257
Absorption and emission of a collective excitation by a fermionic quasiparticle in a Fermi superfluid
We study the process of absorption or emission of a bosonic collective excitation by a fermionic quasiparticle in a superfluid of paired fermions. From the RPA equation of motion of the bosonic excitation annihilation operator, we obtain an expression of the coupling amplitude of this process which is limited neither to resonant processes nor to the long wavelength limit. We confirm our result by independently deriving it in the functional integral approach using the gaussian fluctuation approximation, and by comparing it in the long wavelength limit to the quantum hydrodynamic result. Last, we give a straightforward application of the coupling amplitude we obtain by calculating the lifetime of the bosonic excitations of arbitrary wave number. We find a mode quality factor that decreases from its maximum at low wave numbers and vanishes when the bosonic branch hits the pair-breaking continuum.
118877051
Low-energy modes of spin-imbalanced Fermi gases in BCS phase
Abstract
The low-energy modes of a spin-imbalanced superfluid Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) side are studied. The gas is assumed to be sufficiently dilute so that the pairing of atoms can be considered effective only in s-wave between fermions of different internal state. The order parameter at equilibrium is determined by the mean-field approximation, while the properties of the collective modes are calculated within a Gaussian approximation for the fluctuations of the order parameter. In particular we investigate the effects of asymmetry between the populations of the two different components and of temperature on the frequency and damping of collective modes. It is found that the temperature does not much affect the frequency and the damping of the modes, whereas an increase of the imbalance shifts the frequency toward lower values and enhances the damping sensitively. Besides the Bogoliubov-Anderson phonons, we observe modes at zero frequency for finite values of the wave-number. These modes indicate that an instability develops driving the system toward two separate phases, normal and superfluid.
Graphical abstract