Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

This paper reviews the recent theoretical and experimental advances in the study of ultra-cold gases made of bosonic particles interacting via the long-range, anisotropic dipole–dipole interaction, in addition to the short-range and isotropic contact interaction usually at work in ultra-cold gases. The specific properties emerging from the dipolar interaction are emphasized, from the mean-field regime valid for dilute Bose–Einstein condensates, to the strongly correlated regimes reached for dipolar bosons in optical lattices. (Some figures in this article are in colour only in the electronic version)

https://iopscience.iop.org/article/10.1088/0034-4885/72/12/126401/pdf

The physics of dipolar bosonic quantum gases

The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger liquids relevant for one-dimensional Bose fluids is introduced, and compared with Bose-Einstein condensates existing in dimensions higher than one. The effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations. Finally, the experimental systems that can be described in terms of models of interacting bosons in one dimension are discussed.

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One dimensional bosons: From condensed matter systems to ultracold gases

M. A. Baranov,†,‡,§ M. Dalmonte,†,⊥ G. Pupillo,†,‡,∇ and P. Zoller*,†,‡ †Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria ‡Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria RRC “Kurchatov Institute”, Kurchatov Square 1, 123182, Moscow, Russia Dipartimento di Fisica dell’Universita di Bologna, via Irnerio 46, 40126 Bologna, Italy ISIS (UMR 7006) and IPCMS (UMR 7504), Universite de Strasbourg and CNRS, Strasbourg, France

/pdf/condensed-matter-theory-of-dipolar-quantum-gases-4meo4upruy.pdf

Condensed matter theory of dipolar quantum gases.

We study the superfluid properties of a system of fully polarized dipolar bosons moving in the $XY$ plane. We focus on the general case where the polarization field forms an arbitrary angle $\ensuremath{\alpha}$ with respect to the $Z$ axis, while the system is still stable. We use the diffusion Monte Carlo and the path integral ground state methods to evaluate the one-body density matrix and the superfluid fractions in the region of the phase diagram where the system forms stripes. Despite its oscillatory behavior, the presence of a finite large-distance asymptotic value in the $s$-wave component of the one-body density matrix indicates the existence of a Bose condensate. The superfluid fraction along the stripes direction is always close to 1, while in the $Y$ direction decreases to a small value that is nevertheless different from zero. These two facts confirm that the stripe phase of the dipolar Bose system is a clear candidate for an intrinsic supersolid without the presence of defects as described by the Andreev-Lifshitz mechanism.

/pdf/dipolar-bose-supersolid-stripes-4967y8xmph.pdf

Dipolar Bose Supersolid Stripes

We consider the ground state of a bilayer system of dipolar bosons, where dipoles are oriented by an external field in the direction perpendicular to the parallel planes. Quantum Monte Carlo methods are used to calculate the ground-state energy, the one-body and two-body density matrix, and the superfluid response as a function of the separation between layers. We find that by decreasing the interlayer distance for fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from a single-particle to a pair superfluid. The single-particle superfluid is characterized by a finite value of both the atomic condensate and the super-counterfluid density. The pair superfluid phase is found to be stable against formation of many-body cluster states and features a gap in the spectrum of elementary excitations.

/pdf/single-particle-versus-pair-superfluidity-in-a-bilayer-431p8zqez4.pdf

Single-particle versus pair superfluidity in a bilayer system of dipolar bosons

The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. We propose to use the concept of energy-dependent s-wave scattering length for obtaining estimations of nonuniversal terms in the energy expansion. We test this approach by making a comparison to exactly solvable one-dimensional problems and find that the generated terms have the correct structure. The applicability to two-dimensional systems is analyzed by comparing with results of Monte Carlo simulations. The prediction for the nonuniversal behavior is qualitatively correct and the densities, at which the deviations from the universal equation of state become visible, are estimated properly. Finally, the possibility of observing the nonuniversal terms in experiments with trapped gases is also discussed.

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Low-dimensional weakly interacting Bose gases: Nonuniversal equations of state

A detailed microscopic analysis of the dynamic structure function S(k,omega) of a two-dimensional Bose system of dipoles polarized along the direction perpendicular to the plane is presented and discussed. Starting from ground-state quantities obtained using a quantum diffusion Monte Carlo algorithm, the density-density response is evaluated in the context of the correlated basis functions (CBF) theory. CBF predicts a sharp peak and a multiexcitation component at higher energies produced by the decay of excitations. We discuss the structure of the phonon-roton peak and show that the Feynman and Bogoliubov predictions depart from the CBF result already at low densities. We finally discuss the emergence of a roton in the spectrum, but find the roton energy not low enough to make the system unstable under density fluctuations up to the highest density considered that is close to the freezing point.

Dynamics of a two-dimensional system of quantum dipoles.

A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.

/pdf/microscopic-description-of-anisotropic-low-density-dipolar-1nsmi2olgm.pdf

Ferran Mazzanti

Papers

Dipolar Bose Supersolid Stripes

Single-particle versus pair superfluidity in a bilayer system of dipolar bosons

Low-dimensional weakly interacting Bose gases: Nonuniversal equations of state

Dynamics of a two-dimensional system of quantum dipoles.

Microscopic description of anisotropic low-density dipolar Bose gases in two dimensions