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We report the production of matter-wave solitons in an ultracold lithium-7 gas. The effective interaction between atoms in a Bose-Einstein condensate is tuned with a Feshbach resonance from repulsive to attractive before release in a one-dimensional optical waveguide. Propagation of the soliton without dispersion over a macroscopic distance of 1.1 millimeter is observed. A simple theoretical model explains the stability region of the soliton. These matter-wave solitons open possibilities for future applications in coherent atom optics, atom interferometry, and atom transport.

We consider dynamically generated spin squeezing in interacting bimodal condensates. We show that particle losses and non-zero temperature effects in a multimode theory completely change the scaling of the best squeezing for large atom numbers. We present the new scalings and we give approximate analytical expressions for the squeezing in the thermodynamic limit. Besides reviewing our recent theoretical results, we give here a simple physical picture of how decoherence acts to limit the squeezing. We show in particular that under certain conditions the decoherence due to losses and non-zero temperature acts as a simple dephasing.

We consider a two-component ideal Fermi gas in an isotropic harmonic potential. Some eigenstates have a wavefunction that vanishes when two distinguishable fermions are at the same location, and would be unaffected by s-wave contact interactions between the two components. We determine the other, interaction-sensitive eigenstates, using a Faddeev ansatz. This problem is nontrivial, due to degeneracies and to the existence of unphysical Faddeev solutions. As an application we present a new conjecture for the fourth-order cluster or virial coefficient of the unitary Fermi gas, in good agreement with the numerical results of Blume and coworkers.

In the free three-dimensional space, we consider a pair of identical \\(\\uparrow\\) fermions of some species or in some internal state, and a pair of identical \\(\\downarrow\\) fermions of another species or in another state. There is a resonant \\(s\\)-wave interaction (that is of zero range and infinite scattering length) between fermions in different pairs, and no interaction within the same pair. We study whether this \\(2+2\\) fermionic system can exhibit (as the \\(3+1\\) fermionic system) a four-body Efimov effect in the absence of three-body Efimov effect, that is the mass ratio \\(\\alpha\\) between \\(\\uparrow\\) and \\(\\downarrow\\) fermions and its inverse are both smaller than 13.6069{\\ldots}. For this purpose, we investigate scale invariant zero-energy solutions of the four-body Schr\\''odinger equation, that is positively homogeneous functions of the coordinates of degree {\\(s-7/2\\)}, where \\(s\\) is a generalized Efimov exponent {that becomes purely imaginary in the presence of a four-body Efimov effect.} Using rotational invariance in momentum space, it is found that the allowed values of \\(s\\) are such that \\(M(s)\\) has a zero eigenvalue; here the operator \\(M(s)\\), that depends on the total angular momentum \\(\\ell\\), acts on functions of two real variables (the cosine of the angle between two wave vectors and the logarithm of the ratio of their moduli), and we write it explicitly in terms of an integral matrix kernel. We have performed a spectral analysis of \\(M(s)\\), analytical and for an arbitrary imaginary \\(s\\) for the continuous spectrum, numerical and limited to \\(s = 0\\) and \\(\\ell \\le 12\\) for the discrete spectrum. We conclude that no eigenvalue of \\(M(0)\\) crosses zero over the mass ratio interval \\(\\alpha \\in [1, 13.6069\\ldots]\\), even if, in the parity sector \\((-1)^{\\ell}\\), the continuous spectrum of \\(M(s)\\) has everywhere a zero lower border. As a consequence, there is no possibility of a four-body Efimov effect for the 2+2 fermions. We also enunciated a conjecture for the fourth virial coefficient of the unitary spin-\\(1/2\\) Fermi gas,inspired from the known analytical form of the third cluster coefficient and involving the integral over the imaginary \\(s\\)-axis of \\(s\\) times the logarithmic derivative of the determinant of \\(M(s)\\) summed over all angular momenta.The conjectured value is in contradiction with the experimental results.

We review some unresolved theoretical issues in three-dimensional two-component Fermi gases, drawing on recent experiments on cold atoms in immaterial traps close to a magnetic Feshbach resonance. We distinguish successively (i) the open questions arising in the few-body problem with Wigner-Bethe-Peierls contact interactions - essentially the stability of the gas with respect to the Efimov effect and the calculation of the cluster (or virial) coefficients, (ii) those arising in the effective low-energy theory of Landau and Khalatnikov quantum hydrodynamics - essentially the damping of phonon modes and the coherence time of the condensate of pairs, and finally (iii) questions requiring a complete, microscopic solution of the many-body problem, such as the properties of the acoustic excitation branch (Goldstone) of the condensate of pairs, or its collective excitation branch (Higgs) in the broken-pair continuum.

We present simple arguments suggesting that H. Biss et al [PRL 128, 100401 (2022)] did not measure with the required accuracy the low-wavenumber curvature of the acoustic excitation branch of the ground-state unitary Fermi gas. This difficult-to-calculate quantity is crucial for the relaxation dynamics of the gas at low temperature.

We calculate the fourth cluster coefficients of the homogeneous unitary spin 1/2 Fermi gas as functions of the internal-state mass ratio, over intervals constrained by the 3- or 4-body Efimov effect. For this we use our 2016 conjecture (validated for equal masses by Hou and Drut in 2020) in a numerically efficient formulation making the sum over angular momentum converge faster, which is crucial at large mass ratio. The mean cluster coefficient, relevant for equal chemical potentials, is not of constant sign and increases rapidly close to the Efimovian thresholds. We also get the fourth virial coefficients, which we find to be very poor indicators of interaction-induced 4-body correlations. We obtain analytically for all \\(n\\) the cluster coefficients of order \\(n\\) + 1 for an infinity-mass impurity fermion, matching the conjecture for \\(n=3\\). Finally, in a harmonic potential, we predict a non-monotonic behavior of the 3 + 1 cluster coefficient with trapping frequency, near mass ratios where this coefficient vanishes in the homogeneous case.

We consider a mixture of two single-spin-state fermions with an interaction of negligible range and infinite \\(s\\)-wave scattering length. By varying the mass ratio \\(\\alpha\\) across \\(\\alpha_c\\simeq 13.6069\\) one can switch on-and-off the Efimov effect. We determine analytically the third cluster coefficient of the gas. We show that it is a smooth function of \\(\\alpha\\) across \\(\\alpha_c\\) since, unexpectedly, the three-body parameter characterizing the interaction is relevant even on the non-Efimovian side \\(\\alpha<\\alpha_c\\).

It is generally accepted that the phonon gas of a superfluid always enters a weak coupling regime at sufficiently low temperatures, whatever the strength of the interactions between the underlying particles (constitutive of the superfluid). Thus, in this limit, we should always be able to calculate the damping rate of thermal phonons by applying Fermi's golden rule to the Hamiltonian \\(H_3\\) of cubic phonon-phonon coupling taken from quantum hydrodynamics, at least in the case of a convex acoustic branch and in the collisionless regime (where the eigenfrequency of the considered phonons remains much greater than the gas thermalization rate). Using the many-body Green's function method, we predict that, unexpectedly, this is not true in two dimensions, contrary to the three-dimensional case. We confirm this prediction with classical phonon-field simulations and a non-perturbative theory in \\(H_3\\), where the fourth order is regularized by hand, giving a complex energy to the virtual phonons of the four-phonon collisional processes. For a weakly interacting fluid and a phonon mode in the long-wavelength limit, we predict a damping rate about three times lower than that of the golden rule.

The pair-condensed unpolarized spin-\\(1/2\\) Fermi gases have a collective excitation branch in their pair-breaking continuum (V.A. Andrianov, V.N. Popov, 1976). We study it at zero temperature, with the eigenenergy equation deduced from the linearized time-dependent BCS theory and extended analytically to the lower half complex plane through its branch cut, calculating both the dispersion relation and the spectral weights (quasiparticle residues) of the branch. In the case of BCS superconductors, so called because the effect of the ion lattice is replaced by a short-range electron-electron interaction, we also include the Coulomb interaction and we restrict ourselves to the weak coupling limit \\(\\Delta/\\mu\\to 0^+\\) (\\(\\Delta\\) is the order parameter, \\(\\mu \\) the chemical potential) and to wavenumbers \\(q=O(1/\\xi)\\) where \\(\\xi\\) is the size of a pair; when the complex energy \\(z_q\\) is expressed in units of \\(\\Delta\\) and \\(q\\) in units of \\(1/\\xi\\), the branch follows a universal law insensitive to the Coulomb interaction. In the case of cold atoms in the BEC-BCS crossover, only a contact interaction remains, but the coupling strength \\(\\Delta/\\mu\\) can take arbitrary values, and we study the branch at any wave number. At weak coupling, we predict three scales, that already mentioned \\(q\\approx 1/\\xi\\), that \\(q\\approx(\\Delta/\\mu)^{-1/3}/\\xi\\) where the real part of the dispersion relation has a minimum and that \\(q\\approx (\\mu/\\Delta)/\\xi\\approx k_{\\rm F}\\) (\\(k_{\\rm F}\\) is the Fermi wave number) where the branch reaches the edge of its existence domain. Near the point where the chemical potential vanishes on the BCS side, \\(\\mu/\\Delta\\to 0^+\\), where \\(\\xi\\approx k_{\\rm F}\\), we find two scales \\(q\\approx(\\mu/\\Delta)^{1/2}/\\xi\\) and \\(q\\approx 1/\\xi\\). In all cases, the branch has a limit \\(2\\Delta\\) and a quadratic start at \\(q=0\\). These results were obtained for \\(\\mu>0\\), where the eigenenergy equation admits at least two branch points \\(\\epsilon_a(q)\\) and \\(\\epsilon_b(q)\\) on the positive real axis, and for an analytic continuation through the interval \\([\\epsilon_a(q),\\epsilon_b(q)] \\). We find new continuum branches by performing the analytic continuation through \\([\\epsilon_b(q),+\\infty[\\) or even, for \\(q\\) low enough, where there is a third real positive branch point \\(\\epsilon_c(q)\\), through \\([\\epsilon_b(q),\\epsilon_c(q)]\\) and \\([\\epsilon_c(q),+\\infty[\\). On the BEC side \\(\\mu<0\\) not previously studied, where there is only one real positive branch point \\( \\epsilon_a(q)\\), we also find new collective excitation branches under the branch cut \\([\\epsilon_a (q),+\\infty[\\). For \\(\\mu>0\\), some of these new branches have a low-wavenumber exotic hypoacoustic \\(z_q\\approx q^{3/2}\\) or hyperacoustic \\(z_q\\approx q^{4/5}\\) behavior. For \\(\\mu<0\\), we find a hyperacoustic branch and a nonhypoacoustic branch, with a limit \\(2\\Delta\\) and a purely real quadratic start at \\(q=0\\) for \\(\\Delta/|\\mu|<0.222\\).