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arXiv:2105.15148 · SciPost Physics

Optical lattice with spin-dependent sub-wavelength barriers

E Gvozdiovas, Povilas Račkauskas, Gediminas Juzeliūnas

Published Dec 2, 2021• 7 citations
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Abstract

We analyze a tripod atom light coupling scheme characterized by two dark states playing the role of quasi-spin states. It is demonstrated that by properly configuring the coupling laser fields, one can create a lattice with spin-dependent sub-wavelength barriers. This allows to flexibly alter the atomic motion ranging from atomic dynamics in the effective brick-wall type lattice to free motion of atoms in one dark state and a tight binding lattice with a twice smaller periodicity for atoms in the other dark state. Between the two regimes, the spectrum undergoes significant changes controlled by the laser fields. The tripod lattice can be produced using current experimental techniques. The use of the tripod scheme to create a lattice of degenerate dark states opens new possibilities for spin ordering and symmetry breaking.

DOI
10.21468/scipostphys.11.6.100

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We analyze a tripod atom light coupling scheme characterized by two dark states playing the role of quasi-spin states. It is demonstrated that by properly configuring the coupling laser fields, one can create a lattice with spin-dependent sub-wavelength barriers. This allows to flexibly alter the atomic motion ranging from atomic dynamics in the effective brick-wall type lattice to free motion of atoms in one dark state and a tight binding lattice with a twice smaller periodicity for atoms in the other dark state. Between the two regimes, the spectrum undergoes significant changes controlled by the laser fields. The tripod lattice can be produced using current experimental techniques. The use of the tripod scheme to create a lattice of degenerate dark states opens new possibilities for spin ordering and symmetry breaking.
Standard optical potentials use an off-resonant laser standing-wave-induced ac Stark shift. In a recent development [\L{}\k{a}cki et al., Phys. Rev. Lett. 117, 233001 (2016)] a three-level scheme in a $\mathrm{\ensuremath{\Lambda}}$ configuration coupled coherently by resonant laser fields was introduced, leading to an effective lattice with subwavelength potential peaks. Here, as an extension of that work, a four-level atomic setup in the tripod configuration is used to create spin-12\frac{1}{2}21​-like two-dimensional dark space with one-dimensional motion and the presence of external gauge fields. Most interestingly for possible applications, the lifetime for a dark subspace motion is up to two orders of magnitude longer than for a similar $\mathrm{\ensuremath{\Lambda}}$ system. The model is quite flexible, leading to lattices with significant nearest, next-nearest, or next-to-next-nearest hopping amplitudes J1,J2{J}_{1}, {J}_{2}J1​,J2​, and J3{J}_{3}J3​ offering intriguing possibilities to study, e.g., frustrated systems. The characteristic Wannier functions lead also to a type of intersite interaction not realizable in typical optical lattices.
We consider slow-light propagation in an atomic medium with a tripod level scheme. We show that the coexistence of two types of dark-state polaritons leads to the propagation dynamics, which is qualitatively different from that in a $\mathrm{\ensuremath{\Lambda}}$ medium, and allows therefore for very efficient conversion of signal photons into spin excitations. This efficiency is shown to be very close to 1 even for very long signal light pulses, which could not be entirely compressed into a $\mathrm{\ensuremath{\Lambda}}$ medium at a comparable strength of the control field.
We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice.
In this work we introduce a model for quantum-state transfer between tripod atoms over a dark fiber. Two tripod atoms are confined in separate cavities linked by an optical fiber. The cavities and the fiber sustain two optical modes of opposite circular polarization. For each atom, the two ground states encode the quantum state to be transferred and are coupled to a common excited state by the cavity modes of opposite polarization. The remaining transition for each atom is used to control the transfer process. We demonstrate that by using laser pulses the dynamics of the system can be confined within a degenerate dark state subspace, with the different dark states interacting via nonadiabatic couplings. We solve analytically the dynamics in the dark state subspace, and determine the conditions on the pulse shape for the implementation of the quantum transfer. We identify a possible pulse shape which satisfies the required conditions, and demonstrate the quantum-state transfer via numerical simulations.
We show that the adiabatic motion of ultracold, multilevel atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges, e.g., if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.
Abstract We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda (Λ) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional Λ- or N -type atom-light couplings providing the EIT or absorption, respectively. Thus, the atomic system can experience a transition from the EIT to the absorption by changing the amplitudes or phases of control lasers. Subsequently the scheme is employed to analyze the nonlinear pulse propagation using the coupled Maxwell–Bloch equations. It is shown that a generation of stable slow light optical solitons is possible in such a five-level combined tripod and Λ atomic system.