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      A spin-orbit coupled Bose-Einstein condensate

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          Abstract

          Spin-orbit (SO) coupling -- the interaction between a quantum particle's spin and its momentum -- is ubiquitous in nature, from atoms to solids. In condensed matter systems, SO coupling is crucial for the spin-Hall effect and topological insulators, which are of extensive interest; it contributes to the electronic properties of materials such as GaAs, and is important for spintronic devices. Ultracold atoms, quantum many-body systems under precise experimental control, would seem to be an ideal platform to study these fascinating SO coupled systems. While an atom's intrinsic SO coupling affects its electronic structure, it does not lead to coupling between the spin and the center-of-mass motion of the atom. Here, we engineer SO coupling (with equal Rashba and Dresselhaus strengths) in a neutral atomic Bose-Einstein condensate by dressing two atomic spin states with a pair of lasers. Not only is this the first SO coupling realized in ultracold atomic gases, it is also the first ever for bosons. Furthermore, in the presence of the laser coupling, the interactions between the two dressed atomic spin states are modified, driving a quantum phase transition from a spatially spin-mixed state (lasers off) to a phase separated state (above a critical laser intensity). The location of this transition is in quantitative agreement with our theory. This SO coupling -- equally applicable for bosons and fermions -- sets the stage to realize topological insulators in fermionic neutral atom systems.

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          Quantum Spin Hall Insulator State in HgTe Quantum Wells

          Recent theory predicted that the Quantum Spin Hall Effect, a fundamentally novel quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We have fabricated such sample structures with low density and high mobility in which we can tune, through an external gate voltage, the carrier conduction from n-type to the p-type, passing through an insulating regime. For thin quantum wells with well width d 6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2e^2/h. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nm, is also independently determined from the magnetic field induced insulator to metal transition. These observations provide experimental evidence of the quantum spin Hall effect.
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            Synthetic magnetic fields for ultracold neutral atoms

            Neutral atomic Bose condensates and degenerate Fermi gases have been used to realize important many-body phenomena in their most simple and essential forms, without many of the complexities usually associated with material systems. However, the charge neutrality of these systems presents an apparent limitation - a wide range of intriguing phenomena arise from the Lorentz force for charged particles in a magnetic field, such as the fractional quantum Hall states in two-dimensional electron systems. The limitation can be circumvented by exploiting the equivalence of the Lorentz force and the Coriolis force to create synthetic magnetic fields in rotating neutral systems. This was demonstrated by the appearance of quantized vortices in pioneering experiments on rotating quantum gases, a hallmark of superfluids or superconductors in a magnetic field. However, because of technical issues limiting the maximum rotation velocity, the metastable nature of the rotating state and the difficulty of applying stable rotating optical lattices, rotational approaches are not able to reach the large fields required for quantum Hall physics. Here, we experimentally realize an optically synthesized magnetic field for ultracold neutral atoms, made evident from the appearance of vortices in our Bose-Einstein condensate. Our approach uses a spatially-dependent optical coupling between internal states of the atoms, yielding a Berry's phase sufficient to create large synthetic magnetic fields, and is not subject to the limitations of rotating systems; with a suitable lattice configuration, it should be possible to reach the quantum Hall regime, potentially enabling studies of topological quantum computation.
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              A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential

              We use a two-photon dressing field to create an effective vector gauge potential for Bose-condensed Rb atoms in the F=1 hyperfine ground state. The dressed states in this Raman field are spin and momentum superpositions, and we adiabatically load the atoms into the lowest energy dressed state. The effective Hamiltonian of these neutral atoms is like that of charged particles in a uniform magnetic vector potential, whose magnitude is set by the strength and detuning of Raman coupling. The spin and momentum decomposition of the dressed states reveals the strength of the effective vector potential, and our measurements agree quantitatively with a simple single-particle model. While the uniform effective vector potential described here corresponds to zero magnetic field, our technique can be extended to non-uniform vector potentials, giving non-zero effective magnetic fields.
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                Author and article information

                Journal
                17 March 2011
                Article
                10.1038/nature09887
                1103.3522
                213353c1-b5c1-4ea5-bb6f-0f32383e76a7

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Nature 471, 83-86 (2011)
                25 pages, 4 figures
                cond-mat.quant-gas

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