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arXiv:1309.4369 · Physical Review A

Cavity-assisted dynamical spin-orbit coupling in cold atoms

Lin Dong, Lu Zhou, Biao Wu, B. Ramachandhran, Han Pu

Published Jan 24, 2014• 65 citations
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Abstract

We consider ultracold atoms subjected to a cavity-assisted two-photon Raman transition. The Raman coupling gives rise to effective spin-orbit interaction which couples the atom's center-of-mass motion to its pseudospin degrees of freedom. Meanwhile, the cavity photon field is dynamically affected by the atom. This feedback between the atom and photons leads to a dramatic modification of the atomic dispersion relation, and further leads to dynamical instability of the system. We propose to detect the change in the cavity photon number as a direct way to demonstrate dynamical instability.

DOI
10.1103/physreva.89.011602

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We consider ultracold atoms subjected to a cavity-assisted two-photon Raman transition. The Raman coupling gives rise to effective spin-orbit interaction which couples the atom's center-of-mass motion to its pseudospin degrees of freedom. Meanwhile, the cavity photon field is dynamically affected by the atom. This feedback between the atom and photons leads to a dramatic modification of the atomic dispersion relation, and further leads to dynamical instability of the system. We propose to detect the change in the cavity photon number as a direct way to demonstrate dynamical instability.
We consider an atom inside a ring cavity, where a plane-wave cavity field together with an external coherent laser beam induces a two-photon Raman transition between two hyperfine ground states of the atom. This cavity-assisted Raman transition induces effective coupling between atom’s internal degrees of freedom and its center-of-mass motion. In the meantime, atomic dynamics exerts a back-action to cavity photons. We investigate the properties of this system by adopting a mean-field and a full quantum approach, and show that the interplay between the atomic dynamics and the cavity field gives rise to intriguing nonlinear phenomena.
We consider ultracold atoms inside a ring optical cavity that supports a single plane-wave mode. The cavity field, together with an external coherent laser field, drives a two-photon Raman transition between two internal pseudospin states of the atom. This gives rise to an effective coupling between atom's pseudospin and external center-of-mass (COM) motion. For the case of a single atom inside the cavity, We show how the spin-orbit coupling modifies the static and dynamic properties of the Jaynes-Cummings (JC) model. In the case of many atoms in thermodynamic limit, we show that the spin-orbit coupling modifies the Dicke superradiance phase transition boundary and the non-superradiant normal phase may become reentrant in some regimes.
In cold atom, the coupling between "spin" (atomic internal hyperfine states) and "orbit" (atomic center-of-mass motion) can be induced by Raman transition, where different hyperfine states are coupled by a pair of Raman lasers. In recent years, this synthetic spin-orbit coupling has received tremendous attention, as it leads to a variety of novel quantum phenomena in precisely controllable cold atom systems. In this thesis, we first present a comprehensive analysis of one-, two- and many- particle physics of harmonically trapped atoms with spin-orbit coupling, followed by the study of "novel spin-orbit coupling" in two different systems: (1) cold atom spinor mixtures and (2) cold atoms in an optical cavity. In the first system, we consider a spinor mixture consisting of two species of cold atoms, where the spin-orbit coupling can be transmitted from one species to the other, and we discuss novel topological properties and the supersolid stripe phase in this mixture. In the second system, we consider the coupling among three parts: the cavity photon field, the atomic internal hyperfine states, and the atomic external center-of-mass motion, and we discuss how this coupling affects familiar quantum optical phenomena, such as Rabi oscillation and Dicke superradiance phase transition. Our novel systems contribute new and practical platforms for the research field of synthetic spin-orbit coupling in cold atoms.
The superradiant phase transition represents an important quantum phenomenon that shows collective excitations based on the coupling between atoms and cavity modes. Spin-orbit coupling is another quantum effect which is induced by the interaction of the atomic internal degrees of freedom and center-of-mass momentum. In this work we consider the cavity-assisted dynamical spin-orbit coupling which comes from the combination of these two effects. It can generate a series of interesting quantum phenomena such as the flat spectrum and the discontinuity of the excitation energy spectrum around the critical point of the quantum phase transition. We further discuss the influence of atom decay and nonlinear coupling on the phase diagram. The atom decay suppresses the discontinuity of the phase diagram and the nonlinear coupling can break the symmetric properties of the phase transition. Our work provides a theoretical method to research the rich quantum phenomena in this dynamic many-body system.
We realize a spin-orbit interaction between the collective spin precession and center-of-mass motion of a trapped ultracold atomic gas, mediated by spin- and position-dependent dispersive coupling to a driven optical cavity. The collective spin, precessing near its highest-energy state in an applied magnetic field, can be approximated as a negative-mass harmonic oscillator. When the Larmor precession and mechanical motion are nearly resonant, cavity mediated coupling leads to a negative-mass instability, driving exponential growth of a correlated mode of the hybrid system. We observe this growth imprinted on modulations of the cavity field and estimate the full covariance of the resulting two-mode state by observing its transient decay during subsequent free evolution.
We study the spin-orbit-coupled ultracold Bose-Einstein condensate placed in a single-mode Fabry-P\'erot cavity. The cavity introduces a quantum optical lattice potential which dynamically couples with the atomic degrees of freedom and realizes a generalized modified Bose-Hubbard model whose zero-temperature phase diagram can be controlled by tuning the cavity parameters. In the noninteracting limit, where the atom-atom interaction is set to 0, the resulting atomic dispersion shows interesting features such as a bosonic analog of Dirac points, a cavity-controlled Hofstadter spectrum which bears the hallmark of pseudospin-1/2 bosons in the presence of Abelian and non-Abelian gauge fields (the latter due to spin-orbit coupling) in a cavity-induced optical lattice potential. In the presence of atom-atom interaction, using a mapping to a generalized Bose-Hubbard model of spin-orbit-coupled bosons in a classical optical lattice, we show that the system realizes a host of quantum magnetic phases whose magnetic order can be detected from the cavity transmission. This provides an alternative approach to detecting quantum magnetism in ultracold atoms. We discuss the effects of cavity-induced optical bistability on these phases and their experimental consequences.