We develop an exact solution to the problem of one dimensional chiral bosons interacting via an s-wave Feshbach resonance. This problem is integrable, being the quantum analog of a classical two-wave model solved by the inverse scattering method thirty years ago. Its solution describes one or two branches of dressed chiral right moving molecules depending on the chemical potential (particle density). We also briefly discuss the possibility of experimental realization of such a system.
We develop an exact solution to the problem of one dimensional chiral bosons interacting via an s-wave Feshbach resonance. This problem is integrable, being the quantum analog of a classical two-wave model solved by the inverse scattering method thirty years ago. Its solution describes one or two branches of dressed chiral right moving molecules depending on the chemical potential (particle density). We also briefly discuss the possibility of experimental realization of such a system.
Abstract We study a model of two species of 1D linearly dispersing fermions interacting via an s-wave Feshbach resonance at zero temperature. While this model is known to be integrable, it possesses novel features that have not previously been investigated. Here, we present an exact solution based on the coordinate Bethe Ansatz. In the limit of infinite resonance strength, which we term the strongly interacting limit, the two species of fermions behave as free Fermi gases. In the limit of infinitely weak resonance, or the weakly interacting limit, the gases can be in different phases depending on the detuning, the relative velocities of the particles, and the particle densities. When the molecule moves faster or slower than both species of atoms, the atomic velocities get renormalized and the atoms may even become non-chiral. On the other hand, when the molecular velocity is between that of the atoms, the system may behave like a weakly interacting Lieb–Liniger gas.
We present a study of a gas of bosons confined in one dimension with Feshbach-resonant interactions, at zero temperature. Unlike the gas of one-dimensional bosons with non resonant interactions, which is known to be equivalent to a system of interacting spinless fermions and can be described using the Luttinger liquid formalism, the resonant gas possesses additional features. Depending on its parameters, the gas can be in one of three possible regimes. In the simplest of those, it can still be described by the Luttinger liquid theory, but its Fermi momentum cannot be larger than a certain cutoff momentum dependent on the details of the interactions. In the other two regimes, it is equivalent to a Luttinger liquid at low density only. At higher densities its excitation spectrum develops a minimum, similar to the roton minimum in helium, at momenta where the excitations are in resonance with the Fermi sea. As the density of the gas is increased further, the minimum dips below the Fermi energy, thus making the ground state unstable. At this point the standard ground state gets replaced by a more complicated one, where not only the states with momentum below the Fermi points, but also the ones with momentum close to that minimum, get filled, and the excitation spectrum develops several branches. We are unable so far to study this regime in detail due to the lack of the appropriate formalism.
We discuss an integrable model of interacting fermions in one dimension that allows a complete description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 fermions to the Lieb-Liniger model of repulsive bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from -infinity to +infinity while the system evolves from a BCS-like state through a Tonks-Girardeau gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.
We discuss the BCS-BEC crossover for one-dimensional spin-1∕2 fermions at zero temperature using the boson-fermion resonance model in one dimension. We show that in the limit of a broad resonance, this model is equivalent to an exactly solvable single-channel model, the so-called modified Gaudin-Yang model. We argue that the one-dimensional crossover may be realized either via the combination of a Feshbach resonance and a confinement-induced resonance or using direct photoassociation in a two-component Fermi gas with effectively one-dimensional dynamics. In both cases, the system may be driven from a BCS-like state through a molecular Tonks-Girardeau gas close to resonance to a weakly interacting Bose gas of dimers.
We introduce a family of integrable spin-boson models, focusing on a particular realization describing a system of spinless fermions interacting through a p-wave Feshbach resonance. Unlike the BCS-BEC crossover of the s-wave case, the p-wave model has a third-order quantum phase transition. The critical point coincides with the deconfinement of a single molecule within a BEC of bound dipolar molecules. The exact many-body wave function yields a unique perspective of the quantum critical region, suggesting that the size of the condensate wave function that diverges logarithmically with the chemical potential could be used as an experimental indicator of the phase transition.
The use of Feshbach resonances in the field of ultracold gases has received a lot of attention recently. In first instance it was realized that these resonances can be used to alter the interaction strength in an atomic gas, by means of tuning an external magnetic field. Furthermore, by sweeping the magnetic field from one side of the resonance to the other, a degenerate gas of bosonic molecules can be created, a significant accomplishment. By making the interactions between fermionic atoms strongly attractive, a fermionic superfluid was recently made, a feat that has drawn a lot of attention in the physics community and from the media. We present work that describes these many-particle systems near a Feshbach resonance in a comprehensive way by using the concept of dressed molecules. These dressed molecules are essentially two-particle states that are a superposition of a tightly bound bare molecule, and two unbound bare atoms. This description reduces to the correct paired wave-function in the two-body limit. Moreover it gives a physically correct description of all the phenomena mentioned above: the Bose-condensation of a gas near a Feshbach resonance, that contains molecules, is more correctly interpreted as a Bose-condensation of dressed molecules. The fermionic superfluid contains a condensate of bosonic pairs, normally called Cooper pairs, that can be understood as the dressed molecules. For the latter case, the dressed-molecule picture also gives an elegant characterization of the crossover between a Bose condensate of pure molecules on one side of the resonance, to a fermionic Bardeen-Cooper-Schrieffer superfluid on the other side. Then, the dressed molecules change continuously from being mostly a bare molecule, to being mostly a loose pair of two atoms. It is clear that the nature of the dressed molecules is much determined by the probability for it to be in the bare-molecular state. This probability we denote with a single parameter Z. We present various ways of calculating it, and study how it affects the macroscopic physics.