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arXiv:1610.09425

Investigation of Confinement Induced Resonance in Atomic Waveguides with Different Geometries by Quantum Monte Carlo Methods

Azizi, Sajad, Shahpoor Saeidian

Published Oct 28, 2016• 0 citations
arXivHTMLPDF

Abstract

We have investigated the quantum dynamics of two ultracold bosons inside an atomic waveguide for two different confinement geometries (cigar-shaped and toroidal waveguides) by quantum Monte Carlo methods. For quasi-1D gases, the confining potential of the waveguide leads to the so-called confinement induced resonance (CIR), results in the phase transition of the gas to the impenetrable bosonic regime (known as TG gas). In this regime the bosons repel each other strongly and behave like fermions. We reproduce CIR for a cigar-shaped waveguide and analyze the behavior of the system for different conditions. Moreover, our analysis demonstrates appearance of CIR for a toroidal waveguide. Particularly, we show that the resonance position is dependent on the size of the waveguide, which is in contrast to the cigar shaped waveguides for which it is universal.

DOI
10.48550/arxiv.1610.09425

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We have investigated the quantum dynamics of two ultracold bosons inside an atomic waveguide for two different confinement geometries (cigar-shaped and toroidal waveguides) by quantum Monte Carlo methods. For quasi-1D gases, the confining potential of the waveguide leads to the so-called confinement induced resonance (CIR), results in the phase transition of the gas to the impenetrable bosonic regime (known as TG gas). In this regime the bosons repel each other strongly and behave like fermions. We reproduce CIR for a cigar-shaped waveguide and analyze the behavior of the system for different conditions. Moreover, our analysis demonstrates appearance of CIR for a toroidal waveguide. Particularly, we show that the resonance position is dependent on the size of the waveguide, which is in contrast to the cigar shaped waveguides for which it is universal.
We observe d-wave confinement-induced resonances (CIRs) of bosonic scattering in tightly confining harmonic waveguides. It is shown that the d-wave CIR emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for the position of the d-wave CIR is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from s-wave to d-wave CIRs. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a novel possibility for studying strongly correlated atomic systems beyond s-wave physics. PACS numbers: 03.75.Be, 34.10.+x, 34.50.-s
The diffusion quantum Monte Carlo technique is used to solve the many-body Schr\"odinger equation fully quantum mechanically and nonperturbatively for bosonic atomic gases in cigar-shaped confining potentials. By varying the aspect ratio of the confining potential from 1 (spherical trap) to 10 000 (highly elongated trap), we characterize the transition from the three-dimensional regime to the (quasi-)one-dimensional regime. Our results confirm that the bosonic gas undergoes ``fermionization'' for large aspect ratios. Importantly, many-body correlations are included explicitly in our approach.
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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.
Abstract These two papers, published back to back, provide superb examples of the use of a quantum Monte Carlo method to obtain exact solutions for a problem difficult to treat by other methods. The problem is that of a bosonic atomic gas confined in a cigarshaped trap. As the cigar is narrowed the atoms are less able to pass each other, their behavior approaches that of fermions, and they are said to exhibit “fermionization.” Using diffusion QMC the authors were able to determine the ground-state energies, examine structural properties, confirm that fermionization can occur, and predict conditions under which it might be observed. The calculations by Blume were carried out for 2-20 atoms confined in axially symmetric traps of varied aspect ratios. The confining potential for each atom was given by Vk = CpPl + Czzl (radial and axial positions squared). The atom-atom interactions were simple hard-sphere potentials. The (nodeless) guided diffusion calculations used a trial wavefunction of the Jastrow type, a product of atom-trap terms and atom-atom terms. The calculations by Astrakharchik and Giorgini were carried out similarly but included both hard and soft spheres with numbers in the range of 5 to 100 atoms. Comparisons were made with predictions of the LiebLiniger equation of state.