Goldstone mode and pair-breaking excitations in atomic Fermi superfluids

Abstract

. According to Goldstone's theorem, phase transitions that break continuous symmetries lead to the existence of gapless excitations in the long-wavelength limit 5 . 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-Schrie er (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.When a Hamiltonian is invariant with respect to a continuous symmetry, but the ground state is not, a massless bosonic mode appears in the spectrum of allowed excitations 5 . At temperatures low enough for quantum effects to become prominent, dynamical behaviours, such as superconductivity and superfluidity, are possible only due to the low-energy excitation spectrum. Superfluid and superconducting states break gauge invariance and the resultant Goldstone mode is an oscillation of the phase of the order parameter giving rise to a collective motion of particles that is distinct from single-particle excitations. In superconductors, the Coulomb interaction lifts the collective mode up to the frequency of the classical plasma oscillation 4 , present in the normal phase, such that the Goldstone mode is generally imperceptible 6 . In neutral superfluids, however, the Goldstone mode takes the form of a gapless phonon 7 and provides a dramatic signature of macroscopic order.Ultracold gases of atomic fermions have enabled the creation and study of high-transition-temperature superfluids in the smooth crossover from the BCS to BEC regimes 8 . Both first-sound 9-11 and second-sound 10 propagation have been observed in inhomogeneous Fermi gases, yet the basic elementary excitation spectrum has not been measured. Here, we present a comprehensive study of the low-temperature excitations in a homogeneous Fermi superfluid throughout the whole BCS-BEC crossover. The spectra exhibit both a dominant Goldstone mode, or Bogoliubov-Anderson (BA) phonon, and a single-particle continuum. Our study reveals how the energy and spectral weight of these excitations evolve as a function of the interaction strength. We develop a theory based on the quasiparticle random-phase approximation (QRPA), which provides a good quantitative description of the data.The starting point for our experiments is a harmonically trapped gas of fermionic 6 Li atoms in a balanced mixture of the lowest two hyperfine states with tunable s-wave interactions near a broad Feshbach resonance (see Supplementary Information). Atoms are cooled to temperatures below the superfluid transition te...

Superfluid Fermi atomic gas as a quantum simulator for the study of the neutron-star equation of state in the low-density region

“…3(a). We again find that the NSR results agree well with the recent experiments [30,31], as well as a Monte Carlo simulation [76]. On the other hand, the BCS-Leggett theory overestimates these quantities.…”

“…In panel (c), "QMC" is the result by Monte Carlo simulation [76]. " 6 Li" shows the experimental result by Bragg spectroscopy [31].…”

“…For example, although similarity between an ultracold Fermi gas loaded on a two-dimensional optical lattice and high-T c cuprates [18] has been pointed out [19], the current experimental achievement is still at the s-wave pairing state in the case of a very shallow three-dimensional optical lattice [20,21] (which cannot be described by the Hubbard model). The recent extensive experimental efforts have enabled us to precisely measure various physical quantities in ultracold gases [22][23][24][25][26][27][28][29][30][31]. Thus, when an ultracold atomic gas works as a quantum simulator for another system, the high tunability, as well as these sophisticated experimental techniques, would contribute to understanding this target system.…”

Dynamic density structure factor of a unitary Fermi gas at finite temperature

“…When the transfer frequency is low enough, the former branch of the continuum becomes quite apparent in the curves denoted by the T T 0.1 c = , T 0.5 c . This agrees with the recent experiment [33]. In the inset of panel (a), we present a full scale diagram of χ″ to give a comparison between the peak and the continuum.…”

Absorption and emission of a collective excitation by a fermionic quasiparticle in a Fermi superfluid

“…Since the elementary constituents of the superfluid are pairs of fermions, there also exists a fermionic branch of excitation of the relative motion of the pairs, with a gapped spectrum [13]. Several important experimental results on the ground state and the elementary excitations of this system were obtained recently: the measurement of its zero temperature equation of state [14], and of the dispersion relation of the fermionic [15] and bosonic [16,17] excitations, also at high energy [18]. Experiments can now rather precisely probe the physics of the gas at non-zero temperatures [19], but their description with analytical methods remains a theoretical challenge.…”