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Chinese Journal of Physics

Gauge Fields in Ultracold Bipartite Atoms

H. Wang, W. Wang, X. X. Yi

Published Feb 1, 2009• 1 citation
OpenAlex

Abstract

The effects of entanglement and spin-spin collisions on the gauge fields in ultracold atoms are presented in this paper. Two gauge fields are calculated and discussed. One of the fields comes from space dependent spin-spin collisions in ultracold atoms, while the other results from the usual Born-Oppenheimer method, which separates the center-of-mass motion from the relative motion in the two-body problem. Adiabatic conditions that lead to the key results of this paper are also presented and discussed. Entanglement shared between the two atoms is shown to affect the atomic motion. In the presence of entanglement, the additional scalar potential disappears; this is different from the case of atoms in separable states.

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The effects of entanglement and spin-spin collisions on the gauge fields in ultracold atoms are presented in this paper. Two gauge fields are calculated and discussed. One of the fields comes from space dependent spin-spin collisions in ultracold atoms, while the other results from the usual Born-Oppenheimer method, which separates the center-of-mass motion from the relative motion in the two-body problem. Adiabatic conditions that lead to the key results of this paper are also presented and discussed. Entanglement shared between the two atoms is shown to affect the atomic motion. In the presence of entanglement, the additional scalar potential disappears; this is different from the case of atoms in separable states.
The effects of entanglement and spin-spin collision on the gauge field in ultracold atoms are presented in this paper. Two gauge fields are calculated and discussed. One of the fields comes from space dependent spin-spin collisions in ultra-cold atoms, while another results from the usual Born-Oppenheimer method, which separates the center-of-mass motion from the relative motion in the two-body problem. Adiabatic conditions that lead to the key results of this paper are also presented and discussed. Entanglement shared between the two atoms is shown to affect the atomic motion. In the presence of entanglement, the additional scalar potential disappears, this is different from the case of atoms in separable states.
Two-body scattering constitutes one of the most fundamental processes in various physical systems ranging from ultracold dilute quantum gases to energetic quark- gluon plasmas. In this dissertation, we study the low-energy atomic collision physics in the presence of synthetic gauge fields, which are generated by atom-light interaction. One category of synthetic gauge fields is the artificial spin-orbit coupling. We discuss three different aspects in scattering theory: ultracold collision, scattering resonance, and bound state formation from a few-body perspective when the atomic spin states are coupled with their center-of-mass motion. The understanding of the spin-orbit effects on the modification of the scattering processes not only builds the foundation of collision physics in the presence of non-abelian gauge fields but also paves the way towards unraveling the few-body correlations in many-body systems.
By making use of the improved Born-Oppenheimer approximate method, we deal with the separation of spin variable and space variable of neutral particle with arbitrary spin in inhomogeneous magnetic field and non-adiabatic corrections for the problems are thereby computed as perturbations. We also analysis the geometrical properties of loop phase of the induced gauge potential and point out its observable effects relating to Bitter and Dubbers' experiment. Finally, we discuss the transitions between the instantaneous spin states as non-;-adiabatic effects resulting from inhomogeneity of the magnetic field.
The study of the gauge field is an everlasting topic in modern physics. Spin-orbit coupling is a powerful tool in ultracold atomic systems, resulting in an artificial gauge field that can be easily manipulated and observed in a tabletop environment. Combining optical Raman lattices and atom-atom interactions, the artificial gauge field can be made density dependent. In this work we propose a straightforward way to engineer a one-dimensional density-dependent gauge field in a Bose-Hubbard model in spin-orbit-coupled Raman lattices. We study the model from two perspectives: few-body quantum-walk dynamics and the many-body ground state. From the first perspective, we show that large spin-flipped tunneling can lead to a deep two-body bound state. From the second perspective, mean-field and density-matrix renormalization-group calculations consistently reveal three different phases, i.e., the Mott insulator phase, the superfluid phase, and the magnetic superfluid phase. Finally, we discuss the experimental protocol with Raman lattices based on existing experimental platforms.
Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultrastructure of the Bethe-Salpeter equation, we show that the linear ultraviolet divergence in the bare interaction can be renormalized as usual in terms of low-energy scattering lengths, and that for both bosons and fermions ultraviolet logarithmic divergences are absent. Calculating the leading order effective interaction with full dependence on the spin-orbit coupling strength and the center-of-mass momentum of the colliding pair, we elucidate the relation between mean-field interactions and physical three-dimensional scattering lengths. As a consequence of infrared logarithmic divergences in the two-particle propagator, the effective interaction vanishes as the center-of-mass momentum approaches zero.
We study ultracold atoms subjected to U(2) non-Abelian potentials: we consider gauge potentials having, in the Abelian limit, degenerate Landau levels and we then investigate the effect of general homogeneous non-Abelian terms. The conditions under which the structure of degenerate Landau levels is preserved are classified and discussed. The typical gauge potentials preserving the Landau levels are characterized by a fictitious magnetic field and by an effective spin-orbit interaction (e.g., obtained through the rotation of two-dimensional atomic gases coupled with a tripod scheme). The single-particle energy spectrum can be analytically determined for a class of gauge potentials, whose physical implementation is discussed. The corresponding Landau levels are deformed by the non-Abelian contribution of the potential and their spin degeneracy is split. The related deformed quantum Hall states for fermions and bosons (in the presence of strong intraspecies interaction) are determined far from and at the degeneracy points of the Landau levels, where non-Abelian states appear. We present a discussion of the effect of the angular momentum, as well as results for U(3) gauge potentials.