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arXiv:1401.5131 · Physical Review A

Multichannel scattering resonance of one-dimensional ultracold spinor bosons

Xiaoling Cui

Published Aug 11, 2014• 5 citations
arXivHTMLPDF

Abstract

So far, the interaction of ultracold atoms can only be tuned within one particular scattering channel near a resonance, where the spinor structure of atomic isotopes is destroyed due to the typically large magnetic field. In this work, we propose a scheme to realize multichannel scattering resonance (MCSR) of ultracold bosons in one-dimension while still keeping their spinor structure. The MCSR refers to a simultaneous scattering resonance among all different scattering channels, including those breaking SU(2) and SO(2) spin-rotation symmetries. Essential ingredients for MCSR include the three-dimensional interactions, the confinement potential, and a spin-flipping field. Near MCSR a many-body spinor system exhibits exotic spin-density distributions and pair correlations, which are significantly different from those near a single-channel resonance.

DOI
10.1103/physreva.90.022705

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So far, the interaction of ultracold atoms can only be tuned within one particular scattering channel near a resonance, where the spinor structure of atomic isotopes is destroyed due to the typically large magnetic field. In this work, we propose a scheme to realize multichannel scattering resonance (MCSR) of ultracold bosons in one-dimension while still keeping their spinor structure. The MCSR refers to a simultaneous scattering resonance among all different scattering channels, including those breaking SU(2) and SO(2) spin-rotation symmetries. Essential ingredients for MCSR include the three-dimensional interactions, the confinement potential, and a spin-flipping field. Near MCSR a many-body spinor system exhibits exotic spin-density distributions and pair correlations, which are significantly different from those near a single-channel resonance.
We develop a full multichannel spin model in momentum space to investigate three-body recombination of identical alkali-metal atoms colliding in a magnetic field. The model combines the exact three-atom spin structure and realistic pairwise atom-atom interactions. By neglecting the interaction between two particles when the spectating particle is not in its initial spin state we arrive at an approximate model. With this approximate model we achieve excellent agreement with the recent precise measurement of the ground Efimov resonance position in potassium-39 close to 33.58 G [R. Chapurin et al., Phys. Rev. Lett. 123, 233402 (2019)]. We analyze the limitations of our approximation by comparing to the numerical results for the full system and find that it breaks down for Feshbach resonances at larger magnetic fields in the same spin channel. There the relevant three-body closed channel thresholds are much closer to the open channel threshold, which enhances the corresponding multichannel couplings. Therefore the neglected components of the interaction should be included for those Feshbach resonances.
Mott insulating ultracold gases possess a unique whole-atom exchange interaction which enables large quantum fluctuations between the Zeeman sublevels of each atom. By strengthening this interaction---either through the use of large-spin atoms or by tuning the particle-particle interactions via optical Feshbach resonance---one may enhance fluctuations and facilitate the appearance of the long-sought-after quantum spin liquid phase---all in the highly tunable environment of cold atoms. To illustrate the relationship between the spin magnitude, interaction strength, and resulting magnetic phases, we present and solve a mean-field theory for bosons optically confined to the one-particle-per-site Mott state, using both analytic and numerical methods. We find on square and triangular lattices for bosons of hyperfine spin f>2f>2f>2 that making the repulsive sss-wave scattering length through the singlet channel small---relative to the higher-order scattering channels---accesses a short-range resonating valence bond (s-RVB) spin liquid phase.
Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in confined geometries. We discuss the behavior of ground state atoms inside a quadrupole magnetic field. Such atoms in enough weak magnetic fields can be approximately treated as neutral point-like particles. Complementary to the well-known positive energy resonances, we point out the existence of short-lived negative energy resonances. The latter originate from a fundamental symmetry of the underlying Hamiltonian. We drive a mapping of the two branches of the spectrum. Moreover, we analyze atomic hyperfine resonances in a magnetic quadrupole field. This corresponds to the case for which both the hyperfine and Zeeman interaction, are comparable, and should be taken into account. Finally we develop a general grid method for multichannel scattering of two atoms in a two-dimensional harmonic confienment. With our approach we analyze transverse excitations/deexcitations in the course of the collisional process (distinguishable or identical atoms) including all important partial waves and their couplings due to the broken spherical symmetry. Special attention is paid to suggest a non-trivial extension of the CIRs theory developed so far only for the single-mode regime and zero-energy limit.
Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave lll and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary lll, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary lll, (b) rigorous definitions of ``broad'' and ``narrow'' resonances of arbitrary lll and their different scattering characteristics, and (c) the tuning of the effective range and the generalized effective range by a magnetic field.
We develop a grid method for multichannel scattering of atoms in a waveguide with harmonic confinement. This approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes. Collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency $\ensuremath{\omega}$ permitting the center-of-mass (c.m.) separation are explored in depth. In the zero-energy limit and single mode regime we reproduce the well-known confinement-induced resonances (CIRs) for bosonic, fermionic, and heteronuclear collisions. In the case of the multimode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behavior are identified and analyzed. The behavior of the transmission with varying energy and scattering lengths is discussed in detail. The dual CIR leading to a complete quantum suppression of atomic scattering is revealed in multichannel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.
In recent years, one-dimensional systems have attracted great interest in several fields of research, from condensed-matter physics to material science to chemistry, and more recently in the field of ultracold quantum gases. In our experiments, we produce one-dimensional chains of ultracold atomic gases by means of laser-light induced periodic potentials, modifying interactions in order to realize correlated states, and studying the effect of controlled disorder added on top of the periodic potential. We investigate the dynamical properties of the many-body correlated states with different techniques. In particular, we use inelastic light scattering to study the dynamical structure factor of the collective excitations, or particle-hole spectrum, and the momentum distribution of the system.