arXiv subjects

Yvan Castin

Publications and source records attributed to Yvan Castin.

At least 37 records · Page 2Linked to original sources

arXiv2021

Random walk of a massive quasiparticle in the phonon gas of an ultralow temperature superfluid

We consider a 3D homogeneous superfluid at low temperature $T$ with 2 types of excitations, gapless phonons with a linear dispersion relation at low wavenumber, and gapped quasiparticles with a quadratic dispersion relation around extrema. We calculate the scattering amplitude of a phonon on a quasiparticle to leading order in $T$ for all subsonic quasiparticle velocities, with a $S$-matrix formalism between exact asymptotic states dressed by virtual phonons. We then characterize the erratic motion of the quasiparticle in the superfluid due to its unceasing collisions with thermal phonons through mean force $F(k)$, longitudinal and transverse $k$-dependent momentum diffusion coefficients, and spatial diffusion coefficient. At the minimum location $k_0$ of the dispersion relation, where the velocity vanishes, $F(k)$ varies linearly with velocity with an isotropic friction coefficient; if $k_0=0$, the momentum diffusion is also isotropic and $F(k_0)=0$; if $k_0>0$, it is not, and $F(k_0)$ is nonzero but subleading with respect to friction by one order in $T$. The velocity time correlation function, whose integral is the spatial diffusion coefficient, decays with the mean velocity damping rate if $k_0=0$; if $k_0>0$, it has a second exponential component, with an amplitude and a damping rate lower by a factor $\propto T$ (it is the velocity direction thermalization rate). We also characterize force and momentum diffusion close to the stability domain sonic edge. Our general expressions are expected to be exact to leading order in $T$. We illustrate them in the BCS approximation, for a fermionic quasiparticle (an unpaired fermion) in a superfluid of spin 1/2 fermions, realisable with cold atoms in flat bottom traps. We also refute the statement of Lerch, Bartosch and Kopietz (2008), that there would be no fermionic quasiparticle in such a superfluid.

cond-mat.quant-gas↗

arXiv2021

Bragg spectroscopy and pair-breaking-continuum mode in a superfluid Fermi gas

The superfluid, pair condensed spin-1/2 Fermi gases are supposed to exhibit at nonzero wave vector a still unobserved collective excitation mode in their pair-breaking continuum. Using BCS theory at zero temperature and in the long wavelength limit, we predict that this mode is quantitatively observable (in frequency, width and spectral weight) in the response of a cold atom gas to a laser Bragg excitation, if one measures the perturbation induced on the order parameter modulus rather than on the density.

cond-mat.quant-gas↗

arXiv2020

Collective excitation branch in the continuum of pair-condensed Fermi gases : analytical study and scaling laws

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 $Δ/μ\to 0^+$ ($Δ$ is the order parameter, $μ$ the chemical potential) and to wavenumbers $q=O(1/ξ)$ where $ξ$ is the size of a pair; when the complex energy $z_q$ is expressed in units of $Δ$ and $q$ in units of $1/ξ$, 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 $Δ/μ$ can take arbitrary values, and we study the branch at any wave number. At weak coupling, we predict three scales, that already mentioned $q\approx 1/ξ$, that $q\approx(Δ/μ)^{-1/3}/ξ$ where the real part of the dispersion relation has a minimum and that $q\approx (μ/Δ)/ξ\approx k_{\rm F}$ ($k_{\rm F}$ 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, $μ/Δ\to 0^+$, where $ξ\approx k_{\rm F}$, we find two scales $q\approx(μ/Δ)^{1/2}/ξ$ and $q\approx 1/ξ$. In all cases, the branch has a limit $2Δ$ and a quadratic start at $q=0$. These results were obtained for $μ>0$, where the eigenenergy equation admits at least two branch points $ε_a(q)$ and $ε_b(q)$ on the positive real axis, and for an analytic continuation through the interval $[ε_a(q),ε_b(q)] $. We find new continuum branches by performing the analytic continuation through $[ε_b(q),+\infty[$ or even, for $q$ low enough, where there is a third real positive branch point $ε_c(q)$, through $[ε_b(q),ε_c(q)]$ and $[ε_c(q),+\infty[$. On the BEC side $μ<0$ not previously studied, where there is only one real positive branch point $ ε_a(q)$, we also find new collective excitation branches under the branch cut $[ε_a (q),+\infty[$. For $μ>0$, 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 $μ<0$, we find a hyperacoustic branch and a nonhypoacoustic branch, with a limit $2Δ$ and a purely real quadratic start at $q=0$ for $Δ/|μ|<0.222$.

cond-mat.quant-gas↗

arXiv2019

Landau phonon-roton theory revisited for superfluid helium 4 and Fermi gases

Liquid helium and spin-1/2 cold-atom Fermi gases both exhibit in their superfluid phase two distinct types of excitations, gapless phonons and gapped rotons or fermionic pair-breaking excitations. In the long wavelength limit, revising and extending Landau and Khalatnikov's theory initially developed for helium [ZhETF 19, 637 (1949)], we obtain universal expressions for three- and four-body couplings among these two types of excitations. We calculate the corresponding phonon damping rates at low temperature and compare them to those of a pure phononic origin in high-pressure liquid helium and in strongly interacting Fermi gases, paving the way to experimental observations.

cond-mat.quant-gas↗

arXiv2019

Phase spreading and temporal coherence of a pair-condensed Fermi gas at low temperature

A condensate of pairs in an isolated, homogeneous, unpolarised, finite-size spin 1/2 Fermi gas at low nonzero temperature T, undergoes with time a phase change with a random component, due to coupling to the gas thermal phonons. With the quantum second Josephson relation relating the derivative of the condensate phase operator to the phonon occupation numbers, and linearised kinetic equations giving the evolution of occupation number fluctuations, we access the behaviour of the phase change variance at times much longer than the phonon collision time. The case of a convex phonon branch is similar to the Bose gas case: the leading collisional processes are the Beliaev-Landau 3-phonons processes, and the variance is the sum of a ballistic term and of a delayed diffusive term, whose analytical expressions are given in the thermodynamic limit. The concave case is more exotic. It is analysed at time scales $T^{-9}$, allowing one to restrict to 2 phonons $\rightarrow$ 2 phonons small-angle Landau-Khalatnikov processes. The total number of phonons is conserved and the phonon mean occupation numbers at equilibrium can exhibit a negative chemical potential, assumed isotropic. The phase change variance is then the sum of a ballistic term, of a diffusive term, of exotic subsubleading terms and of a constant term. The analytic expression of some of the corresponding coefficients is obtained, as well as the diverging leading behavior of the other ones when the phonon chemical potential tends to 0. When this chemical potential is 0, the variance sub-ballistic part becomes superdiffusive, with an exponent 5/3 and an exactly-known coefficient. For a nonzero infinitesimal phonon chemical potential, a law is found, interpolating between superdiffusive and diffusive phase spreading. Also new results are obtained on the phonon Landau-Khalatnikov damping rate, in particular at negative phonon chemical potential.

cond-mat.quant-gas↗

arXiv2018

Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions

We derive relations between various observables for N particles with zero-range or short-range interactions, in continuous space or on a lattice, in two or three dimensions, in an arbitrary external potential. Some of our results generalise known relations between large-momentum behavior of the momentum distribution, short-distance behavior of the pair correlation function and of the one-body density matrix, derivative of the energy with respect to the scattering length or to time, and the norm of the regular part of the wavefunction; in the case of finite-range interactions, the interaction energy is also related to dE/da. The expression relating the energy to a functional of the momentum distribution is also generalised, and is found to break down for Efimov states with zero-range interactions, due to a subleading oscillating tail in the momentum distribution. We also obtain new expressions for the derivative of the energy of a universal state with respect to the effective range, the derivative of the energy of an efimovian state with respect to the three-body parameter, and the second order derivative of the energy with respect to the inverse (or the logarithm in the two-dimensional case) of the scattering length. The latter is negative at fixed entropy. We use exact relations to compute corrections to exactly solvable three-body problems and find agreement with available numerics. For the unitary gas, we compare exact relations to existing fixed-node Monte-Carlo data, and we test, with existing Quantum Monte Carlo results on different finite range models, our prediction that the leading deviation of the critical temperature from its zero range value is linear in the interaction effective range r_e with a model independent numerical coefficient.

cond-mat.quant-gas↗

arXiv2018

Coherence time of a Bose-Einstein condensate in an isolated harmonically trapped gas

We study the condensate phase dynamics in a low-temperature equilibrium gas of weakly interacting bosons, harmonically trapped and isolated from the environment. We find that at long times, much longer than the collision time between Bogoliubov quasiparticles, the variance of the phase accumulated by the condensate grows with a ballistic term quadratic in time and a diffusive term affine in time. We give the corresponding analytical expressions in the limit of a large system, in the collisionless regime and in the ergodic approximation for the quasiparticle motion. When properly rescaled, they are described by universal functions of the temperature divided by the Thomas-Fermi chemical potential. The same conclusion holds for the mode damping rates. Such universality class differs from the previously studied one of the homogeneous gas.

cond-mat.quant-gas↗

arXiv2018

Polaron residue and spatial structure in a Fermi gas

We study the problem of a mobile impurity of mass $M$ interacting {\sl via} a s-wave broad or narrow Feshbach resonance with a Fermi sea of particles of mass $m$. Truncating the Hilbert space to at most one pair of particle-hole excitations of the Fermi sea, we determine ground state properties of the polaronic branch other than its energy, namely the polaron quasiparticle residue $Z$, and the impurity-to-fermion pair correlation function $G(x)$. We show that $G(x)$ deviates from unity at large distances as $-(A\_4+B\_4 \cos 2 k\_F x)/(k\_F x)^4$, where $k\_F$ is the Fermi momentum; since $A\_4>0$ and $B\_4>0$, the polaron has a diverging rms radius and exhibits Friedel-like oscillations. In the weakly attractive limit, we obtain analytical results, that in particular detect the failure of the Hilbert space truncation for a diverging mass impurity, as expected from Anderson orthogonality catastrophe; at distances between $\sim 1/k\_F$ and the asymptotic distance where the $1/x^4$ law applies, they reveal that $G(x)$ exhibits an intriguing multiscale structure.

cond-mat.quant-gas↗

arXiv2017

Three-phonon and four-phonon interaction processes in a pair-condensed Fermi gas

We study the interactions among phonons and the phonon lifetime in a pair-condensed Fermi gas in the BEC-BCS crossover in the collisionless regime. To compute the phonon-phonon coupling amplitudes we use a microscopic model based on a generalized BCS Ansatz including moving pairs, which allows for a systematic expansion around the mean field BCS approximation of the ground state. We show that the quantum hydrodynamic expression of the amplitudes obtained by Landau and Khalatnikov apply only on the energy shell, that is for resonant processes that conserve energy. The microscopic model yields the same excitation spectrum as the Random Phase Approximation, with a linear (phononic) start and a concavity at low wave number that changes from upwards to downwards in the BEC-BCS crossover. When the concavity of the dispersion relation is upwards at low wave number, the leading damping mechanism at low temperature is the Beliaev-Landau process 2 phonons $\leftrightarrow$ 1 phonon while, when the concavity is downwards, it is the Landau-Khalatnikov process 2 phonons $\leftrightarrow$ 2 phonons. In both cases, by rescaling the wave vectors to absorb the dependence on the interaction strength, we obtain a universal formula for the damping rate. This universal formula corrects and extends the original analytic results of Landau and Khalatnikov [ZhETF {\bf 19}, 637 (1949)] for the $2\leftrightarrow2$ processes in the downward concavity case. In the upward concavity case, for the Beliaev 1$\leftrightarrow$ 2 process for the unitary gas at zero temperature, we calculate the damping rate of an excitation with wave number $q$ including the first correction proportional to $q^7$ to the $q^5$ hydrodynamic prediction, which was never done before in a systematic way.

cond-mat.quant-gas↗

arXiv2017

Mesoscopic quantum superpositions in bimodal Bose-Einstein condensates: decoherence and strategies to counteract it

We study theoretically the interaction-induced generation of mesoscopic coherent spin state superpositions (small cat states) from an initial coherent spin state in bimodal Bose-Einstein condensates and the subsequent phase revival, including decoherence due to particle losses and fluctuations of the total particle number. In a full multimode description, we propose a preparation procedure of the initial coherent spin state and we study the effect of preexisting thermal fluctuations on the phase revival, and on the spin and orbito-spinorial cat fidelities.

cond-mat.quant-gas↗

arXiv2017

General relations for quantum gases in two and three dimensions. Two-component fermions

We derive exact relations for $N$ spin-1/2 fermions with zero-range or short-range interactions, in continuous space or on a lattice, in $2D$ or in $3D$, in any external potential. Some of them generalize known relations between energy, momentum distribution $n(k)$, pair distribution function $g^{(2)}(r)$, derivative of the energy with respect to the scattering length $a$. Expressions are found for the second order derivative of the energy with respect to $1/a$ (or to $\ln a$ in $2D$). Also, it is found that the leading energy corrections due to a finite interaction range, are proportional to the effective range $r\_e$ in $3D$ (and to $r\_e^2$ in $2D$) with exprimable model-independent coefficients, that give access to the subleading short distance behavior of $g^{(2)}(r)$ and to the subleading $1/k^6$ tail of $n(k)$. This applies to lattice models for some magic dispersion relations, an example of which is given. Corrections to exactly solvable two-body and three-body problems are obtained. For the trapped unitary gas, the variation of the finite-$1/a$ and finite $r\_e$ energy corrections within each $SO(2,1)$ energy ladder is obtained; it gives the frequency shift and the collapse time of the breathing mode. For the bulk unitary gas, we compare to fixed-node Monte Carlo data, and we estimate the experimental uncertainty on the Bertsch parameter due to a finite $r\_e$.

cond-mat.quant-gas↗

arXiv2017

Landau-Khalatnikov phonon damping in strongly interacting Fermi gases

We derive the phonon damping rate due to the four-phonon Landau-Khalatnikov process in low temperature strongly interacting Fermi gases using quantum hydrodynamics, correcting and extending the original calculation of Landau and Khalatnikov [ZhETF, 19 (1949) 637]. Our predictions can be tested in state-of-the-art experiments with cold atomic gases in the collisionless regime.

cond-mat.quant-gas↗

arXiv2016

Thermal blurring of a coherent Fermi gas

It is generally assumed that a condensate of paired fermions at equilibrium is characterized by a macroscopic wavefunction with a well-defined, immutable phase. In reality, all systems have a finite size and are prepared at non-zero temperature; the condensate has then a finite coherence time, even when the system is isolated in its evolution and the particle number $N$ is fixed. The loss of phase memory is due to interactions of the condensate with the excited modes that constitute a dephasing environment. This fundamental effect, crucial for applications using the condensate of pairs' macroscopic coherence, was scarcely studied. We link the coherence time to the condensate phase dynamics, and we show with a microscopic theory that the time derivative of the condensate phase operator $\hatθ\_0$ is proportional to a chemical potential operator that we construct including both the pair-breaking and pair-motion excitation branches. In a single realization of energy $E$, $\hatθ\_0$ evolves at long times as $-2μ\_{\rm mc}(E)t/\hbar$ where $μ\_{\rm mc}(E)$ is the microcanonical chemical potential; energy fluctuations from one realization to the other then lead to a ballistic spreading of the phase and to a Gaussian decay of the temporal coherence function with a characteristic time $\propto N^{1/2}$. In the absence of energy fluctuations, the coherence time scales as $N$ due to the diffusive motion of $\hatθ\_0$. We propose a method to measure the coherence time with ultracold atoms, which we predict to be tens of milliseconds for the canonical ensemble unitary Fermi gas.

cond-mat.quant-gas↗

arXiv2016

Simple theoretical tools for low dimension Bose gases

We first consider an exactly solvable classical field model to understand the coherence properties and the density fluctuations of a one-dimensional (1D) weakly interacting degenerate Bose gas with repulsive interactions at temperatures larger than the chemical potential. In a second part, using a lattice model for the quantum field, we explain how to carefully generalize the usual Bogoliubov approach to study a degenerate and weakly interacting Bose gas in 1D, 2D or 3D in the regime of weak density fluctuations. In the last part, using the mapping to an ideal Fermi gas in second quantized formalism, we calculate and discuss physically the density fluctuations and the coherence properties of a gas of impenetrable bosons in 1D.

cond-mat.other↗

arXiv2016

Concavity of the collective excitation branch of a Fermi gas in the BEC-BCS crossover

We study the concavity of the dispersion relation $q\mapsto ω\_{\mathbf{q}}$ of the bosonic excitations of a three-dimensional spin-$1/2$ Fermi gas in the Random Phase Approximation (RPA). In the limit of small wave numbers $q$ we obtain analytically the spectrum up to order $5$ in $q$. In the neighborhood of $q=0$, a change in concavity between the convex BEC limit and the concave BCS limit takes place at $Δ/μ\simeq0.869$ [$1/(k\_F a)\simeq-0.144$], where $a$ is the scattering length between opposite spin fermions, $k\_F$ is the Fermi wave number and $Δ$ the gap according to BCS theory, and $μ$ is the chemical potential. At that point the branch is concave due to a negative fifth-order term. Our results are supplemented by a numerical study which shows the evolution of the border between the zone of the $(q,Δ)$ plane where $q\mapsto ω\_{\mathbf{q}}$ is concave and the zone where it is convex.

cond-mat.quant-gas↗

arXiv2015

The Landau critical velocity for a particle in a Fermi superfluid

We determine {à} la Landau the critical velocity $v\_c^{L}$ of a moving impurity in a Fermi superfluid, that is by restricting to the minimal excitation processes of the superfluid. $v\_c^{L}$ is then the minimal velocity at which these processes are energetically allowed. The Fermi superfluid actually exhibits two excitation branches~: one is the fermionic pair-breaking excitation, as predicted by BCS theory; the other one is bosonic and sets pairs into motion, as predicted by Anderson's RPA. $v\_c^{L}$ is the smallest of the two corresponding critical velocities $v\_{c,f}^{L}$ and $v\_{c,b}^{L}$. In the parameter space (superfluid interaction strength, fermion-to-impurity mass ratio), we identify two transition lines, corresponding to a discontinuity of the first-order and second-order derivatives of $v\_c^{L}$. These two lines meet in a triple point and split the plane in three domains. We briefly extend this analysis to the very recently realized case at ENS, where the moving object in the Fermi superfluid is a weakly interacting Bose superfluid of impurities, rather than a single impurity. For a Bose chemical potential much smaller than the Fermi energy, the topology of the transition lines is unaffected; a key result is that the domain $v\_c^{L}=c$, where $c$ is the sound velocity in the Fermi superfluid, is turned into a domain $v\_c^{L}=c+c\_B$, where $c\_B$ is the sound velocity in the Bose superfluid, with slightly shifted boundaries.

cond-mat.quant-gas↗

arXiv2014

The self-energy of an impurity in an ideal Fermi gas to second order in the interaction strength

We study in three dimensions the problem of a spatially homogeneous zero-temperature ideal Fermi gas of spin-polarized particles of mass $m$ perturbed by the presence of a single distinguishable impurity of mass $M$. The interaction between the impurity and the fermions involves only the partial $s$-wave through the scattering length $a$, and has negligible range $b$ compared to the inverse Fermi wave number $1/\kf$ of the gas. Through the interactions with the Fermi gas the impurity gives birth to a quasi-particle, which will be here a Fermi polaron (or more precisely a {\sl monomeron}). We consider the general case of an impurity moving with wave vector $\KK\neq\OO$: Then the quasi-particle acquires a finite lifetime in its initial momentum channel because it can radiate particle-hole pairs in the Fermi sea. A description of the system using a variational approach, based on a finite number of particle-hole excitations of the Fermi sea, then becomes inappropriate around $\KK=\mathbf{0}$. We rely thus upon perturbation theory, where the small and negative parameter $\kf a\to0^-$ excludes any branches other than the monomeronic one in the ground state (as e.g.\ the dimeronic one), and allows us a systematic study of the system. We calculate the impurity self-energy $Σ^{(2)}(\KK,ω)$ up to second order included in $a$. Remarkably, we obtain an analytical explicit expression for $Σ^{(2)}(\KK,ω)$ allowing us to study its derivatives in the plane $(K,ω)$. These present interesting singularities, which in general appear in the third order derivatives $\partial^3 Σ^{(2)}(\KK,ω)$. In the special case of equal masses, $M=m$, singularities appear already in the physically more accessible second order derivatives $\partial^2 Σ^{(2)}(\KK,ω)$; using a self-consistent heuristic approach based on $Σ^{(2)}$ we then regularise the divergence of the second order derivative $\partial\_K^2 ΔE(\KK)$ of the complex energy of the quasi-particle found in reference [C. Trefzger, Y. Castin, Europhys. Lett. {\bf 104}, 50005 (2013)] at $K=\kf$, and we predict an interesting scaling law in the neighborhood of $K=\kf$. As a by product of our theory we have access to all moments of the momentum of the particle-hole pair emitted by the impurity while damping its motion in the Fermi sea, at the level of Fermi's golden rule.

cond-mat.quant-gas↗

arXiv2014

A liquid-gas transition for bosons with attractive interaction in one dimension

We consider a one dimensional system of $N$ bosons interacting via an attractive Dirac delta function potential. We place the bosonic quantum particles at thermal equilibrium in a box of length $L$ with periodic boundary conditions. At large $N$ and for $L$ much larger than the diameter of a two particle bound state, we predict by numerical and analytical studies of a simple model derived from first principles that the system exhibits a first order phase transition in a high temperature, non-degenerate regime. The higher temperature phase is an almost pure atomic gas, with a small fraction of dimers, a smaller fraction of trimers, etc. The lower temperature phase is a mesoscopic or macroscopic bound state that collects all the particles of the system with the exception of a small gaseous fraction composed mainly of atoms. We term this phase, which is the quantum equivalent of the classical bright soliton, a liquid.---Nous considerons, en dimension un, une assemblee de $N$ particules quantiques bosoniques interagissant par un potentiel de Dirac attractif, a l'equilibre thermique dans une boite de quantification de longueur L avec des conditions aux limites periodiques. Pour de grandes valeurs de N, et lorsque L est bien superieur au diametre de l'etat dimere dans l'espace reel, nous predisons, par etude numerique et analytique d'un modele simple mais deduit des premiers principes, que le systeme presente, a haute temperature c'est-a-dire dans le regime non degenere, une transition du premier ordre entre deux phases. La phase privilegiee a haute temperature est un gaz presque pur d'atomes, avec une faible fraction de dimeres, et des fractions encore plus faibles de trimeres, etc. La phase qui la supplante a moins haute temperature est un etat lie mesoscopique ou macroscopique que nous qualifions de liquide, equivalent quantique du soliton brillant de la theorie de champ classique, et qui renferme toutes les particules du systeme, a l'exception d'une petite fraction gazeuse composee essentiellement d'atomes.

cond-mat.quant-gas↗