arXiv subjects

Yvan Castin

Publications and source records attributed to Yvan Castin.

At least 19 recordsLinked to original sources

arXiv2026

Phonon number relaxation in a 3D superfluid with a concave acoustic branch

We consider the collisional evolution towards equilibrium of a spatially homogeneous and isotropic phonon gas of a three-dimensional superfluid with a concave acoustic excitation branch, at a non-zero but arbitrarily low temperature $T$. Three-phonon collisions $1ϕ\leftrightarrow 2ϕ$ are forbidden by conservation of energy-momentum. Four-phonon collisions $2ϕ\to 2ϕ$ of Landau and Khalatnikov lead, after a time $\propto T^{-7}$, only to a partial thermal equilibrium, a Bose law of non-zero chemical potential for the phonons, because they conserve the total number of phonons. Relaxation towards complete thermochemical equilibrium is therefore ensured by the much slower five-phonon collisions $2ϕ\leftrightarrow 3ϕ$ of Khalatnikov, in a time $\propto T^{-9}$. Using kinetic equations on the occupation numbers of the phonon modes and explicitly calculating the $2ϕ\to 3ϕ$ collisional amplitude with quantum hydrodynamics at low temperature, we determine the corresponding evolution of the fugacity $z_ϕ$ of the phonon gas from the non-degenerate regime $z_ϕ=0^+$ to complete equilibrium $z_ϕ=1^-$. Using the conservation of total energy, we find that the fugacity varies with a non-integer power law $\propto t^{4/5}$ at short times and an exponential law at long times; the speed of change of entropy, always positive, is asymptotically proportional to the square of the speed of change of fugacity, $(\mathrm{d}/\mathrm{d}t)S_ϕ\propto[(\mathrm{d}/\mathrm{d}t)z_ϕ]^2$, as Landau predicted for an arbitrarily slow adiabatic transformation. Our results bring to a close the study initiated by Khalatnikov in 1950 and could be experimentally verified in a gas of cold spin-1/2 fermionic atoms in the sector of the BEC-BCS crossover where the acoustic branch has a concave start, or in superfluid liquid helium-4 at sufficiently high pressure.

cond-mat.quant-gas↗

arXiv2026

Limit of Spin Squeezing in Finite Temperature Bose-Einstein Condensates

We show that, at finite temperature, the maximum spin squeezing achievable using interactions in Bose-Einstein condensates has a finite limit when the atom number $N\to \infty$ at fixed density and interaction strength. We calculate the limit of the squeezing parameter for a spatially homogeneous system and show that it is bounded from above by the initial non-condensed fraction.

cond-mat.quant-gas↗

arXiv2026

Optimum spin-squeezing in Bose-Einstein condensates with particle losses

The problem of spin squeezing with a bimodal condensate in presence of particle losses is solved analytically by the Monte Carlo wavefunction method. We find the largest obtainable spin squeezing as a function of the one-body loss rate, the two-body and three-body rate constants, and the $s$-wave scattering length.

quant-ph↗

arXiv2026

Integral equations for the four-body problem

We consider the four-boson and 3+1 fermionic problems with a model Hamiltonian which encapsulates the mechanism of the Feshbach resonance involving the coherent coupling of two atoms in the open channel and a molecule in the closed channel. The model includes also the pair-wise direct interaction between atoms in the open channel and in the bosonic case, the direct molecule-molecule interaction in the closed channel. Interactions are modeled by separable potentials which makes it possible to reduce the four-body problem to the study of a single integral equation. We take advantage of the rotational symmetry and parity invariance of the Hamiltonian to reduce the general eigenvalue equation in each angular momentum sector to an integral equation for functions of three real variables only. A first application of this formalism in the zero-range limit is given elsewhere [Y. Castin, C. Mora, L. Pricoupenko, Phys. Rev. Lett. 105, 223201 (2010)].

cond-mat.quant-gas↗

arXiv2026

Limit of spin squeezing in trapped Bose-Einstein condensates

The evolution of an interacting two-component Bose-Einstein condensate from an initial phase state leads to a spin squeezed state that may be used in atomic clocks to increase the signal-to-noise ratio, opening the way to quantum metrology. The efficiency of spin squeezing is limited by the finite temperature of the gas, as was shown theoretically in a spatially homogeneous system. Here we determine the limit of spin squeezing in the realistic trapped case, with classical field simulations, and with a completely analytical treatment that includes the quantum case.

quant-ph↗

arXiv2026

Bose-Einstein Condensates in Time Dependent Traps

We present analytical results for the macroscopic wave function of a Bose-Einstein condensate in a time dependent harmonic potential. The evolution of the spatial density is a dilatation, characterized by three scaling factors which allow a classical interpretation of the dynamics. This approach is an efficient tool for the analysis of recent experimental results on the expansion and collective excitation of a condensate.

cond-mat.quant-gas↗

arXiv2026

Exact scaling transform for a unitary quantum gas in a time dependent harmonic potential

A unitary quantum gas is a gas of quantum particles with a binary interaction of infinite scattering length and negligible range. It has been produced in recent experiments with gases of fermionic atoms by means of a Feshbach resonance. Using the Fermi pseudo-potential model for the atomic interaction, we show that the time evolution of such a gas in an isotropic three-dimensional time dependent harmonic trap is exactly given by a gauge and scaling transform.

cond-mat.other↗

arXiv2026

The unitary three-body problem in a trap

We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting via a short range potential of infinite scattering length and trapped in an isotropic harmonic potential. For a zero-range model, we obtain analytically the exact spectrum and eigenfunctions: for fermions all the states are universal; for bosons there is a coexistence of decoupled universal and efimovian states. All the universal states, even the bosonic ones, have a tiny 3-body loss rate. For a finite range model, we numerically find for bosons a coupling between zero angular momentum universal and efimovian states; the coupling is so weak that, for realistic values of the interaction range, these bosonic universal states remain long-lived and observable.

cond-mat.other↗

arXiv2026

Pair distribution functions of a superfluid spin-1/2 Fermi gas with contact interactions in the linearized time-dependent BCS theory

We show that the minimal mean-field theory to use for calculating the pair distribution functions $g_{σσ'}(\vec{r},\vec{r}\,')$ of a spatially homogeneous, unpolarized spin-1/2 superfluid Fermi gas is not the ordinary static BCS theory, but the linearized time-dependent BCS theory implemented via the fluctuation-dissipation theorem. Indeed, the former completely ignores the acoustic excitation branch - the phonons - of the superfluid, while the latter explicitly takes it into account, as well as the quantum fluctuations induced by the broken-pair continuum. Unlike the first, the second theory (i) reflects the effect of these collective excitations on the system's equation of state, including at zero temperature, (ii) allows the function $g_{\uparrow\downarrow}(\vec{r},\vec{r}\,')$ to go at sufficiently large distances strictly below its asymptotic value $(ρ/2)^2$ where $ρ$ is the gas density, as expected according to the quantum hydrodynamics of Landau and Khalatnikov at low temperatures, and (iii) predicts in the function $g_{\uparrow\uparrow}(\vec{r},\vec{r}\,')$ at short distances subdominant contributions $|\vec{r}-\vec{r}\,'|^2\ln|\vec{r}-\vec{r}\,'|$ in 3D and $|\vec{r}-\vec{r}\,'|^2\ln(-\ln|\vec{r}-\vec{r}\,'|)$ in 2D, alongside the dominant contributions $|\vec{r}-\vec{r}\,'|$ in 3D and $|\vec{r}-\vec{r}\,'|^2\ln|\vec{r}-\vec{r}\,'|$ in 2D already present in static BCS theory but with a lower coefficient. This discussion is relevant to the recent theoretical work of Obeso-Jureidini and Romero-Rochin, and to the ongoing experiments on cold atomic gases at ENS and MIT.

cond-mat.quant-gas↗

arXiv2025

Open questions for strongly interacting Fermi gases with zero-range interactions

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 specific properties of the acoustic excitation branch (Goldstone) of the condensate of pairs, or its collective excitation branch (Higgs) in the broken-pair continuum.

cond-mat.quant-gas↗

arXiv2024

The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas

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.

cond-mat.quant-gas↗

arXiv2024

Comment on "Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas"

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.

cond-mat.quant-gas↗

arXiv2024

The third virial coefficient of a two-component unitary Fermi gas across an Efimov-effect threshold

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 $α$ across $α_c\simeq 13.6069$ 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 $α$ across $α_c$ since, unexpectedly, the three-body parameter characterizing the interaction is relevant even on the non-Efimovian side $α<α_c$.

cond-mat.quant-gas↗

arXiv2024

Phonon damping in a 2D superfluid: insufficiency of Fermi's golden rule at low temperature

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.

cond-mat.quant-gas↗

arXiv2024

Unitary boson-boson and boson-fermion mixtures: third virial coefficient and three-body parameter on a narrow Feshbach resonance

We give exact integral expressions of the third cluster or virial coefficients of binary mixtures of ideal Bose or Fermi gases, with interspecies interactions of zero range and infinite s-wave scattering length. In general the result depends on three-body parameters Rt appearing in three-body contact conditions, because an Efimov effect is present or because the mixture is in a preefimovian regime with a mass ratio close to an Efimov effect threshold. We give a new, exact integral expression of Rt for the microscopic narrow Feshbach resonance model. A divergence of Rt in the preefimovian regime at a scaling exponent s = 1/2 is predicted and physically discussed. The analytical results are applied to typical species used in cold atom experiments.

cond-mat.quant-gas↗

arXiv2023

Absence of a four-body Efimov effect in the 2 + 2 fermionic problem

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 $α$ 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 $α\in [1, 13.6069\ldots]$, 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.

cond-mat.quant-gas↗

arXiv2022

Fourth cluster and virial coefficients of a unitary Fermi gas for an arbitrary mass ratio

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.

cond-mat.quant-gas↗

arXiv2021

Nuclear spin squeezing by continuous quantum non-demolition measurement: a theoretical study

We propose to take advantage of the weak coupling of ground-state helium-3 nuclear spin to its environment to produce long-lived macroscopic quantum states, nuclear spin squeezed states, in a gas cell at room temperature. To perform a quantum non-demolition measurement of a transverse component of the polarized collective nuclear spin, we maintain a population in helium-3 metastable state with a discharge. The collective spin associated to $F=1/2$ metastable level hybridizes with the ground state one by metastability exchange collisions. To access nuclear spin fluctuations, one continuously measures the light leaking out of an optical cavity, where it has interacted dispersively with the metastable state collective spin. In a three coupled collective spin model (nuclear, metastable and Stokes), we calculate moments of the nuclear spin squeezed component $I_z$ conditioned on the time averaged optical signal. In the photon counting scheme, the squeezed observable is $I_z^2$ rather than $I_z$. In the homodyne detection scheme, we solve the stochastic equation for the system state conditioned on the measurement; the conditional expectation value of $I_z$ depends linearly on the signal and the conditional variance of $I_z$ does not depend on it. The conditional variance decreases as $(Γ_{\rm sq}t)^{-1}$, where the squeezing rate $Γ_{\rm sq}$ depends linearly on the light intensity in the cavity at weak atom-field coupling and saturates at strong coupling to the ground state metastability exchange effective rate, proportional to the metastable atom density. Including de-excitation of metastable atoms at the walls, which induces nuclear spin decoherence with an effective rate $γ_α$, we find a limit $\propto(γ_α/Γ_{\rm sq})^{1/2}$ on the conditional variance reached in a time $\propto(γ_αΓ_{\rm sq})^{-1/2}$.

physics.atom-ph↗