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arXiv:0705.1668 · Physical Review Letters

Cold Dipolar Gases in Quasi-One-Dimensional Geometries

Subhasis Sinha, Luis Santos

Published Oct 5, 2007• 178 citations
arXivHTMLPDF

Abstract

We analyze the physics of cold dipolar gases in quasi-one-dimensional geometries, showing that the confinement-induced scattering resonances produced by the transversal trapping are crucially affected by the dipole-dipole interaction. As a consequence, the dipolar interaction may drastically change the properties of quasi-1D dipolar condensates, even for situations in which the dipolar interaction would be completely overwhelmed by the short-range interactions in a 3D environment.

DOI
10.1103/physrevlett.99.140406

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We analyze the physics of cold dipolar gases in quasi-one-dimensional geometries, showing that the confinement-induced scattering resonances produced by the transversal trapping are crucially affected by the dipole-dipole interaction. As a consequence, the dipolar interaction may drastically change the properties of quasi-1D dipolar condensates, even for situations in which the dipolar interaction would be completely overwhelmed by the short-range interactions in a 3D environment.
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.
We develop a theoretical framework for the quasi-low-dimensional confinement-induced resonances (CIRs) of particles with three-dimensional two-body interactions describable by the Huang-Yang pseudopotential. Using this approach, we analytically obtain the universal properties of dipolar CIRs in quasi-one-dimensional (quasi-1D) waveguides. We also show that the tilting angle between the dipole moment and the waveguide can be used as a control knob for scatterings in quasi-1D geometry. More importantly, the tilting-angle-induced dipolar CIRs in quasi-1D Cr, Er, and Dy atomic gases are experimentally detectable.
Dipolar quantum gases, encompassing atoms and molecules with significant dipole moments, exhibit unique long-range and anisotropic dipole-dipole interactions (DDI), distinguishing them from systems dominated by short-range contact interactions. This review explores their behavior across dimensions, focusing on magnetic atoms in quasi-2D in comparison to 3D. In 3D, strong DDI leads to phenomena like anisotropic superfluidity, quantum droplets stabilized by Lee-Huang-Yang corrections, and supersolid states with density modulations. In 2D, we discuss a new scenario where DDI induces angle-dependent Berezinskii-Kosterlitz-Thouless transitions and potential supersolidity, as suggested by recent experimental realizations of strongly dipolar systems in quasi-2D geometries. We identify key challenges for future experimental and theoretical work on strongly dipolar 2D systems. The review concludes by highlighting how these unique 2D dipolar systems could advance fundamental research as well as simulate novel physical phenomena.
Fundamental aspects of ultracold collisions between identical bosonic or fermionic dipoles are studied under quasi-two-dimensional (Q2D) confinement. In the strongly dipolar regime, bosonic and fermion species are found to share important collisional properties as a result of the confining geometry, which suppresses the inelastic rates irrespective of the quantum statistics obeyed. A potential negative is that the confinement causes dipole-dipole resonances to be extremely narrow, which could make it difficult to explore Q2D dipolar gases with tunable interactions. Such properties are shown to be universal, and a simple WKB model reproduces most of our numerical results. In order to shed light on the many-body behavior of dipolar gases in Q2D we have analyzed the scattering amplitude and developed an energy-analytic form of the pseudopotentials for dipoles.
Dipolar interactions support the formation of intersite soliton molecules in a stack of quasi-one-dimensional (quasi-1D) traps. We show that the stability and properties of individual solitons and soliton molecules in such a geometry crucially depend on the interplay between contact and dipolar interactions. In particular, two different quasi-1D soliton regimes are possible: a one-dimensional (1D) soliton characterized by purely repulsive dipole-dipole interactions (DDI) and a three-dimensional (3D) soliton for which a sufficiently large dipole moment renders the DDI attractive. Furthermore, we find that in contrast to the dimers of polar molecules the soliton dimers exhibit a nontrivial behavior of the elementary excitations that stems from the competition between onsite and intersite DDI. Finally, we prove the existence of soliton trimers in a regime where molecular trimers do not occur. We demonstrate that the soliton molecules that we report are well feasible under realistic experimental conditions.