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arXiv:0910.4165 · New Journal of Physics

Off-diagonal correlations in a one-dimensional gas of dipolar bosons

Tommaso Roscilde, Massimo Boninsegni

Published Mar 16, 2010• 12 citations
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Abstract

We present a quantum Monte Carlo study of the one-body density matrix (OBDM) and the momentum distribution of one-dimensional (1D) dipolar bosons, with dipole moments polarized perpendicular to the direction of confinement. We observe that the long-range nature of the dipole interaction has dramatic effects on the off-diagonal correlations: although the dipoles never crystallize, the system goes from a quasi-condensate regime at low interactions to a regime in which quasi-condensation is discarded in favor of quasi-solidity. For all strengths of the dipolar interaction we considered, the OBDM shows an oscillatory behavior coexisting with an overall algebraic decay, while the momentum distribution shows sharp kinks at the wavevectors of the oscillations, Q =±2π n (where n is the atom density), beyond which it is strongly suppressed. This momentum filtering effect introduces a characteristic scale in the momentum distribution, which can be arbitrarily squeezed by lowering the atom density. This shows that 1D dipolar Bose gases, realized e.g. by trapped dipolar molecules, show strong signatures of the dipolar interaction in time-of-flight measurements.

DOI
10.1088/1367-2630/12/3/033032

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We present a quantum Monte Carlo study of the one-body density matrix (OBDM) and the momentum distribution of one-dimensional (1D) dipolar bosons, with dipole moments polarized perpendicular to the direction of confinement. We observe that the long-range nature of the dipole interaction has dramatic effects on the off-diagonal correlations: although the dipoles never crystallize, the system goes from a quasi-condensate regime at low interactions to a regime in which quasi-condensation is discarded in favor of quasi-solidity. For all strengths of the dipolar interaction we considered, the OBDM shows an oscillatory behavior coexisting with an overall algebraic decay, while the momentum distribution shows sharp kinks at the wavevectors of the oscillations, Q =±2π n (where n is the atom density), beyond which it is strongly suppressed. This momentum filtering effect introduces a characteristic scale in the momentum distribution, which can be arbitrarily squeezed by lowering the atom density. This shows that 1D dipolar Bose gases, realized e.g. by trapped dipolar molecules, show strong signatures of the dipolar interaction in time-of-flight measurements.
We study the ground state of few bosons with repulsive dipole-dipole interaction in a quasi-one-dimensional harmonic trap by means of the exact diagonalization method. Up to three interaction regimes are found, depending on the strength of the dipolar interaction and the ratio of transverse to axial oscillator lengths: a regime where the dipolar Bose gas resembles a system of weakly $\ensuremath{\delta}$-interacting bosons, a second regime where the bosons are fermionized, and a third regime where the bosons form a Wigner crystal. In the first two regimes, the dipole-dipole potential can be replaced by a $\ensuremath{\delta}$ potential. In the crystalline state, the overlap between the localized wave packets is strongly reduced and all the properties of the boson system equal those of its fermionic counterpart. The transition from the Tonks-Girardeau gas to the solidlike state is accompanied by a rapid increase of the interaction energy and a considerable change of the momentum distribution, which we trace back to the different short-range correlations in the two interaction regimes.
Ultracold bosonic and fermionic quantum gases confined to quasi-one-dimensional (1D) geometry are promising candidates for probing fundamental concepts of Luttinger liquid (LL) physics. They can also be exploited for devising applications in quantum information processing and precision measurements. Here, we focus on 1D dipolar Bose gases, where evidence of super-strong coupling behavior has been demonstrated by analyzing the low-energy static and dynamical structures of the fluid at zero temperature by a combined reptation quantum Monte Carlo (RQMC) and bosonization approach. Fingerprints of LL behavior emerge in the whole crossover from the already strongly interacting Tonks–Girardeau at low density to a dipolar density wave regime at high density. We have also shown that a LL framework can be effectively set up and utilized to describe this strongly correlated crossover physics in the case of confined 1D geometries after using the results for the homogeneous system in LL hydrodynamic equations within a local density approximation. This leads to the prediction of observable quantities such as the frequencies of the collective modes of the trapped dipolar gas under the more realistic conditions that could be found in ongoing experiments. The present paper provides a description of the theoretical framework in which the above results have been worked out, making available all the detailed derivations of the hydrodynamic Luttinger equations for the inhomogeneous trapped gas and of the correlation functions for the homogeneous system.
We explore the effect of tunable integrability breaking dipole-dipole interactions in the equilibrium states of highly magnetic 1D Bose gases of dysprosium at low temperatures. We experimentally observe that in the strongly correlated Tonks-Girardeau regime, rapidity and momentum distributions are nearly unaffected by the dipolar interactions. By contrast, we also observe that significant changes of these distributions occur when decreasing the strength of the contact interactions. We show that the main experimental observations are captured by modeling the system as an array of 1D gases with only contact interactions, dressed by the contribution of the short-range part of the dipolar interactions. Improvements to theory-experiment correspondence will require new tools tailored to near-integrable models possessing both short and long-range interactions.
In this paper we consider dipolar quantum gases in a quasi-one-dimensional tube with dipole moment perpendicular to the tube direction. We deduce the effective one-dimensional interaction potential and show that this potential is not purely repulsive, but rather has an attractive part due to high-order scattering processes through transverse excited states. The attractive part can induce bound states and cause scattering resonances. This represents the dipole-induced resonance in low dimension. We work out an unconventional behavior of low-energy phase shift for this effective potential and show how it evolves across a resonance. Based on the phase shift, the interaction energy of spinless bosons is obtained using the asymptotic Bethe ansatz. Despite the long-range nature of dipolar interaction, we find that the behavior is similar to a short-range Lieb-Liniger gas emerging at the resonance region.
Strongly interacting finite ensembles of dipolar bosons in commensurately filled one-dimensional optical lattices exhibit diverse quantum phases that are rich in physics. As the strength of the long-range boson–boson interaction increases, the system transitions across different phases: from a superfluid, through a Mott-insulator and a Tonks–Girardeau gas to a crystal state. The signature of these phases and their transitions can be unequivocally identified by an experimentally detectable order parameter, recently described in Phys. Rev. A 98 235301 (2018 [ 33 ]). Herein, we calculate the momentum distributions and the normalized Glauber correlation functions of dipolar bosons in a one-dimensional optical lattice in order to characterize all their phases. To understand the behavior of the correlations across the phase transitions, we first investigate the eigenfunctions and eigenvalues of the one-body reduced density matrix as a function of the dipolar interaction strength. We then analyze the real- and momentum-space Glauber correlation functions, thereby gaining a spatially and momentum-resolved insight into the coherence properties of these quantum phases. We find an intriguing structure of non-local correlations that, independently of other observables, reveal the phase transitions of the system. In particular, spatial localization and momentum delocalization accompany the formation of correlated islands in the density as interactions become stronger. Our study showcases that precise control of intersite correlations is possible through the manipulation of the depth of the lattice, while intrasite correlations can be influenced by changing the dipolar interaction strength.
A strongly correlated Luttinger-liquid behavior is found to emerge well beyond the Tonks-Girardeau (TG) regime in a one-dimensional Bose gas with dipolar repulsions at T=0T=0T=0, persisting for a wide range of densities. After combining reptation quantum Monte Carlo and bosonization techniques, we provide a unifying theory of the underlying crossover physics, evolving from the TG gas at low density into a classical quasiordered state at high density. The density dependent Luttinger parameters extracted from the numerical data provide all that is needed to determine the low-energy behavior from analytical expressions. Our quantitative predictions, in the whole crossover, for measurable quantities such as the structure factor and the momentum distribution, are estimated to be accessible in underway experiments with ultracold polar molecules.