Effect of Induced Spin-Orbit Coupling for Atoms via Laser Fields

Abstract

We propose an experimental scheme to observe spin-orbit coupling effects of a two-dimensional (2D) Fermi atomic gas cloud by coupling its internal electronic states (pseudospins) to radiation in a Lambda configuration. The induced spin-orbit (SO) coupling can be of the Dresselhaus and Rashba type with and without a Zeeman term. We show that the optically induced SO coupling can lead to a spin-dependent effective mass under appropriate condition, with one of them able to be tuned between positive and negative effective masses. As a direct observable we show that in the expansion dynamics of the atomic cloud the initial atomic cloud splits into two clouds for the positive effective mass case regime, and into four clouds for the negative effective mass regime. [3,4]. In correspondence to the spin of an electron, the internal degree of freedom of an atom (pseudospin) is represented by the superposition of its electronic states (hyperfine levels). SO coupling can be equivalently depicted as the interaction between an effective non-Abelian gauge potential and a particle with (pseudo)spin. In quantum systems, the idea generating a gauge field adiabatically was proposed by Wilczek and Zee more than twenty years ago [5]. Recently, such an idea was applied to atomic systems, where the motion of atoms in a position dependent laser configuration gives rise to an effective non-Abelian gauge potential [6,7,8,9,10], which can lead to an effective SO interaction in an ultracold atomic gas [11,12,13].Realization of SO interaction in atomic gases opens new possibility of studying spintronic effects, e.g. spin relaxation [11], Zitterbewegung [12] and SHE, in atomic systems which provide an extremely clean environment, allowing in a controllable fashion unique access to the study of complex physics. However, experimental detection of such SO effects in atoms requires to measure the pseudospins (not just hyperfine levels) that are usually not directly observable for atomic systems. In this letter, we propose an experimental scheme to study SO coupling effects, based on a trapped two-dimensional (2D) Fermi atomic gas with a simple internal three-level Λ-type setup. We demonstrate that an effective SO interaction, e.g. Rashba and linear Dresselhaus terms, can be obtained by coupling atoms with a three-level configuration to spatially varying laser fields. The optically induced SO coupling can lead to a spin-dependent effective masses under proper condition. A direct observable of this effects is in the expansion dynamics for each of the effective mass cases after the external trap is switched off and we predict that the initial atomic cloud splits into two or four clouds.|c>(1/2)Ω We consider a cloud of quasi 2D (y-z plane) Fermi atomic gas with internal three-level Λ-type configuration (see Fig. 1 (a)) coupled to radiation. The transition |b → |a is coupled by the laser field with Rabi-frequency Ω 1 = Ω 10 exp[iφ 1 (r)] and the transition |c → |a is coupled by another laser field Ω 2 = Ω 20 exp[iφ 2 (r)], where φ 1,2 (r) are positi...

Measurement of noncommuting spin components using spin-orbit interaction

“…To evaluate possible switching times T for electrons in semiconductors, we use recent estimates [9,10] r 0 ∼ 10 −5 cm, α ∼ 10 6 cm/s, and the effective mass M ∼ 10 −28 g, thus obtaining T ∼ 10 −11 s, meaning that r 0 /R so cannot be less than 0.1. For cold atoms with [11,12] r 0 ∼ 10 −4 cm, α ∼ 10 cm/s, and atomic mass of M ∼ 10 −22 g, we obtain a broader range of durations, 10 −5 ≤ T ≤ 10 −3 s, suitable for an accurate simulation of a joint von Neumann measurement of the two spin components.…”

“…Modulation of the SO coupling strength, including switching it on and off on demand, can be achieved for electrons in semiconductor structures by applying external bias to the metallic gates attached to the system [9,10]. For cold atoms similar effect can be realized with specially designed optical fields [11][12][13][14]. With the above in mind, for a particle of mass M , we will consider one of the following Hamiltonians ( = 1):…”

“…We also suggest an optimal experimental technique for simulating a joint von Neumann measurement on a generic spin-1/2 system, of interest in quantum information. For the latter we propose the use of modern techniques developed for controlling spin-orbit (SO) interactions in solids [9,10] and for cold atoms in optical lattices [11][12][13][14]. The key feature of such systems, currently attracting interest for both fundamental and applied reasons (for a review see [10]), is entanglement between the translational and the spin (pseudospin) degrees of freedom.…”

Macroscopic Klein tunneling in spin-orbit-coupled Bose-Einstein condensates

“…In the large detuning case, the two eigenstates corresponding to the first two eigenvalues span a near-degenerate subspace, and can be considered as a pseudo-spin with spin-orbit coupling induced by a gauge potential [7,14]. Under this condition we obtain an effective Hamiltonian…”

Dispersion and wave-function symmetry in cold atoms experiencing artificial gauge fields

“…In the experiments of Lin et al [1,2,4,5], Rubidium atoms in the F=1 hyperfine manifold interact with two co-propagating lasers. These lasers drive Raman transitions between the three magnetic hyperfine states m = −1, 0, 1.…”