# One-dimensional gas of bosons with Feshbach-resonant interactions

## Abstract

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 onesmore »

- Authors:

- Department of Physics, CB390, University of Colorado, Boulder, Colorado 80309 (United States)

- Publication Date:

- OSTI Identifier:
- 20786970

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.033612; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ABSORPTION SPECTRA; BOSONS; DENSITY; EXCITATION; FERMIONS; GROUND STATES; LIQUIDS; RESONANCE

### Citation Formats

```
Gurarie, V.
```*One-dimensional gas of bosons with Feshbach-resonant interactions*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Gurarie, V.
```*One-dimensional gas of bosons with Feshbach-resonant interactions*. United States. doi:10.1103/PHYSREVA.73.0.

```
Gurarie, V. Wed .
"One-dimensional gas of bosons with Feshbach-resonant interactions". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20786970,
```

title = {One-dimensional gas of bosons with Feshbach-resonant interactions},

author = {Gurarie, V.},

abstractNote = {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.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 3,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}