arXiv subjects

Ludovic Pricoupenko

Publications and source records attributed to Ludovic Pricoupenko.

At least 19 recordsLinked to original sources

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↗

arXiv2025

Universal spectrum of isolated three-body resonances

The exact wavefunction of an isolated three-body resonance at finite scattering length is obtained for two identical particles interacting with another one via a pairwise zero-range potential. The corresponding universal spectrum is studied as a function of the scattering length. The universality of the results is illustrated by considering a model with finite-range interactions.

cond-mat.quant-gas↗

arXiv2023

General features and contact modeling of $N$-body isolated resonances near threshold

$N$-body non efimovian bound or quasi-bound states for particles with short range interactions are considered in arbitrary dimensions. The different resonance regimes near the threshold are depicted by using a generalization of the effective range approximation. This two-parameter description can be used in various contexts from ultra-cold to hadronic physics. The universal character of these states makes it possible a formulation in terms of a contact model. The singularity at the contact imposes the introduction of a modified scalar product to solve the normalization catastrophe and to restore the self-adjoint character of the model. An equivalence with the standard scalar product used for realistic finite range models is derived.

cond-mat.quant-gas↗

arXiv2023

Universality of isolated $N$-body resonances at large scattering length

Non Efimovian $N$-body resonances are investigated in the regime of a large two-body s wave scattering length. In view of a universal description of low-energy bound and quasi-bound states, a contact model is introduced. The modeling requires two parameters in addition to the scattering length. Using a modified scalar product, the contact model provides a normalization of bound states, possibly not square-integrable, that coincides with that of the corresponding finite range model.

cond-mat.quant-gas↗

arXiv2022

Shallow Trimers of Two Identical Fermions and One Particle in Resonant Regimes

We consider two identical fermions interacting in the p-wave channel. Each fermion also interacts with another particle in the vicinity of an s-wave resonance. We find that in addition to the Kartavtsev-Malykh universal trimer states resulting from the s-wave particle-fermion interaction, the fermion-fermion p-wave interaction induces one or two shallow trimers in a large domain of the control parameters, including a borromean regime where the ground-state trimer exists in the absence of dimers at any mass ratio between the fermions and the particle. A generic picture of the trimer spectrum emerges from this work in terms of the low-energy parameters of the interactions.

cond-mat.quant-gas↗

arXiv2019

Width and shift of Fano-Feshbach resonances for van der Waals interactions

We revisit the basic properties of Fano-Feshbach resonances in two-body systems with van der Waals tail interactions, such as ultracold neutral atoms. Using a two-channel model and two different methods, we investigate the relationship between the width and shift of the resonances and their dependence on the low-energy parameters of the system. Unlike what was previously believed [Rev. Mod. Phys. 82, 1225 (2010)] for magnetic resonances, we find that the ratio between the width and the shift of a resonance does not depend only on the background scattering length, but also on a closed-channel scattering length. We obtain different limits corresponding to different cases of optical and magnetic resonances. Although the generalisation of the theory to the multi-channel case remains to be done, we found that our two-channel predictions are verified for a specific resonance of lithium-6.

cond-mat.quant-gas↗

arXiv2018

The three-body pseudo-potential for atoms confined in one dimension

Following a strong analogy with two-dimensional physics, the three-body pseudo-potential in one dimension is derived. The Born approximation is then considered in the context of ultracold atoms in a linear harmonic waveguide. In the vicinity of the dimer threshold a direct connection is made between the zero-range potential and the dimensional reduction of the three-body Schr{ö}dinger equation.

cond-mat.quant-gas↗

arXiv2018

A Pure Confinement Induced Trimer in One-Dimensional Atomic Waveguides

Shallow trimers composed of three bosonic atoms in one-dimensional harmonic waveguides are studied in the vicinity of a Feshbach resonance. It is shown that for arbitrarily large values of the one-dimensional scattering length, an excited trimer branch exists in coexistence with the dimer and the trimer of the Lieb-Liniger model.

cond-mat.quant-gas↗

arXiv2016

Second-order virial expansion for an atomic gas in a harmonic waveguide

The virial expansion for cold two-component Fermi and Bose atomic gases is considered in the presence of a waveguide and in the vicinity of a Feshbach resonance. The interaction between atoms and the coupling with the Feshbach molecules is modeled using a quantitative separable two-channel model. The scattering phase-shift in an atomic waveguide is defined. This permits us to extend the Beth-Uhlenbeck formula for the second-order virial coefficient to this inhomogeneous case.

cond-mat.quant-gas↗

arXiv2016

One-dimensional ultracold atomic gases: Impact of the effective range on integrability

Three identical bosons or fermions are considered in the limit of zero-range interactions and finite effective range. By using a two channel model, we show that these systems are not integrable and that the wave function verifies specific continuity conditions at the contact of three particles. This last feature permits us to solve a contradiction brought by the contact model which can lead to an opposite result concerning the integrability issue. For fermions, the vicinity of integrability is characterized by large deviations with respect to the predictions of the Bethe ansatz.

cond-mat.quant-gas↗

arXiv2015

Ultracold-atom collisions in atomic waveguides : A two-channel analysis

Low dimensional behavior of two ultra-cold atoms trapped in two-and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with the ones of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known resonances are used to illustrate the bound state properties.

cond-mat.quant-gas↗

arXiv2013

Many Bosons in a Narrow Magnetic Feshbach Resonance

The many-boson problem in presence of an asymptotically narrow Feshbach resonance is considered. The low energy properties are investigated using a two-channel Hamiltonian. The energy spectrum of this model is shown to be bounded from below in the limit of zero range interaction. This implies the promising possibility of achieving a strongly interacting bosonic phase in a dilute regime where the details of the actual interatomic forces are irrelevant. The integral relation between the energy and the one-body momentum distribution is derived.

quant-ph↗

arXiv2011

Modified scalar product for the effective range approach: the molecular contribution

The modified scalar product which permits to restore the self-adjoint character of the effective range approach is derived for one-channel contact models where a more general internal structure is included. In the case of the effective range approach, the modified scalar product is interpreted in the light of a generic two-channel model for a narrow Feshbach resonance as a way to take into account implicitly the molecular contribution of the closed channel.

quant-ph↗

arXiv2011

Ultracold bosons in the vicinity of a narrow resonance: shallow dimer and recombination

The different resonant regimes that can be achieved by using a magnetic Feshbach resonance are analyzed with a separable two-channel model. Emphasis is put on the case of narrow resonances in a region of intermediate detuning where a shallow dimer exists and an approximate law including the background scattering length for the three-body recombination rate is derived.

cond-mat.quant-gas↗

arXiv2011

Isotropic contact forces in arbitrary representation: heterogeneous few-body problems and low dimensions

The Bethe-Peierls asymptotic approach which models pairwise short-range forces by contact conditions is introduced in arbitrary representation for spatial dimensions less than or equal to 3. The formalism is applied in various situations and emphasis is put on the momentum representation. In the presence of a transverse harmonic confinement, dimensional reduction toward two-dimensional (2D) or one-dimensional (1D) physics is derived within this formalism. The energy theorem relating the mean energy of an interacting system to the asymptotic behavior of the one-particle density matrix illustrates the method in its second quantized form. Integral equations that encapsulate the Bethe-Peierls contact condition for few-body systems are derived. In three dimensions, for three-body systems supporting Efimov states, a nodal condition is introduced in order to obtain universal results from the Skorniakov Ter-Martirosian equation and the Thomas collapse is avoided. Four-body bound state eigenequations are derived and the 2D '3+1' bosonic ground state is computed as a function of the mass ratio.

cond-mat.quant-gas↗

arXiv2011

Implicit ladder summation in the Hartree-Fock-Bogoliubov approach

The fully variational Hartree Fock Bogoliubov approach for bosons is studied in the limit of zero range forces in two- and three-dimensions. The equation of state obtained in two-dimensions is expressed in a parametric form. It is shown that the $Λ$ potential permits to perform an implicit summation of the ladder diagrams without leaving the variational scheme, restoring thus the consistency of this approximation.

cond-mat.quant-gas↗

arXiv2010

Crossover in the Efimov spectrum

A filtering method is introduced for solving the zero-range three-boson problem. This scheme permits to solve the original Skorniakov Ter-Martirosian integral equation for an arbitrary large Ultra-Violet cut-off and to avoid the Thomas collapse of the three particles. The method is applied to a more general zero-range model including a finite background two-body scattering length and the effective range. A cross-over in the Efimov spectrum is found in such systems and a specific regime emerges where Efimov states are long-lived.

cond-mat.quant-gas↗

arXiv2010

Universal 1+2-body bound states in planar atomic wave guides

Shallow heteronuclear trimers are predicted for mixtures of two atomic species strongly trapped in a quasi two-dimensional atomic wave guide. The binding energies are functions of the 2D-scattering length and of the mass ratio and can be thus tuned by various ways. These universal trimers are composed of two identical non interacting particles and of a third particle of the other species. Depending on the statistics of the two identical particles, the trimers have an odd (fermions) or even (bosons) internal angular momentum. These results permit to draw conclusions on the stability issue for the quasi-2D gaseous phase of heteronuclear dimers.

cond-mat.other↗