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arXiv:1705.08727 · Journal of Physics B Atomic Molecular and Optical Physics

Dipolar confinement-induced molecular states in harmonic waveguides

Gao‐Ren Wang, Panagiotis Giannakeas, Peter Schmelcher

Published Nov 21, 2017• 1 citation
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Abstract

Abstract The bound states of two identical dipoles in a harmonic waveguide are investigated. In the regime of weak dipole–dipole interactions, the local frame transformation method is applied to determine the spectrum of dipolar confinement-induced bound states analytically. The accuracy of the local frame transformation approach is discussed by comparing the analytical results with the numerical ones based on a solution of the close-coupling equations. It is found that close to the threshold energy in the waveguide, the local frame transformation method needs to include more partial wave states to obtain accurate bound state energies. As the binding energy increases, the local frame transformation method using a single partial wave state becomes more accurate. We also compare the bound states in waveguides and in free space. For the bosonic case, the s -wave dominated bound state looks like a free-space state when its energy is below a certain value. For the fermionic case, the p -wave dominated bound state energies in waveguides and in free-space coincide even close to zero energy.

DOI
10.1088/1361-6455/aa9c32

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Abstract The bound states of two identical dipoles in a harmonic waveguide are investigated. In the regime of weak dipole–dipole interactions, the local frame transformation method is applied to determine the spectrum of dipolar confinement-induced bound states analytically. The accuracy of the local frame transformation approach is discussed by comparing the analytical results with the numerical ones based on a solution of the close-coupling equations. It is found that close to the threshold energy in the waveguide, the local frame transformation method needs to include more partial wave states to obtain accurate bound state energies. As the binding energy increases, the local frame transformation method using a single partial wave state becomes more accurate. We also compare the bound states in waveguides and in free space. For the bosonic case, the s -wave dominated bound state looks like a free-space state when its energy is below a certain value. For the fermionic case, the p -wave dominated bound state energies in waveguides and in free-space coincide even close to zero energy.
Abstract The two-body bound and scattering properties in an one-dimensional harmonic waveguide close to free space magnetic Feshbach resonances are investigated based on the local frame transformation approach within a single partial wave approximation. An energy and magnetic field dependent free space phase shift is adopted in the current theoretical framework. For both s - and p -wave interaction, the least bound state in the waveguide dissociates into the continuum at the resonant magnetic field where the effective one-dimensional scattering length a 1D diverges. Consequently, the association of atoms into molecules in the waveguide occurs when the magnetic field is swept adiabatically across the pole of a 1D . In the vicinity of broad s -wave resonances, the resonant magnetic field is nearly independent on the transverse confining frequency ω ⊥ of the waveguide. Close to p -wave and narrow s -wave resonances, the resonant magnetic field changes as ω ⊥ varies.
We develop a nonperturbative theoretical framework to treat collisions with generic anisotropic interactions in quasi-one-dimensional geometries. Our method avoids the limitations of pseudopotential theory and allows us to include accurately long-range anisotropic interactions. For ultracold dipolar collisions in a harmonic waveguide we predict dipolar confinement-induced resonances (DCIRs) which are attributed to different angular momentum states. The analytically derived resonance condition reveals in detail the interplay of the confinement with the anisotropic nature of the dipole-dipole interactions. The results are in excellent agreement with ab initio numerical calculations confirming the robustness of the presented approach. The exact knowledge of the positions of DCIRs may pave the way for the experimental realization of, e.g., Tonks-Girardeau-like or super-Tonks-Girardeau-like phases in effective one-dimensional dipolar gases.
We study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail. In the limit of a strong interaction between the particles, the occupancies and the von Neumann entropies of the bosonic and fermionic ground states are derived in closed analytic forms by applying the harmonic approximation. The strong correlation regimes of the system with the dipolar bosons and the system with the charged ones are compared with each other in regard to aspects of their entanglement.
A wave-packet propagation method is developed and applied to investigate the quantum dynamics of scattering processes of identical and distinguishable atoms in harmonic waveguides. The quantum dynamics of the confinement-induced resonances (CIRs) for ultracold collisions of identical particles, sss-wave CIRs for bosons and ppp-wave CIRs for fermions, is explored in detail. Our multigrid approach allows us to fully take into account the coupling between the center-of-mass (c.m.) and relative motions in the case of distinguishable atoms. The latter includes, in particular, sss- and ppp-partial-wave mixing, caused by the confining trap, which acts differently on the different atomic species. Specifically, we explore in detail the recently discovered [J. I. Kim, V. S. Melezhik, and P. Schmelcher, Phys. Rev. Lett. 97, 193203 (2006)] dual CIR, which is based on a destructive interference mechanism leading to complete transmission in the waveguide, although the corresponding scattering in free space exhibits strong sss- and ppp-wave scattering.
Dipolar Bose and Fermi gases, which are currently being studied extensively experimentally and theoretically, interact through anisotropic, long-range potentials. Here, we replace the long-range potential by a zero-range pseudopotential that simplifies the theoretical treatment of two dipolar particles in a harmonic trap. Our zero-range pseudopotential description reproduces the energy spectrum of two dipoles interacting through a shape-dependent potential under external confinement very well, provided that sufficiently many partial waves are included, and readily leads to a classification scheme of the energy spectrum in terms of approximate angular momentum quantum numbers. The results may be directly relevant to the physics of dipolar gases loaded into optical lattices.
The universal aspects of two-body collisions in the presence of a harmonic confinement are investigated for both bosons and fermions. The main focus of this study are the confinement-induced resonances (CIRs) which are attributed to different angular momentum states $\ensuremath{\ell}$, and we explicitly show that in alkaline collisions only four universal $\ensuremath{\ell}$-wave CIRs emerge given that the interatomic potential is deep enough. Going beyond the single mode regime the energy dependence of $\ensuremath{\ell}$-wave CIRs is studied. In particular we show that all the $\ensuremath{\ell}$-wave CIRs may emerge even when the underlying two-body potential cannot support any bound state. We observe that the intricate dependence on the energy yields resonant features where the colliding system within the confining potential experiences an effective free-space scattering. Our analysis is done within the framework of the generalized KKK-matrix theory, and the relevant analytical calculations are in very good agreement with the corresponding ab initio numerical scattering simulations.