Spin-dependent Optical Lattice Research Articles

Three-Dimensional Moiré Crystal in Ultracold Atomic Gases.

The work intends to extend the moiré physics to three dimensions. Three-dimensional moiré patterns can be realized in ultracold atomic gases by coupling two spin states in spin-dependent optical lattices with a relative twist, a structure currently unachievable in solid-state materials. We give the commensurate conditions under which the three-dimensional moiré pattern features a periodic structure termed a three-dimensional moiré crystal. We emphasize a key distinction of three-dimensional moiré physics: In three dimensions, the twist operation generically does not commute with the rotational symmetry of the original lattice, unlike in two dimensions, where these two always commute. Consequently, the moiré crystal can exhibit a crystalline structure that differs from the original underlying lattice. We demonstrate that twisting a simple cubic lattice can generate various crystal structures. This capability of altering crystal structures by twisting offers a broad range of tunability for three-dimensional band structures.

Topological phases and edge modes of an uneven ladder

Abstract We investigate the topological properties of a two-chain quantum ladder with uneven legs, i.e., the two chains differ in their periods by a factor of 2. Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps. It also provides opportunities to explore fundamental concepts concerning band topology and edge modes, including the difference of intracellular and intercellular Zak phases, and the role of the inversion symmetry (IS). We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation. We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap, while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgaps but also within the band continuum. Furthermore, by projecting to the two sublattices, we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su–Schrieffer–Heeger model or the Rice–Mele model whose hopping amplitudes depend on the quasimomentum. In this way, the topological phases can be efficiently extracted through winding numbers. We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.

A quantum register using collective excitations in a Bose-Einstein condensate

A qubit made up of an ensemble of atoms is attractive due to its resistance to atom losses. In this work, we consider an experimentally feasible protocol to coherently load a spin-dependent optical lattice from a spatially overlapping Bose-Einstein condensate. Identifying each lattice site as a qubit, with an empty or filled site as the qubit basis, we discuss how high-fidelity single-qubit operations, two-qubit gates between arbitrary pairs of qubits, and nondestructive measurements could be performed. In this setup, the effect of atom losses has been mitigated, the atoms never need to be removed from the ground state manifold, and separate storage and computational bases for the qubits are not required, all of which can be significant sources of decoherence in many other types of atomic qubits.

Chimera patterns in conservative Hamiltonian systems and Bose–Einstein condensates of ultracold atoms

Experimental realizations of chimera patterns, characterized by coexisting regions of phase coherence and incoherence, have so far been achieved for non-conservative systems with dissipation and exclusively in classical settings. The possibility of observing chimera patterns in quantum systems has rarely been studied and it remains an open question if chimera patterns can exist in closed, or conservative quantum systems. Here, we tackle these challenges by first proposing a conservative Hamiltonian system with nonlocal hopping, where the energy is well-defined and conserved. We show explicitly that such a system can exhibit chimera patterns. Then we propose a physical mechanism for the nonlocal hopping by using an additional mediating channel. This leads us to propose a possible experimentally realizable quantum system based on a two-component Bose–Einstein condensate (BEC) with a spin-dependent optical lattice, where an untrapped component serves as the matter-wave mediating field. In this BEC system, nonlocal spatial hopping over tens of lattice sites can be achieved and simulations suggest that chimera patterns should be observable in certain parameter regimes.

Atomic Bose-Einstein condensate in twisted-bilayer optical lattices.

Observation of strong correlations and superconductivity in twisted-bilayer graphene1-4 has stimulated tremendous interest in fundamental and applied physics5-8. In this system, the superposition of two twisted honeycomb lattices, generating a moiré pattern, is the key to the observed flat electronic bands, slow electron velocity and large density of states9-12. Extension of the twisted-bilayer system to new configurations is highly desired, which can provide exciting prospects to investigate twistronics beyond bilayer graphene. Here we demonstrate a quantum simulation of superfluid to Mott insulator transition in twisted-bilayer square lattices based on atomic Bose-Einstein condensates loaded into spin-dependent optical lattices. The lattices are made of two sets of laser beams that independently address atoms in different spin states, which form the synthetic dimension accommodating the two layers. The interlayer coupling is highly controllable by a microwave field, which enables the occurrence of a lowest flat band and new correlated phases in the strong coupling limit. We directly observe the spatial moiré pattern and the momentum diffraction, which confirm the presence of two forms of superfluid and a modified superfluid to insulator transition in twisted-bilayer lattices. Our scheme is generic and can be applied to different lattice geometries and for both boson and fermion systems. This opens up a new direction for exploring moiré physics in ultracold atoms with highly controllable optical lattices.

Mesoscopic transport signatures of disorder-induced non-Hermitian phases

We investigate the impact on basic quantum transport properties of disorder-induced exceptional points (EPs) that emerge in a disorder-averaged Green's function description of two-dimensional Dirac semimetals with spin- or orbital-dependent potential scattering. Remarkably, we find that EPs may promote the nearly vanishing conductance of a finite sample at the Dirac point to a sizable value that increases with disorder strength. This striking behavior exhibits a strong directional anisotropy that is closely related to the Fermi arcs connecting the EPs. We corroborate our results by numerically exact simulations, thus revealing the fingerprints of characteristic non-Hermitian spectral features also on the localization properties of the considered systems. Finally, several candidates for the experimental verification of our theoretical analysis are discussed, including disordered electronic square-net materials and cold atoms in spin-dependent optical lattices.

Atoms in a spin dependent optical potential: ground state topology and magnetization

We investigate a Bose–Einstein condensate of F = 187Rb atoms in a 2D spin-dependent optical lattice generated by intersecting laser beams with a superposition of polarizations. For 87Rb the effective interaction of an atom with the electromagnetic field contains scalar and vector (called a fictitious magnetic field, B fic) potentials. The Rb atoms behave as a quantum rotor (QR) with angular momentum given by the sum of the atomic rotational motion angular momentum and the hyperfine spin. The ground state of the QR is affected upon applying an external magnetic field, B ext, perpendicular to the plane of QR motion and a sudden change of its topology occurs as the ratio B ext/B fic exceeds a critical value. It is shown that the change of topology of the QR ground state is a result of combined action of Zeeman and Einstein–de Haas effects. The first transfers atoms to the largest hyperfine component to polarize the sample along the field as the external magnetic field is increased. The second sweeps spin to rotational angular momentum, modifying the kinetic energy of the atoms.

Experimental study of tune-out wavelengths for spin-dependent optical lattice in 87Rb Bose–Einstein condensation

We study the periodic potential of a one-dimensional optical lattice originating from a scalar shift and vector shift by manipulating the lattice polarizations. The ac Stark shift of an optical lattice is measured by Kapitza–Dirac scattering of 87 R b Bose–Einstein condensate, and the characteristics of a spin-dependent optical lattice are presented by scanning the lattice wavelength between the D1 and D2 lines. At the same time, tune-out wavelengths that the ac Stark shift cancels can be probed by the optical lattice. We give the tune-out wavelengths in more general cases of balancing the contributions of both scalar and vector shifts. Our results provide a clear interpretation for a spin-dependent optical lattice and tune-out wavelengths, and help to design it by choosing the appropriate lattice wavelength.

Microscopic study of the coupled-wire construction and plausible realization in spin-dependent optical lattices

Coupled-wire constructions offer particularly simple and powerful models to capture the essence of strongly correlated topological phases of matter. They often rely on effective theories valid in the low-energy and strong coupling limits, which impose severe constraints on the physical systems where they could be realized. We investigate the microscopic relevance of a class of coupled-wire models and their possible experimental realization in cold-atom experiments. We connect with earlier results and prove the emergence of fractional quantum Hall states in the limit of strong inter-wire tunneling. Contrary to previous studies relying on renormalization group arguments, our microscopic approach exposes the connection between coupled-wire constructions and model wavefunctions in continuum Landau levels. Then, we use exact diagonalization methods to investigate the appearance of these fractional quantum Hall states in more realistic settings. We examine the parameter regimes where these strongly correlated phases arise, and provide a way to detect their appearance in cold-atom experiments through standard time-of-flight measurements. Motivated by this experimental probe, we finally propose a realization of our model with cold-atom in spin-dependent optical lattices. Our estimates show that the previous fractional quantum Hall phases lie within experimentally accessible parameter regimes, giving a viable route towards their experimental study.

Topological quantum pumping in spin-dependent superlattices with glide symmetry

Topological charge pumping represents an important quantum phenomenon that shows the fundamental connection to the topological properties of dynamical systems. Here, we introduce a pumping process in a spin-dependent double-well optical lattice with glide symmetry. In the dynamic process, the glide symmetry protects the band touching points and topological properties of the system are characterised by the non-Abelian Berry curvature. By engineering suitable form of interaction between different spin components, the model not only demonstrates topological phase transition, but also shows hybridisation between the spatial and temporal domain with novel topological features captured by the Wilson line along the synthetic directions. Our work provides a new model based on ultracold atoms towards the implementation of versatile topological matters and topological phenomena.

Topological supersolidity of dipolar Fermi gases in a spin-dependent optical lattice

We investigate the topological supersolid states of dipolar Fermi gases trapped in a spin-dependent 2D optical lattice. Our results show that topological supersolid states can be achieved via the combination of topological superfluid states with the stripe order. Different from the general held belief that supersolid state in fermionic system can only survive with simultaneous coexistence of the repulsive and attractive dipolar interaction. We demonstrate that it can be maintained when the dipolar interaction is attractive in both x and y direction. By adjusting the ratio of hopping amplitude between different directions and dipolar interaction strength U, the system will undergo a phase transition among px + ipy superfluid state, py-wave superfluid state, and the topological supersolid state. The supersolid state in the attractive environment is proved to be stable by the positive sign of the inverse compressibility. We also design an experimental protocol to realize the staggered next-next-nearest-neighbor hopping via the laser assisted tunneling technique, which is the key to simulate the spin-dependent potential.

Preparing Atomic Topological Quantum Matter by Adiabatic Nonunitary Dynamics.

Motivated by the outstanding challenge of realizing low-temperature states of quantum matter in synthetic materials, we propose and study an experimentally feasible protocol for preparing topological states such as Chern insulators. By definition, such (nonsymmetry protected) topological phases cannot be attained without going through a phase transition in a closed system, largely preventing their preparation in coherent dynamics. To overcome this fundamental caveat, we propose to couple the target system to a conjugate system, so as to prepare a symmetry protected topological phase in an extended system by intermittently breaking the protecting symmetry. Finally, the decoupled conjugate system is discarded, thus projecting onto the desired topological state in the target system. By construction, this protocol may be immediately generalized to the class of invertible topological phases, characterized by the existence of an inverse topological order. We illustrate our findings with microscopic simulations on an experimentally realistic Chern insulator model of ultracold fermionic atoms in a driven spin-dependent hexagonal optical lattice.

Stripe and supersolid phases of spin–orbit coupled spin-2 Bose–Einstein condensates in an optical lattice

We study the ground-state phases of two-dimensional spin–orbit coupled spin-2 Bose–Einstein condensates in a one-dimensional spin-dependent optical lattice. Due to the competition among optical lattice, spin–orbit coupling and spin-exchange interaction, the exotic ground-state phases are found, i.e. three types of the stripe phases and three types of the supersolid phases. The spin-exchange interaction can adjust the direction of the stripe in the stripe phase and generate various vortex lattice structures in the supersolid phase, which shows that the spin-exchange interaction plays an important role in the formation of the stripe and supersolid phases of spin–orbit coupled spin-2 Bose–Einstein condensates in an optical lattice.

Atoms trapped by a spin-dependent optical lattice potential: Realization of a ground-state quantum rotor

In a cold atom gas subject to a 2D spin-dependent optical lattice potential with hexagonal symmetry, trapped atoms undergo orbital motion around the potential minima. Such atoms are elementary quantum rotors. We develop the theory of such quantum rotors. Wave functions, energies, and degeneracies are determined for both bosonic and fermionic atoms, and magnetic dipole transitions between the states are elucidated. Quantum rotors in optical lattices with precisely one atom per unit cell can be used as high precision rotation sensors, accelerometers, and magnetometers.

Ring phases of spin-orbit coupled Bose-Einstein condensate in the radial optical lattices

We study the ground-state phases of two-dimensional spin-orbit coupled Bose-Einstein condensate loaded in the spin-dependent radial optical lattices. For strong depth of the spin-dependent radial optical lattice, three new types of the ring phases are found with isotropic spin-orbit coupling, i.e., the ring-stripe phase with the periodic density modulation along the radial direction, the ring-supersolid phase with the periodic density modulation both the radial and azimuthal directions and the windmill-supersolid phase with four vanes along the azimuthal direction. By increasing spin-orbit coupling, the system undergoes a sequence phase transitions from the ring-stripe phase to the ring-sueprsolid phase, and to the windmill-supersolid phase for the weak depth of radial optical lattice, however, the ring-stripe phase transforms to the windmill-supersolid phase directly for the strong depth of radial optical lattice. We also discuss the ground-state phases with anisotropic spin-orbit coupling, two-component Bose-Einstein condensates are easier condensed along the direction with larger spin-orbit coupling.

Compact gravimeter with an ensemble of ultracold atoms in spin-dependent optical lattices

Atomic interferometry in optical lattices is a new trend of developing practical quantum gravimeter. Here, we propose a compact and portable gravimetry scheme with an ensemble of ultracold atoms in gravitationally tilted spin-dependent optical lattices. The fast, coherent separation and recombination of atoms can be realized via polarization-synthesized optical lattices. The input atomic wavepacket is coherently split into two parts by a spin-dependent shift and a subsequent $\frac{\pi}{2}$ pulse. Then the two parts are held for accumulating a relative phase related to the gravity. Lastly the two parts are recombined for interference by a $\frac{\pi}{2}$ pulse and a subsequent spin-dependent shift. The $\frac{\pi}{2}$ pulses not only preclude the spin-dependent energies in the accumulated phase, but also avoid the error sources such as dislocation of optical lattices in the holding process. In addition, we develop an analytical method for the sensitivity in multi-path interferometry.

Ground-state phases of a rotating spin-orbit–coupled Bose-Einstein condensate in an optical lattice

We study the ground-state phases of a two-dimensional rotating spin-orbit–coupled Bose-Einstein condensate loaded in a one-dimensional spin-dependent optical lattice. In the absence of rotation, the system undergoes a phase transition from the stripe phase to the supersolid phase gradually for weak spin-orbit coupling strength and directly for strong spin-orbit coupling strength as the depth of the optical lattice increases. With increasing the rotation strength, the stripe phase transforms to the ringlike state, and the domain number of the ringlike state increases when the Bose-Einstein condensate is in the weak depth of the optical lattice. The supersolid phase transforms to the phase with a single domain of a vortex line for small rotation strength, and alternating vortex lines along the x-direction appear for large rotation strength when the Bose-Einstein condensate is in the strong depth of the optical lattice. The spin textures of the ground-state phases are also discussed.

Two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry

The Su-Schrieffer-Heeger (SSH) model lays the foundation of many important concepts in quantum topological matters. Since it tells one that topological states may be distinguished by abelian geometric phases, a question naturally arises as to what happens if one assembles two topologically distinct states. Here, we show that a spin-dependent double-well optical lattice allows one to couple two topologically distinct SSH chains in the bulk and realise a glided-two-leg SSH model that respects the glide reflection symmetry. Such model gives rise to intriguing quantum phenomena beyond the paradigm of a traditional SSH model. It is characterised by Wilson line that requires non-abelian Berry connections, and the interplay between the glide symmetry and interaction automatically leads to charge fractionalisation without jointing two lattice potentials at an interface. Our work demonstrates the power of ultracold atoms to create new theoretical models for studying topological matters.

Ising antiferromagnet in the two-dimensional Hubbard model with mismatched Fermi surfaces

We study the phase diagram of the two-dimensional repulsive Hubbard model with spin-dependent anisotropic hopping at half-filling. The system develops Ising antiferromagnetic long-range order already at infinitesimal repulsive interaction strength in the ground state. Outside the perturbative regime, unbiased predictions for the critical temperatures of the Ising antiferromagnet are made for representative interaction values by a variety of state-of-the-art quantum Monte Carlo methods, including the diagrammatic Monte Carlo, continuous-time determinantal Monte Carlo and path-integral Monte Carlo methods. Our findings are relevant to ultracold atom experiments in the p-orbital or with spin-dependent optical lattices.

Artificial topological models based on a one-dimensional spin-dependent optical lattice

Topological matter is a popular topic in both condensed matter and cold atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in materials. As a fully controllable system, cold atoms trapped in optical lattices provide an ideal platform to simulate and realize these topological models. Here we present a proposal for synthesizing topological models in cold atoms based on a one-dimensional (1D) spin-dependent optical lattice potential. In our system, features such as staggered tunneling, staggered Zeeman field, nearest-neighbor interaction, beyond-near-neighbor tunneling, etc. can be readily realized. They underlie the emergence of various topological phases. Our proposal can be realized with current technology and hence has potential applications in quantum simulation of topological matter.