We propose a Bragg spectroscopy experiment to measure the onset of superfluid pairing in ultracold trapped Fermi gases. In particular, we study two-component Fermi gases in the weak coupling BCS and Bose Einstein condensation limits as well as in the strong coupling unitarity limit. The low-temperature Bragg spectrum exhibits a gap directly related to the pair-breaking energy. Furthermore, the Bragg spectrum has a large maximum just below the critical temperature when the gas is superfluid in the BCS limit. In the unitarity regime, we show how the pseudogap in the normal phase leads to a significant suppression of the low-frequency Bragg spectrum.
We demonstrate the existence of a collective excitation branch in the pair-breaking continuum of superfluid Fermi gases and BCS superconductors. At zero temperature, we analytically continue the equation on the collective mode energy in Anderson's Random Phase Approximation or Gaussian fluctuations through its branch cut associated with the continuum, and obtain the full complex dispersion relation, including in the strong coupling regime. The branch exists as long as the chemical potential μ is positive and the wave number below sqrt[2mμ]/ℏ (with m the fermion mass). In the long wavelength limit, the branch varies quadratically with the wave number, with a complex effective mass that we compute analytically for an arbitrary interaction strength.
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. Spontaneous symmetry breaking is a central paradigm of elementary particle physics1, magnetism2, superfluidity3 and superconductivity4. According to Goldstone’s theorem, phase transitions that break continuous symmetries lead to the existence of gapless excitations in the long-wavelength limit5. These Goldstone modes can become the dominant low-energy excitation, showing that symmetry breaking has a profound impact on the physical properties of matter. Here, we present a comprehensive study of the elementary excitations in a homogeneous strongly interacting Fermi gas through the crossover from a Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC) of molecules using two-photon Bragg spectroscopy. The spectra exhibit a discrete Goldstone mode, associated with the broken-symmetry superfluid phase, as well as pair-breaking single-particle excitations. Our techniques yield a direct determination of the superfluid pairing gap and speed of sound in close agreement with strong-coupling theories.
Les gaz superfluides de fermions de spin 1 / 2 , condensés par paires, sont censés présenter à vecteur d’onde non nul un mode d’excitation collectif encore inobservé dans leur continuum de paire brisée. À l’aide de la théorie BCS à température nulle et dans la limite des grandes longueurs d’onde, nous prédisons que ce mode est quantitativement observable (en fréquence, largeur et poids spectral) dans la réponse d’un gaz d’atomes froids à une excitation de Bragg par laser, si l’on mesure la perturbation induite sur le module du paramètre d’ordre plutôt que sur la densité.
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
Δ/
μ > 1.210 (very close to unitarity in a superfluid Fermi gas), where
Δ is the order parameter and
μ the chemical potential, the real part of the branch is wholly within the band gap [0, 2
Δ].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.
Studying the collective pairing phenomena in a two-component Fermi gas, we predict the appearance near the transition temperature
Tc of a well-resolved collective mode of quadratic dispersion. The mode is visible both above and below
Tc in the system's response to a driving pairing field. When approaching
Tc from below, the phononic and pair-breaking branches, characteristic of the zero temperature behavior, reduce to a very low energy-momentum region when the pair correlation length reaches its critical divergent behavior
ξpair∝∣Tc−T∣−1/2; elsewhere, they are replaced by the quadratically-dispersed pairing resonance, which thus acts as a precursor of the phase transition. In the strong-coupling and Bose-Einstein Condensate regime, this mode is a weakly-damped propagating mode associated to a Lorentzian resonance. Conversely, in the BCS limit it is a relaxation mode of pure imaginary eigenenergy. At large momenta, the resonance disappears when it is reabsorbed by the lower-edge of the pairing continuum. At intermediate temperatures between 0 and
Tc, we unify the newly found collective phenomena near
Tc with the phononic and pair-breaking branches predicted from previous studies, and we exhaustively classify the roots of the analytically continued dispersion equation, and show that they provided a very good summary of the pair spectral functions.