Session T6: Focus Session: Synthetic Gauge Fields in Ultracold Systems

Light-induced Abelian and non-Abelian gauge potentials for cold atoms

In the initial part of the talk we shall review schemes enabling to produce an artificial magnetic field for cold atoms using several light beams. We discuss possibilities to create both Abelian and also non-Abelian gauge potentials. Subsequently we present a novel scheme simulating a spin-orbit coupling of the Rashba-Dresselhaus (RD) type for cold atoms [1]. The RD coupling is known to be described by a non-Abelian vector potential proportional to the spin-1/2 operator. It applies not only to electrons in semiconductors and also to cold atoms. For cold atoms, the RD coupling can be generated by means of a tripod scheme in which the laser beams couple three atomic ground states with an extra state [2-6]. The RD coupling is then formed for atoms populating two internal dark states. However the dark states are not the ground states of the tripod atom. This is a drawback in studying the Bose-Einstein condensation in the presence of the RD coupling [7,8]. Here we propose and analyze an alternative setup where the light beams couple three or four atomic levels in a close loop topology [1]. By properly setting amplitudes and phases of the laser beams, one can arrive at a twice degenerate atomic ground state manifold affected by the RD coupling. We discuss implementations of this scheme using the Raman transitions between the hyperfine levels of the ground state manifold. \newline \newline [1] D. L. Campbell, G. Juzeliunas and I. B. Spielman, arXiv:1102.3945. [2] T.D. Stanescu and C. Zhang and V. Galitski, Phys. Rev. Lett 99, 110403 (2007). [3] A. Jacob et al, Appl. Phys. B 89, 439 (2007). [4] J. Y. Vaishnav, and C. W. Clark, Phys. Phys. Lett. 100, 153002 (2008). [5] G. Juzeliunas et al, Phys. Rev. Lett. A 100, 200405 (2008). [6] J. Dalibard, F. Gerbier, G. Juzeliunas, and P. Ohberg, arXiv 1008.5378. [7] T. D. Stanescu, B. Anderson, and V. Galitski, Phys. Rev. A 78, 023616 (2008). [8] C. Wang et al., Phys. Rev. Lett. 105, 160403 (2010).   

Spin-orbit coupled Bose-Einstein condensates

Ultracold atoms are quantum systems under precise experimental control, ideal for realizing and characterizing novel artificial gauge fields [1-4]. Our latest experiments [5- 7] with $^{87}$Rb Bose-Einstein condensates (BECs) have demonstrated and explored Abelian, both scalar and matrix valued, light-induced gauge potentials. We optically dressed our BECs with a pair of far detuned Raman lasers. The resulting dressed states are spin and momentum superpositions, and we adiabatically load the atoms into the lowest energy of these dressed states. The nature of the dressed states is experimentally tunable via the strength of the laser coupling and the detuning from Raman resonance, thereby introducing gauge fields into the Hamiltonian. I will discuss Spin-Orbit (SO) coupling [6], the interaction between a quantum particle's spin and its momentum. We experimentally realized SO coupling with equal contributions of Rashba and Dresselhaus coupling, which modified the interaction between the \textit{dressed spin states} and resulted in a phase transition from a spatially \textit{spin}- mixed state to a phase-separated state as a function of laser power. The location of this transition is in agreement with our calculations. Finally I conclude by focusing on our most recent progress on artificial gauge fields. This work was performed in collaboration with Y.-J. Lin, R. A. Williams, L. J. LeBlanc, M. Beeler, W. D. Phillips, J. V. Porto and I. B. Spielman. \\[4pt] [1] J. Dalibard, F. Gerbier, G. Juzeli\=unas, and P.\"Ohberg, arXiv:1008.5378v1[cond-mat.quant-gas] (2010)\\[0pt] [2] G. Juzeli\=unas, J. Ruseckas, P. \"Ohberg, and M. Fleischhauer, Phys. Rev. A 73, 025602 (2006)\\[0pt] [3] J. Ruseckas, G. Juzeli\=unas, P. \"Ohberg, and M. Fleischhauer, Phys. Rev. Lett. 95, 010404 (2005)\\[0pt] [4] I. B. Spielman, Phys. Rev. A. 79, 063613 (2009)\\[0pt] [5] Y.-J. Lin, R. Compton, K. Jim\'enez- Garc\'ia, J. V. Porto, and I. B. Spielman, Nature 95, 628-632 (2009)\\[0pt] [6] Y.-J. Lin et. al, Spin-orbit coupled Bose-Einstein condensates (Submitted, 2011)\\[0pt] [7] Y.-J. Lin et. al, A synthetic electric force acting on neutral atoms (Submitted, 2011)   

Bose-Einstein Condensate in a Non-abelian Gauge Potential

We studied a Bose-Einstein condensate in two different types of non-abelian gauge potential. One corresponds to an isotropic Rashba spin-orbit coupling, and the other corresponds to highly anisotropic spin-orbit coupling realized in recent NIST experiment. In both cases, we find the system will develop spin stripes in certain parameters regimes, and will exhibit spin-stripe to plane wave phase transition as parameters change.   

Transport dynamics of a $^{87}$Rb BEC in an artificial magnetic field

Despite the electrical neutrality of ultracold quantum gases, the combination of far-detuned Raman lasers and spatially-dependent Zeeman energies can be used to effect a Lorentz force for ultracold atoms [1]. The transport dynamics of a Bose-Einstein condensate (BEC) in an artificial magnetic field are similar to those in a solid, displaying, for example, the Hall effect. Using external forces to drive a mass current, we study transport in a $^{87}$Rb BEC as a function of the applied artificial magnetic field and explore the resulting Hall coefficients. \\[4pt] [1] Y.-J. Lin \emph{et al.} Nature {\bf 462}, 628 (2009).   

Rashba spin-orbit coupling for neutral atoms

We theoretically describe a new class of atom-laser coupling schemes which lead to effective spin-orbit coupled Hamiltonians for ultra-cold neutral atoms. By properly setting the optical phases, a pair of degenerate spin states emerge as the lowest energy states in the spectrum, and are thus immune to collisionally induced decay. These schemes use $N$ cyclically coupled ground or metastable internal states but we will specialize to the four-level case for this talk. Time permitting, we will describe a possible implementation of this scheme for $^{87}$Rb that adds a controllable Dresselhaus component to the effective Hamiltonian in a natural way.   

Higher Order Partial Waves in a Bose-Einstein Condensate

The interactions of bosons at the low temperatures associated with quantum degeneracy are usually well-described by a purely isotropic (s-wave) interaction. We study collisions between Bose-Einstein condensates dressed by counter-propagating Raman beams, where the eigenstates of the Raman-dressed system are spin-momentum superpositions. Higher order (beyond s-wave) partial wave interactions between colliding BECs in the ground Raman dressed state are observed at collision velocities orders of magnitude below those traditionally required to surpass the s-wave scattering regime. Furthermore we investigate scattering in excited Raman-dressed states and observe collision-induced decay to lower energy Raman-dressed states which can be p-wave or d-wave in character.   

Majorana Fermions in Cold Atom Quantum Wires

Majorana fermions, which unlike ordinary fermions are their own antiparticles, are widely sought for their exotic exchange statistics and potential for topological quantum information processing. We propose to create and detect Majorana fermions using optically trapped 1D fermionic atoms. The background molecular BEC cloud induces an s-wave pairing for the atoms. Two internal states of the atoms are coupled via an optical Raman transition, which simultaneously induces an effective spin-orbit interaction as well as an effective external magnetic field. We find that the cold atom quantum wire can support Majorana fermions at phase boundaries. When we periodically drive the quantum wire, it can also support Floquet Majorana fermions. We analyze experimental parameters, detection schemes, and various imperfections.