arXiv subjects

Manuel Valiente

Publications and source records attributed to Manuel Valiente.

50 records · Page 3Linked to original sources

arXiv2012

Single-branch theory of ultracold Fermi gases with artificial Rashba spin-orbit coupling

We consider interacting ultracold fermions subject to Rashba spin-orbit coupling. We construct a single-branch interacting theory for the Fermi gas when the system is dilute enough so that the positive helicity branch is not occupied at all in the non-interacting ground state. We show that the theory is renormalizable in perturbation theory and therefore yields a model of polarized fermions that avoids a multi-channel treatment of the problem. Our results open the path towards a much more straightforward approach to the many-body physics of cold atoms subject to artificial vector potentials.

cond-mat.quant-gas↗

arXiv2012

Universal properties of Fermi gases in arbitrary dimensions

We consider spin-1/2 Fermi gases in arbitrary, integer or non-integer spatial dimensions, interacting via a Dirac delta potential. We first generalize the method of Tan's distributions and implement short-range boundary conditions to arbitrary dimension and we obtain a set of universal relations for the Fermi gas. Three-dimensional scattering under very general conditions of transversal confinement is described by an effectively reduced-dimensional scattering length, which we show depends on the three-dimensional scattering length in a universal way. Our formula for non-integer dimensions interpolates between the known results in integer dimensions 1, 2 and 3. Without any need to solve the associated multichannel scattering problem, we find that confinement-induced resonances occur in all dimensions different from D=2, while reduced-dimensional contacts, related to the tails of the momentum distributions, are connected to the three-dimensional contact by a correction factor of purely geometric origin.

hep-th↗

arXiv2012

Exact equivalence between one-dimensional Bose gases interacting via hard-sphere and zero-range potentials

We prove the equivalence between the hard-sphere Bose gas and a system with momentum-dependent zero-range interactions in one spatial dimension, which we call extended hard-sphere Bose gas. The two-body interaction in the latter model has the advantage of being a regular pseudopotential. The most immediate consequence is the existence of its Fourier transform, permitting the formulation of the problem in momentum space, not possible with the original hard-core interaction. In addition, in the extended system, interactions are defined in terms of the scattering length, positive or negative, identified with the hard-sphere diameter only when it is positive. We are then able to obtain, directly in the thermodynamic limit, the ground state energy of the strongly repulsive Lieb-Liniger gas and, more importantly, the energy of the lowest-lying super Tonks-Girardeau gas state with finite, strongly attractive interactions, in perturbation theory from the novel extended hard-sphere Bose gas. Tan relations involving the large-momentum behavior of the Lieb-Liniger gas are also derived, and then applied to the super Tonks-Girardeau gas within our perturbative approach.

cond-mat.quant-gas↗

arXiv2011

Universal relations for the two-dimensional spin-1/2 Fermi gas with contact interactions

We present universal relations for a two-dimensional Fermi gas with pairwise contact interactions. The derivation of these relations is made possible by obtaining the explicit form of a generalized function -- selector -- in the momentum representation. The selector implements the short-distance boundary condition between two fermions in a straightforward manner, and leads to simple derivations of the universal relations, in the spirit of Tan's original method for the three-dimensional gas.

cond-mat.quant-gas↗

arXiv2011

Tan's distributions and Fermi-Huang pseudopotential in momentum space

The long-standing question of finding the momentum representation for the s-wave zero-range interaction in three spatial dimensions is here solved. This is done by expressing a certain distribution, introduced in a formal way by S. Tan [Ann. Phys. 323, 2952 (2008)], explicitly. The resulting form of the Fourier-transformed pseudopotential remains very simple. Operator forms for the so-called Tan's selectors which, together with Fermi-Huang pseudopotential, largely simplify the derivation of Tan's universal relations for the Fermi gas, are here derived and are also very simple. A momentum cut-off version of the pseudopotential is also provided, and with this no apparent contradiction with the notion of integrals in Tan's methods is left. The equivalence, even at the intermediate step level, between the pseudopotential approach and momentum-space renormalization of the bare Dirac delta interaction is then shown by using the explicit form of the cut-off pseudopotential.

cond-mat.other↗

arXiv2011

Lattice oscillator model, scattering theory and a many-body problem

We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be annihilated by the annihilation operator defined here, and its excitation spectrum is obtained numerically. The versatility of the model is then used to calculate, in a simple way, the generalized position-dependent scattering length for a particle colliding with a single static impurity in a periodic potential and the exact ground state of an interacting many-body problem in a one-dimensional ring.

quant-ph↗

arXiv2011

Quasi-one-dimensional scattering in a discrete model

We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasi- momenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonance appear due to the non-separability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann- Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.

quant-ph↗

arXiv2010

Frustrated collisions and unconventional pairing on a quantum superlattice

We solve the problem of scattering and binding of two spin-1/2 fermions on a one-dimensional superlattice with a period of twice the lattice spacing analytically. We find the exact bound states and the scattering states, consisting of a generalized Bethe ansatz augmented with an extra scattering product due to "asymptotic" degeneracy. If a Bloch band is doubly occupied, the extra wave can be a bound state in the continuum corresponding to a single-particle interband transition. In all other cases, it corresponds to a quasi-momentum changing, frustrated collision.

cond-mat.str-el↗

arXiv2010

Lattice two-body problem with arbitrary finite range interactions

We study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering states and the "low-energy" solutions by very efficient and easy-to-implement numerical means. All bound states are proven to be characterized by roots of a polynomial whose degree depends linearly on the range of the potential, and we discuss the connections between the number of bound states and the scattering lengths. "Low-energy" resonances can be located with great precission with the methods we introduce. Further generalizations to include more exotic interactions are also discussed.

cond-mat.other↗

arXiv2010

Exotic few-body bound states in a lattice

Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our recent work on complete characterization of the bound and scattering states of two and three bosonic atoms in a one-dimensional optical lattice. In the case of two atoms, there is a family of interaction-bound "dimer" states of co-localized particles that exists invariantly for either attractive or repulsive on-site interaction, with the energy below or above the two-particle scattering continuum, respectively. Adding then the third particle -- "monomer" -- we find that, apart from the simple strongly-bound "trimer" corresponding to all three particles occupying the same lattice site, there are two peculiar families of weakly-bound trimers with energies below and above the monomer-dimer scattering continuum, the corresponding binding mechanism being an effective particle exchange interaction.

cond-mat.quant-gas↗

arXiv2009

Three-body bound states in a lattice

We pursue three-body bound states in a one-dimensional tight-binding lattice described by the Bose-Hubbard model with strong on-site interaction. Apart from the simple strongly-bound "trimer" state corresponding to all three particles occupying the same lattice site, we find two novel kinds of weakly-bound trimers with energies below and above the continuum of scattering states of a single particle ("monomer") and a bound particle pair ("dimer"). The corresponding binding mechanism can be inferred from an effective Hamiltonian in the strong-coupling regime which contains an exchange interaction between the monomer and dimer. In the limit of very strong on-site interaction, the exchange-bound trimers attain a universal value of the binding energy. These phenomena can be observed with cold atoms in optical lattices.

cond-mat.other↗

arXiv2009

Scattering resonances and two-particle bound states of the extended Hubbard model

We present a complete derivation of two-particle states of the one-dimensional extended Hubbard model involving attractive or repulsive on-site and nearest-neighbour interactions. We find that this system possesses scattering resonances and two families of energy-dependent interaction-bound states which are not present in the Hubbard model with the on-site interaction alone.

quant-ph↗

arXiv2008

Two-particle states in the Hubbard model

We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle states, which can be classified as (i) scattering states of asymptotically free particles and (ii) interaction-bound dimer states. Our results provide a very transparent framework to understand the properties of interacting pairs of particles in a lattice.

quant-ph↗

arXiv2008

Quantum dynamics of one and two bosonic atoms in a combined tight-binding periodic and weak parabolic potential

Strongly interacting bosonic particles in a tight-binding periodic potential superimposed by a weak parabolic trap is a paradigm for many cold atom experiments. Here, after revisiting the single particle problem, we study interaction-bound dimers of bosonic atoms in the combined lattice and parabolic potential. We consider both repulsively- and attractively-bound dimers and find pronounced differences in their behaviour. We identify conditions under which attractive and repulsive dimers exhibit analogous dynamics. Our studies reveal that coherent transport and periodic oscillations of appropriately prepared one- and two-atom wavepackets can be achieved, which may facilitate information transfer in optical lattice based quantum computation schemes.

quant-ph↗