Two-dimensional Optical Superlattice Research Articles

Multiorder topological superfluid phase transitions in a two-dimensional optical superlattice

Higher-order topological superfluids have gapped bulk and symmetry-protected Majorana zero modes with various localizations. Motivated by recent advances, we present a proposal for synthesizing multi-order topological superfluids that support various Majorana zero modes in ultracold atomic gases. For this purpose, we use the two-dimensional optical superlattice that introduces a spatial modulation to the spin-orbit coupling in one direction, providing an extra degree of freedom for the emergent higher-order topological state. We find the topologically trivial superfluids, first-order and second-order topological superfluids, as well as different topological phase transitions among them with respect to the experimentally tunable parameters. Besides the conventional transition characterized by the Chern number associated with the bulk gap closing and reopening, we find the system can support the topological superfluids with Majorana corner modes, but the topological phase transition undergoes no gap-closing of bulk bands. Instead, the transition is refined by the quadrupole moment and signaled out by the gap-closing of edge states. The proposal is based on the $s$-wave interaction and is valid using existing experimental techniques, which unifies multi-order topological phase transitions in a simple but realistic system.

Geometric effects in the effective-mass theory and topological optical superlattices

Cold atoms tailored by an optical lattice have become a fascinating arena for simulating quantum physics. In this area, one important and challenging problem is creating effective spin-orbit coupling (SOC), especially for fashioning a cold atomic gas into a topological phase, for which prevailing approaches mainly rely on the Raman coupling between the atomic internal states and a laser field. Herein, a strategy for realizing effective SOC is proposed by exploiting the geometric effects in the effective-mass theory, without resorting to internal atomic states. It is shown that the geometry of Bloch states can have nontrivial effects on the wave-mechanical states under external fields, leading to effective SOC and an effective Darwin term, which have been neglected in the standard effective-mass approximation. It is demonstrated that these relativisticlike effects can be employed to introduce effective SOC in a two-dimensional optical superlattice, and induce a nontrivial topological phase.

Isolated structures in two-dimensional optical superlattice

Overlaying commensurate optical lattices with various configurations called superlattices can lead to exotic lattice topologies and, in turn, a discovery of novel physics. In this study, by overlapping the maxima of lattices, a new isolated structure is created, while the interference of minima can generate various “sublattice” patterns. Three different kinds of primitive lattices are used to demonstrate isolated square, triangular, and hexagonal “sublattice” structures in a two-dimensional optical superlattice, the patterns of which can be manipulated dynamically by tuning the polarization, frequency, and intensity of laser beams. In addition, we propose the method of altering the relative phase to adjust the tunneling amplitudes in “sublattices”. Our configurations provide unique opportunities to study particle entanglement in “lattices” formed by intersecting wells and to implement special quantum logic gates in exotic lattice geometries.

Simulating Weyl points and nodal loops in an optical superlattice

We propose a scheme to simulate Weyl points and nodal loops with ultracold atoms in an optical lattice that is subjected to realizable synthetic magnetic field and synthetic dimension. We show that a Hofstadter-like Hamiltonian with a cyclically parameterized on-site energy term can be realized in a tunable two-dimensional optical superlattice, based on the laser-assisted atomic tunneling method. This model effectively describes a three-dimensional periodic lattice system under magnetic fluxes, where a synthetic dimension is encoded by a cyclical phase of the optical lattice potential. For different atomic hopping configurations, the single-particle bands are demonstrated to, respectively, exhibit Weyl points and nodal loops in the extended three-dimensional Brillouin zone. Furthermore, we illustrate that the mimicked Weyl points and nodal loops can be experimentally detected by measuring the atomic transfer fraction in Bloch---Zener oscillations.

Ultrafast exciton–polariton scattering towards the Dirac points

Using the Feynman–Dyson diagram technique, we study nonlinear polariton–polariton scattering in a two-dimensional micropillar-based optical superlattice with hexagonal symmetry. We demonstrate that both the emerging polariton chirality and the loop Feynman diagrams up to infinite order should be strictly accounted for in the evaluation of the self-energy of the system. Further, we explicitly show that in such a design the time of polariton scattering towards the Dirac points can be drastically decreased which can be used, for instance, in engineering novel classes of polariton lasers with substantially reduced thresholds.

Theory of second-harmonic generation in a chirped 2D nonlinear optical superlattice under nonlinear Raman-Nath diffraction

We analyze second-harmonic generation (SHG) in a two-dimensional nonlinear optical superlattice (NLOS) with its modulation period being chirped in the propagation direction and constant in the transverse direction. This results in efficient multiple SHG via nonlinear Raman–Nath diffraction. We obtain exact analytical expressions for a SH amplitude generated in chirped 2D NLOSs and for its quasi-phase-matching bandwidth. The results of analytical calculations are in excellent agreement with the numerical ones. We show that the process is robust to angular deviations of NLOS and it can be applied to enable tunable and broadband frequency conversion.

Hard-Core Bosons on a Two-Dimensional Square Optical Superlattice* *Supported by the National Natural Science Foundation of China under Grant Nos. 10904096, 10604024, 11474025, and the Natural Science Foundation of Beijing under Grant No. 1092009

In this work, we theoretically study hard-core bosons on a two-dimensional square optical superlattice at T = 0. First of all, we present the mean field phase diagram of this model in terms of the chemical potential μ and the alternating potential strength Δ. Besides a superfluid (SF) phase at Δ = 0 and a charge density wave (CDW) phase in the large Δ at half filling, we demonstrate that a supersolid (SS) phase emerges in the moderate Δ. Then, we focus on the μ = 0, e.g., half filling case, using large-S semiclassical spin-wave approximation to study the SS to CDW quantum phase transition. In particular, we calculate the ground-state energy and the superfluid density at the level of 1/S correction. We then compare the spin-wave results with the large scale quantum Monte Carlo (QMC) simulations using the cluster stochastic series expansion (CSSE) algorithm, and find that while the spin wave method is intuitive with clear physical pictures, the quantum critical point is quite different from that of numerical results which is believed to be accurate. We suggest that as simple as it is, this model still exhibits strong quantum fluctuations near the quantum critical point beyond the power of semiclassical spin-wave approach.

The effect of angle fluctuations in the multi-second-harmonic generation process of two-dimensional aperiodic optical superlattices

The dependence of multi-frequency second-harmonic generation efficiency on the fluctuation in the angle between the interacting waves in the two-dimensional aperiodic optical superlattice is investigated in this paper. It is found that the efficiency of second-harmonic generation is a function of parameters that have an essential and critical role in maintaining the phase-matching condition, one of which is the angle between interacting waves in nonlinear crystal. Applying a comparison between the exact and fluctuated situations in a two-dimensional nonlinear aperiodic optical superlattice causes the output efficiency of the multi-frequency process to be decreased.

Enhancement of nonlinear Raman-Nath diffraction in two-dimensional optical superlattice

We study second harmonic generation via nonlinear Raman-Nath diffraction in an optical superlattice that maintains a periodic modulation of the second-order nonlinear coefficient χ((2)) in transverse direction but undergoes random modulation in longitudinal direction. We show that the random χ((2)) modulation offers a continuous set of reciprocal lattice vectors to compensate for the phase mismatch of nonlinear Raman-Nath diffraction in the longitudinal direction, leading to more efficient harmonic generation for a wide range of wavelengths. We also characterize the intensity dependence of nonlinear Raman-Nath diffraction on the degree of randomness of the optical supperlattice.

Controllable polarization coupled dual-focused second-harmonic generations in a two-dimensional optical superlattice

The nonlinear Huygens-Fresnel principle has been used to design multifunctional nonlinear optical devices. Focused second-harmonic generations have been observed with strong polarization sensitivity. Numerical simulations have been performed, and the results fit well with the experiments.

Numerical simulation of nonlinear field distributions in two-dimensional optical superlattices

A finite difference method in real space is presented for calculating nonlinear optical processes in two-dimensional optical superlattices. The focused second-harmonic generation under the local quasi-phase-matched condition is calculated as an example. The field distribution of both the fundamental and the harmonic wave can be simulated well using this method, and the result agrees well with previous theoretical predictions and experimental studies. It is shown that this method is a simple and rapid technique to analysis nonlinear processes in optical superlattices.

Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices

Dirac-Weyl fermions are massless relativistic particles with a well-defined helicity which arise in the context of high-energy physics. Here we propose a quantum simulation of these paradigmatic fermions using multicomponent ultracold atoms in a two-dimensional square optical lattice. We find that laser-assisted spin-dependent hopping, specifically tuned to the $(2s+1)$-dimensional representations of the $\mathfrak{su}$(2) Lie algebra, directly leads to a regime where the emerging massless excitations correspond to Dirac-Weyl fermions with arbitrary pseudospin $s$. We show that this platform hosts two different phases: a semimetallic phase that occurs for half-integer $s$, and a metallic phase that contains a flat zero-energy band at integer $s$. These phases host a variety of interesting effects, such as a very rich anomalous quantum Hall effect and a remarkable multirefringent Klein tunneling. In addition we show that these effects are directly related to the number of underlying Dirac-Weyl species and zero modes.

QUANTUM PHASES OF ULTRACOLD BOSONIC ATOMS IN A TWO-DIMENSIONAL OPTICAL SUPERLATTICE

We study quantum phases of ultracold bosonic atoms in a two-dimensional optical superlattice. The extended Bose–Hubbard model derived from the system of ultracold bosonic atoms in an optical superlattice is solved numerically with the Gutzwiller approach. We find that the modulated superfluid (MS), Mott-insulator (MI) and density-wave (DW) phases appear in some regimes of parameters. The experimental detection of the first-order correlations and the second-order correlations of different quantum phases with time-of-flight and noise-correlation techniques is proposed.

Multiple quasi-phase-matching in two-dimensional domain-inverted aperiodic optical superlattice

Quasi-phase-matching (QPM) is an alterative approach for nonlinear optical frequency conversion compared to conventional birefringent method in the bulk crystal. In this Letter, two-dimensional aperiodic optical superlattice (2DAOS) for achieving multi-QPM is proposed. A special optical superlattice structure containing pre-designed values of the reciprocal lattice vector G that can accomplish multi-QPM process is given by using stimulated annealing (SA) algorithm.

Fractional-filling Mott domains in two-dimensional optical superlattices

Ultracold bosons in optical superlattices are expected to exhibit fractional-filling insulating phases for sufficiently large repulsive interactions. On strictly one-dimensional systems, the exact mapping between hard-core bosons and free spinless fermions shows that any periodic modulation in the lattice parameters causes the presence of fractional-filling insulator domains. Here, we focus on two recently proposed realistic two-dimensional structures where such mapping does not hold, i.e., the two-leg ladder and the trimerized kagom\'e lattice. Based on a cell strong-coupling perturbation technique, we provide quantitatively satisfactory phase diagrams for these structures, and give estimates for the occurrence of the fractional-filling insulator domains in terms of the intercell to intracell hopping amplitude ratio.

Optical Bistability in Incident-Dependent Two-Dimensional Nonlinear Optical Superlattices

It is shown that, when two coherent waves are obliquely incident to a one-dimensional nonlinear optical superlattice containing Kerr-form dielectric nonlinearity, an incident-dependent two-dimensional nonlinear optical superlattice can be constructed. This structure can be bistable. There exist two types of optical bistable mechanism, i.e., the index-modulation mechanism and distributed feedback mechanism. Owing to the index-modulation mechanism, the threshold for the bistability is lower than that of a more traditional one-dimensional distributed feedback structure.

Gap shift and bistability in two-dimensional nonlinear optical superlattices.

Gap shift and bistability in two-dimensional nonlinear optical superlattices.

Bistable switching in two-dimensional nonlinear optical superlattices

A theoretical study of optical wave propagation in a two-dimensional optical superlattice with Kerr-type nonlinearity is performed. For proper ratio of index modulation strengths of the periodic medium, a stop gap in the linear frequency spectra is found in the vicinity of Bragg angle incidence of the structure. The location of the stop gap and its width depends sensitively on the input power. The nonlinear system is shown to possess a bistable switching between states in pass band and states in stop gap. This bistability is based on the nonlinear mechanism on the stop gap.

A New Type of Bistable Switching in Two-Dimensional Nonlinear Optical Superlattices

We investigate theoretically optical response in a two-dimensional optical superlattice with Kerr-type nonlinearity. We find that in addition to the bistability reported in Phys. Rev. Lett. 71 (1993) 1003 by Xu et al., a new type of bistable switching behavior exists. This bistability is based on the occurrence of the stop gap in the linear spectra and the nonlinear mechanism on it, which makes switching between transmitting and non-transmitting states achievable.

Dynamics of light transmission in two-dimensional nonlinear optical superlattices.

A set of coupled-mode equations is developed to describe the multiwave diffraction of light in two-dimensional nonlinear superlattices, and is solved by numerical methods. At low incident intensities, the solution is time-independent and shows that bistable behavior may appear in the incident-diffracted relations. With an increasing incident intensity, the solution becomes unstable and eventually turns chaotic through the route of intermittance. The threshold intensity for chaos varies with the index-modulation strengths of the superlattice. If the relaxation time of the Kerr-form nonlinearity exceeds the transmission time, only stable solutions are obtained.