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Europhysics Letters (EPL)

Wave function engineering and circulating spin current in trapped Bose-Einstein condensates

Jian Jun Song, Bradley A. Foreman, X.-J. Liu, C. H. Oh

Published Oct 1, 2008• 7 citations
Publisher

Abstract

We propose a novel scheme to manipulate the wave function of a trapped Bose-Einstein condensate (BEC) by coupling its internal degrees of freedom to external optical vortex modes. The atom-light coupling induces an effective magnetic field on the center-of-mass motion, which drives the trapped BEC to vortex or non-vortex states determined by the effective magnetic flux. With a suitable external trap, the wave function of the optical mode can be fully written into the BEC and stored there. Based on this model, we also propose new techniques to generate static spin accumulation and circulating spin current in cold atomic systems.

DOI
10.1209/0295-5075/84/20012

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We propose a novel scheme to manipulate the wave function of a trapped Bose-Einstein condensate (BEC) by coupling its internal degrees of freedom to external optical vortex modes. The atom-light coupling induces an effective magnetic field on the center-of-mass motion, which drives the trapped BEC to vortex or non-vortex states determined by the effective magnetic flux. With a suitable external trap, the wave function of the optical mode can be fully written into the BEC and stored there. Based on this model, we also propose new techniques to generate static spin accumulation and circulating spin current in cold atomic systems.
Using laser beams to generate gauge potentials in cold atoms provides an opportunity to study interesting quantum phenomena in condensed matter physics. In this thesis, a scheme to manipulate atomic wave functions and generate spin current in a trapped BEC—whose ground state can be freely controlled to be a vortex or non-vortex state—has been studied and discussed. Laguerre-Gaussian beams, which carry non-zero orbital angular momentum, can be used to create coupling between the 23S1 and 23P1 states in 4He atoms. Wavefunctions in atoms interacting with these beams have been expressed in new dressed states. For atoms moving adiabatically, the coupling among the dressed states can be neglected through adiabatic approximation and centre of mass of atoms would experience both effective vector potential and effective scalar potential. The eigenenergies and wavefunctions of a single atom have been calculated by computational methods. In addition, the ground-state energies, wavefunctions and spin current of many-body systems, in which the non-linear Gross-Pitaevskii particle-particle interaction is included, have been found. Comparing the result of a many-body system and those in the single particle system, the wavefunctions of the many-body system spread over a larger region than that in the single particle system, causing a significant difference in their spin current density. Also, the ground-state energy per particle in the many-body system is higher than that in the single particle system.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.
It has been shown that a vortex in a Bose-Einstein condensate with spin degrees of freedom can be created by manipulating with external magnetic fields. In the previous work [Phys. Rev. A 61, 063610 (2000)] an optical plug along the vortex axis has been introduced to avoid Majorana flips, which take place when the external magnetic field vanishes along the vortex axis while it is created. In the present work, in contrast, we study the same scenario without introducing the optical plug. The magnetic field vanishes only in the center of the vortex at a certain moment of the evolution and hence we expect that the system will lose only a fraction of the atoms by Majorana flips even in the absence of an optical plug. Our conjecture is justified by numerically solving the Gross-Pitaevskii equation, where the full spinor degrees of freedom of the order parameter are properly taken into account. A significant simplification of the experimental realization of the scenario is attained by the omission of the optical plug.
Atom optic techniques are proposed to control the excitation of a Bose-Einstein condensate in an atomic trap. We show that by employing the dipole potential induced by four highly detuned traveling-wave laser beams with appropriate phases and frequencies, one can coherently excite a trapped Bose-Einstein condensate composed of ultracold alkali-metal atoms into a state rotating around the trap center. Pure vortex states can be created with this scheme if the condensate is trapped in an anharmonic trap.
Realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates are discussed. It is shown that, contrary to common intuition, rotation of the trap containing a spin-orbit condensate does not lead to an equilibrium state with static vortex structures but gives rise instead to nonequilibrium behavior described by an intrinsically time-dependent Hamiltonian. We propose here the following alternative methods to induce thermodynamically stable static vortex configurations: (i) to rotate both the lasers and the anisotropic trap and (ii) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. Effective Hamiltonians for spin-orbit condensates under such perturbations are derived for most currently known realistic laser schemes that induce synthetic spin-orbit couplings. The Gross-Pitaevskii equation is solved for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates, the appearance of unusual vortex arrangements, and parity effects in vortex nucleation where the topological excitations are predicted to appear in pairs. All these phenomena are shown to be highly nonuniversal and depend strongly on a specific laser scheme and system parameters.
We present experimental results on the coherent transfer of orbital angular momentum (OAM) from optical fields to the center-of-mass motion of a Bose-Einstein condensate (BEC), using an approach which results in negligible linear momentum change. Two collinear optical beams of differing OAM are used to couple discrete sublevels of the atomic ground state via a stimulated Raman process. We demonstrate several of the possible optical field configurations which place the BEC into various spinor and vortex states. We also show how this approach can be used to create coherent superpositions of these states and use the interference patterns of such superpositions to confirm the presence of quantized vortices.