Spin-orbit coupling in periodically driven optical lattices

Abstract

We propose a method for the emulation of artificial spin-orbit coupling in a system of ultracold, neutral atoms trapped in a tight-binding lattice. This scheme does not involve near-resonant laser fields, avoiding the heating processes connected to the spontaneous emission of photons. In our case, the necessary spin-dependent tunnel matrix elements are generated by a rapid, spin-dependent, periodic force, which can be described in the framework of an effective, time-averaged Hamiltonian. An additional radio-frequency coupling between the spin states leads to a mixing of the spin bands.PACS numbers: 03.65.Vf, 71.70.Ej, 37.10.Jk The phenomenon of spin-orbit coupling (SOC) generally describes an interplay between the spin state of a particle and its motional degrees of freedom. This effect naturally arises in the framework of relativistic quantum mechanics described by the Dirac equation. A spinful particle moving through an electric field experiences a magnetic field in the co-moving reference frame. The resulting interaction between the spin and the magnetic field depends on the amplitude of the field and thus on the velocity of the particle, leading to the coupling of motion and spin. In solid state materials, SOC can result in exotic phases and phenomena, such as topological insulators [1,2] or the spin Hall effect [3][4][5][6][7].The experimental realization of synthetic spin-orbit interactions with equal Rashba [8] and Dresselhaus [9] contributions for bosonic [10,11] and fermionic quantum gases [12,13] has raised considerable interest over the last years ([14] and references therein). For ultracold atomsinteracting via s-wave scattering -SOC can lead to effective interactions with higher partial wave contributions [15][16][17]. In a single-component Fermi gas this could lead to stable p-wave interactions and topological superfluids [18][19][20]. All of the experimentally implemented schemes rely on near-resonant Raman-laser coupling schemes and thus suffer from spontaneous emission, leading to excitations and particle loss. Currently a lot of effort is directed towards novel methods for the creation of artificial SOC avoiding this issue, e.g., by using magnetic field pulses [21,22] or far-off-resonant light [23].As thoroughly investigated over the last years a rapid, periodic lattice drive coherently manipulates the tunneling processes in an optical lattice. This allows for, e.g., the coherent destruction of tunneling and sign inversion of the tunnel elements [24-27], photon assisted tunneling [28,29], and the creation of artificial gauge fields [30][31][32][33][34][35][36][37][38]. In this manuscript, we propose to engineer a * E-mail address: jstruck@mit.edu; HKin represents the spin-independent nearest-neighbour tunneling processes, HRF describes the radio frequency coupling of the two spin states and HForce corresponds to the spin-dependent driving of the atoms in the lattice. The drive originates from an oscillating magnetic field gradient.time-periodic and spin-dependent drive in order to realize ...

Beyond the Hubbard bands in strongly correlated lattice bosons

“…The 3U triplon excitation is interesting in its own right and in connection with Efimov physics [50][51][52]. Our findings are also relevant in the context of driven experiments, e.g., for generating gauge fields [30][31][32] and spin-orbit interactions [33][34][35], where energy absorption at the driving frequency needs to be minimized. It would also be interesting to study the fine-structure changes in the spectral function induced by the higher bands of the optical lattice through effective multibody interactions [53][54][55] and renormalized hopping [56,57].…”

“…They have been found in the spectral function at zero temperature using the variational cluster approach (VCA) [27,28] and strong-coupling calculations [26], and they are also reproduced in the current and kinetic energy susceptibilities calculated by DMRG [29]. The recently renewed interest in high-dimensional lattice bosons out-of-equilibrium to realize complex effective Hamiltonians including gauge fields [30][31][32] and spin-orbit interactions [33][34][35] by nonequilibrium driving, and the recent real-time generalization [36] of bosonic dynamical mean-field theory * hugo.strand@unifr.ch † philipp.werner@unifr.ch (BDMFT) [37][38][39][40][41], call for a systematic investigation of the positions, origins, and temperature behaviors of these high-energy fluctuations.…”

Tunable spin-orbit coupling for ultracold atoms in two-dimensional optical lattices

“…Although SOC with equal Rashba and Dresselhaus magnitudes have been proposed [28][29][30] and realized [31,32], to access more general forms of SOC, most proposals [33][34][35][36][37] and recent experimental work [38] focus on generating non-Abelian gauge fields, which can be considered as TR-breaking forms of SOC. There exist only a few proposals for specific forms of (TR-invariant) SOC [39,40] and, thus far, no experimental realization.…”

“…Our method relies on a combination of microwave (MW) drives to change the spin states and lattice shaking [29] to couple the spins with the atomic motion. If the optical lattice is inversion symmetric, the resulting SOC can be TR invariant.…”

Spin-orbit coupled ultracold gases in optical lattices: High-band physics and insufficiency of tight-binding models

“…A fascinating property of such system is that the effective flux in each plaquette is on the order of one flux quanta, large enough to reach the quantum Hall regime and enable the exploration of topological signatures [3][4][5][6][7][8][9][10]. Theoretical studies have also revealed various interaction effects in such system [12][13][14][15][16][17][18][19][20][21][22][23][24], and in particular, pointed out the possibilities of majorana fermions [20,22] and exotic spin textures [15,18].To date, most studies on the spin-orbit coupled atomic gases in optical lattices have concentrated on the lowest-band physics under various tight-binding approximations [12][13][14][15][16][17][18][19][20][21][22][23][24], while the high-band physics has been rarely explored. Moreover, even for the lowest band(s), it is questionable whether the conventional Wannier wavefunction without SOC can still be used to construct the tight-binding model, as the SOC can induce coupling between different bands and the original Wannier basis could be problematic.…”