Low-Lying Collective Excitations of Superconductors and Charged Superfluids

We investigate theoretically the momentum-dependent frequency and damping of low-lying collective excitations of superconductors and charged superfluids in the BCS-BEC crossover regime. The study is based on the Gaussian pair-and-density fluctuation method for the propagator of Gaussian fluctuations of the pair and density fields. Eigenfrequencies and damping rates are determined in a mutually consistent nonperturbative way as complex poles of the fluctuation propagator. Particular attention is paid to new features with respect to preceding theoretical studies, which were devoted to collective excitations of superconductors in the far BCS regime. We find that at a sufficiently strong coupling, new branches of collective excitations appear, which manifest different behavior as functions of the momentum and the temperature.Comment: 10 pages, 5 figures, Proceedings of SuperFluctuations 2022 Conference (Padova, 2022

Collective excitations of superfluid Fermi gases near the transition temperature

Studying the collective pairing phenomena in a two-component Fermi gas, we predict the appearance near the transition temperature $T_c$ of a well-resolved collective mode of quadratic dispersion. The mode is visible both above and below $T_c$ in the system's response to a driving pairing field. When approaching $T_c$ 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 $\xi_{\rm pair}\propto|T_c-T|^{-1/2}$; 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 $T_c$, we unify the newly found collective phenomena near $T_c$ 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.Comment: 44 pages, 17 figures, accepted in Physical Review A (2021

Phononic collective excitations in superfluid Fermi gases at nonzero temperatures

We study the phononic collective modes of the pairing field $\Delta$ and their corresponding signature in both the order-parameter and density response functions for a superfluid Fermi gas at all temperatures below $T_c$ in the collisionless regime. The spectra of collective modes are calculated within the Gaussian Pair Fluctuation approximation. We deal with the coupling of these modes to the fermionic continuum of quasiparticle-quasihole excitations by performing a non-perturbative analytic continuation of the pairing field propagator. At low temperature, we recover the known exponential temperature dependence of the damping rate and velocity shift of the Anderson-Bogoliubov branch. In the vicinity of $T_c$, we find analytically a weakly-damped collective mode whose velocity vanishes with a critical exponent of $1/2$, and whose quality factor diverges logarithmically with $T_c-T$, thereby clarifying an existing debate in the literature (Andrianov et al. Th. Math. Phys. 28, 829, Ohashi et al. J. Phys. Jap. 66, 2437). A transition between these two phononic branches is visible at intermediary temperatures, particularly in the BCS limit where the phase-phase response function displays two maxima.Comment: 31 pages, 15 figure

Pair-Breaking Collective Branch in 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. 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 $\mu$ is positive and the wave number below $\sqrt{2m\mu}/\hbar$ (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.Comment: 6-7 pages, 4 figures, in English et en fran\c{c}ai

Bose-Einstein condensation of Efimovian triples in the unitary Bose gas

In an atomic Bose-Einstein condensate quenched to the unitary regime, we predict the sequential formation of a significant fraction of condensed pairs and triples. At short-distances, we demonstrate the two-body and Efimovian character of the condensed pairs and triples, respectively. As the system evolves, the size of the condensed pairs and triples becomes comparable to the interparticle distance, such that many-body effects become significant. The structure of the condensed triples depends on the relative size of Efimov states to density scales. Unexpectedly, we find universal condensed triples in the limit where these scales are well-separated. Our findings provide a new framework for understanding dynamics in the unitary regime as the Bose-Einstein condensation of few-body composites

Cumulant theory of the unitary Bose gas: Prethermal and Efimovian dynamics

We study the quench of a degenerate ultracold Bose gas to the unitary regime, where interactions are as strong as allowed by quantum mechanics. We lay the foundations of a cumulant theory able to capture simultaneously the three-body Efimov effect and ergodic evolution. After an initial period of rapid quantum depletion, a universal prethermal stage is established characterized by a kinetic temperature and an emergent Bogoliubov dispersion law while the microscopic degrees of freedom remain far-from-equilibrium. Integrability is then broken by higher-order interaction terms in the many-body Hamiltonian, leading to a momentum-dependent departure from power law to decaying exponential behavior of the occupation numbers at large momentum. We find also signatures of the Efimov effect in the many-body dynamics and make a precise identification between the observed beating phenomenon and the binding energy of an Efimov trimer. Throughout the work, our predictions for a uniform gas are quantitatively compared with experimental results for quenched unitary Bose gases in uniform potentials.Comment: 34 pages, 12 figure

Higgs Oscillations in a Unitary Fermi Superfluid

Symmetry-breaking phase transitions are central to our understanding of states of matter. When a continuous symmetry is spontaneously broken, new excitations appear that are tied to fluctuations of the order parameter. In superconductors and fermionic superfluids, the phase and amplitude can fluctuate independently, giving rise to two distinct collective branches. However, amplitude fluctuations are difficult to both generate and measure, as they do not couple directly to the density of fermions and have only been observed indirectly to date. Here, we excite amplitude oscillations in an atomic Fermi gas with resonant interactions by an interaction quench. Exploiting the sensitivity of Bragg spectroscopy to the amplitude of the order parameter, we measure the time-resolved response of the atom cloud, directly revealing amplitude oscillations at twice the frequency of the gap. The magnitude of the oscillatory response shows a strong temperature dependence, and the oscillations appear to decay faster than predicted by time-dependent Bardeen-Cooper-Schrieffer theory applied to our experimental setup.</p

Material-independent crack arrest statistics: Application to indentation experiments

An extensive experimental study of indentation and crack arrest statistics is presented for four different brittle materials (alumina, silicon carbide, silicon nitride, glass). Evidence is given that the crack length statistics can be described by a universal (i.e. material independent) distribution. The latter directly derives from results obtained when modeling crack propagation as a depinning phenomenon. Crack arrest (or effective toughness) statistics appears to be fully characterized by two parameters, namely, an asymptotic crack length (or macroscopic toughness) value and a power law size dependent width. The experimental knowledge of the crack arrest statistics at one given scale thus gives access to its knowledge at all scales