Bosonizing one-dimensional cold atomic gases

By M. Cazalilla. 2003

312 citations recorded by the source corpus.

We present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The results are obtained using Haldane's harmonic-fluid approach (also known as 'bosonization'), and are valid for both bosons and fermions, in weakly and strongly interacting regimes. The harmonic-fluid approach and the method of computing the correlation functions using conformal transformations are explained in great detail. As an application relevant to one-dimensional systems of cold atomic gases, we consider the model of bosons interacting with a zero-range potential. The Luttinger-liquid parameters are obtained from the exact solution by solving the Bethe-ansatz equations in finite-size systems. The range of applicability of the approach is discussed, and the prefactor of the one-body density matrix of bosons is fixed by finding an appropriate parametrization of the weak-coupling result. The formula thus obtained is shown to be accurate, when compared with recent diffusion Monte Carlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/485f6907c1af062b36aedf381486e70bad8a9e73

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. I. Bloch
2. A. Polkovnikov
3. Marcos Rigol
4. J. Dalibard
5. V. Gritsev
6. W. Zwerger
7. Jörg Schmiedmayer
8. E. Demler

In Condensed Matter Physics

1. I. Bloch
2. A. Imambekov
3. J. Dalibard
4. W. Zwerger
5. A. Polkovnikov
6. T. Schmidt
7. L. Glazman
8. Marcos Rigol

Citations in the corpus

• Probing quantum and thermal noise in an interacting many-body system (2007, methodology): “The effective approach to the Lieb-Liniger model, capturing the long-distance behavior of all correlation functions is known as the Luttinger liquid formalism [35, 36, 37].”
• One dimensional bosons: From condensed matter systems to ultracold gases (2011, methodology): “In addition, on the lattice it is also possible to show (see e.g. the appendix in Cazalilla (2004a)) the equivalence of the Jordan-Wigner approximation and Girardeau’s Bose-Fermi mapping, which applies to the many-body wavefunctions of both models and is reviewed in Sec.”
• Phase space representation of quantum dynamics (2009, background): “(Cazalilla, 2004; De Grandi et al., 2008), where large K corresponds to weak interactions 41 spectrum of the SG model is quite rich.”
• Tonks–Girardeau gas of ultracold atoms in an optical lattice (2004, background): “At finite temperatures a new momentum scale sets i”
• Many-Body Physics with Ultracold Gases (2007, methodology): “Indeed, the Bose-Hubbard model in one dimension at n 1 describes a Luttinger liquid with K = 1 + 4πn/γL + . . ., where γL = U/J is the effective coupling parameter on a lattice (Cazalilla, 2004).”
• One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm (2011, background): “For example, for spinless fermions at ρ|x±vt| 1, one has (Cazalilla, 2004)〈 Ψ†(0, 0)Ψ(x, t) 〉 LL ∼ (136)∑ n ρei(2n+1)kF x 2i(−1)n Cn (iρ(vt+ x) + 0) µL (iρ(vt− x) + 0)µR , where Cn are “nonuniversal” prefactors, and µR(L) = (2n+ 1) 2K/4± (2n+ 1)/2 + 1/4K ≥ 0.”