Bosonizing one-dimensional cold atomic gases

Abstract

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 to compute 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 Montecarlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.

39 pages + 14 EPS figures; typos corrected, references updated

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• Are the Tonks regimes in the continuum and on the lattice truly equivalent?
• Experimental Observation of Curved Light-Cones in a Quantum Field Simulator
• Luttinger Liquid in Non-equilibrium Steady State
• Entanglement entropies of inhomogeneous Luttinger liquids
• Relaxation of Bosons in One Dimension and the Onset of Dimensional Crossover
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• Interferometric probe of paired states
• Quantum decoupling transition in a one-dimensional Feshbach-resonant superfluid
• Continuous matrix product states for non-relativistic quantum fields: a lattice algorithm for inhomogeneous systems
• Polar bosons in one-dimensional disordered optical lattices
• Disordered one-dimensional Bose-Fermi mixtures: The Bose-Fermi glass
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• Theory of Electromagnetically Induced Transparency in Strongly Correlated Quantum Gases
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• Entanglement dynamics of a hard-core quantum gas during a Joule expansion
• Separation of quadrupole, spin, and charge across the magnetic phases of a one-dimensional interacting spin-1 gas
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