Two-dimensional Optical Lattice Research Articles

Transfer of solitons and half-vortex solitons via adiabatic passage

We show that the transfer of matter-wave solitons and half-vortex solitons in a spin-orbit coupled Bose-Einstein condensate between two (or more) arbitrarily chosen sites of an optical lattice can be implemented using the adiabatic passage. The underlying linear Hamiltonian has a flat band in its spectrum, so that even sufficiently weak interatomic interactions can sustain well-localized Wannier solitons which are involved in the transfer process. The adiabatic passage is assisted by properly chosen spatial and temporal modulations of the Rabi frequency. Within the framework of a few-mode approximation, the mechanism is enabled by a dark state created by coupling the initial and target low-energy solitons with a high-energy extended Bloch state, like in the conventional stimulated Raman adiabatic passage used for the coherent control of quantum states. In real space, however, the atomic transfer between initial and target states is sustained by the current carried by the extended Bloch state, which remains populated during the whole process. The full description of the transfer is provided by the Gross-Pitaevskii equation. Protocols for the adiabatic passage are described for one- and two-dimensional optical lattices, as well as for splitting and subsequent transfer of an initial wave packet simultaneously to two different target locations. Published by the American Physical Society 2024

Centrosymmetric multipole solitons with fractional-order diffraction in two-dimensional parity-time-symmetric optical lattices

Multipole solitons in higher-dimensional nonlinear Schrödinger equation with fractional diffraction are of high current interest. This paper studies multipole gap solitons in parity-time (PT)-symmetric lattices with fractional diffraction. The results obtained demonstrate that both on-site and off-site eight-pole solitons with fractional-order diffraction can be stabilized in a two-dimensional (2D) PT-symmetric optical lattice with defocusing Kerr nonlinearity. These solitons are in-phase and centrosymmetric. On-site eight-pole solitons propagate in a square formation, while off-site solitons propagate in a two-by-four formation. Both on-site and off-site solitons are found to be stable within a low-power range in the first band gap. As the Lévy index decreases, the stability regions of both on-site and off-site solitons narrow. Off-site eight-pole solitons can approach the lower edge of the first Bloch band, whereas on-site eight-pole solitons cannot. Additionally, we investigate the transverse power flow vector of these multipole gap solitons, illustrating the transverse energy flow from gain to loss regions.

Free electrons spin-dependent Kapitza–Dirac effect in two-dimensional triangular optical lattice

Abstract The free electron spin dynamics in Kapitza–Dirac (KD) effect had been studied theoretically in one-dimensional standing wave of EUV to X-ray laser with extremely high intensity, which is far beyond experimental realization. Here, we propose to achieve the free electron spin-dependent KD effect in two-dimensional triangular optical lattice with spatial inversion symmetry breaking, and the theoretical results reveal that laser with wavelength in visible or near-IR and five orders of magnitude decreased intensity could lead to obvious spin-dependent KD effect. This work provides the way to realize the free electron spin-dependent KD effect experimentally.

Hidden-vortex quantum droplets in an optical lattice

We explore discrete quantum droplets with hidden-vortex structures in a deep two-dimensional optical lattice containing a Bose-Bose mixture. Using the extended Gross-Pitaevskii equation, and considering local interactions and Lee-Huang-Yang corrections, we affirm the stable existence of these droplets, which are identified by identical density patterns and opposing vortices in both components. We extensively study the droplets with lower topological charges, focusing on their morphological changes. Despite the expansion of internal boundaries within the vortex mode with increased charge, the lattice symmetry and phase change limit the boundary growth, leading to a unique mode pattern degeneracy exclusive to discrete systems. By fixing the norm of the states (representing the particle number of the system), we identify multiple degenerate modes with topological charges up to 5, plotting their chemical potential curves and providing a theoretical explanation for the energy changes linked to topological charge. Our simulations confirm these outcomes, validating our discoveries.

Lattice polaron in a Bose–Einstein condensate of hard-core bosons

Lattice polarons, quasiparticles arising from the interaction between an impurity and its surrounding bosonic environment confined to a lattice system, have emerged as a platform for generating complex few-body states, probing many-body phenomena, and addressing long-standing problems in physics. In this study, we employ a variational ansatz to investigate the quasiparticle and spectral properties of an impurity coupled to a condensate gas of hard-core bosons in a two-dimensional optical lattice. Our findings demonstrate that the polaron features can be tuned by adjusting the filling factor of the bath, revealing intriguing polaron characteristics in the strongly interacting regime. These results offer valuable insights for lattice polaron experiments with ultracold gases and can serve as a guide for new experiments in emergent quantum devices, such as moiré materials, where optical excitations can be described in terms of hard-core bosons.

Spin–orbit-coupled Bose gas with Rydberg interactions confined in a two-dimensional optical lattice

We consider the ground state of Rydberg-dressed Bose gas with spin–orbit coupling and confined in a two-dimensional optical lattice. The effects of system’s parameters, especially the nonlocal Rydberg interaction and spin–orbit coupling, on the ground-state structure of such a system are explored in full parameter space. It is found that in the absence of spin–orbit coupling, the ground-state structure of the system changes from the initial optical lattice structure to a two-dimensional periodic one with the cell size decreasing with the strength of Rydberg interaction. In the presence of spin–orbit coupling, both the phase and the internal structure of unit cell show strong dependence on the strength of spin–orbit coupling. Finally, the strong interacting gas is also considered.

Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model.

We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum MonteCarlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.

Interference-induced anisotropy in a two-dimensional dark-state optical lattice

We describe a two-dimensional optical lattice for ultracold atoms with spatial features below the diffraction limit created by a bichromatic optical standing wave. At every point in space these fields couple the internal atomic states in a three-level Lambda coupling configuration. Adiabatically following the local wavefunction of the resulting dark state yields a spatially uniform Born-Oppenheimer potential augmented by geometric scalar and vector potentials appearing due to spatially rapid changes of the wavefunction. Depending on system parameters, we find that the geometric scalar potential can interpolate from a 2D analogue of the Kronig-Penney lattice, to an array of tubes with a zig-zag shaped barrier. The geometric vector potential induces a spatially periodic effective magnetic field (the Berry's curvature) that can be tuned to cause destructive interference between neighboring tubes, thereby decoupling them at a critical point in parameter space. We numerically investigate the energy spectrum including decay from the excited state, and find that the adiabatic approximation is sound for strong coupling strengths, leading to negligible loss in the dark state manifold. Furthermore, the spectrum is well-described by a non-Hermitian tight binding model with on-site losses, and hopping characterized by both loss and, surprisingly, gain.

Vortices number and the critical atoms number of a rotating Bose–Einstein condensates in two-dimensional optical lattice

In this paper, the vortices number and the critical atoms number are calculated. Calculations are performed for ultracold trapped Bose gas in two-dimensional deep optical lattice. Hellmann–Feynman theorem is used here to calculate the expectation values of the angular momentum and thermal average of square radius (in situ size). The above-mentioned parameters are calculated from the thermodynamic grand potential [Formula: see text]. The latter is calculated using a conventional semi-classical approximation. This thermodynamic grand potential allows us to investigate the impacts of the finite size and inter-atomic interaction effects. The obtained result for the vortices number has a peak with increase in the rate of rotation. While the critical atoms number has increase in nature with increase in the critical temperature. These parameters show a major dependence on the inter-atomic interaction, depth of optical lattice and number of particles.

Formation controllable two-dimensional surface optical lattices

The evanescent light field created by total internal reflection at a dielectric-vacuum interface has tight spatial confinement and high local intensity. These properties become more robust when a dual layer of dielectric thin films with different thicknesses is deposited on a planar dielectric surface. Optical construction is promising in nanoscale trapping of absorbed atoms congregating at extreme light field intensity distribution regions on the dielectric surface. Here, we theoretically demonstrate the controllable two-dimensional surface optical lattices based on the evanescent electric field generated by the Hermite-Gaussian light beam. By considering the coupling of lattice to quadrupole-active atomic transitions, we show that the topologies cannot just have high stability, but also the optical potential deep, and thus the dynamic trapping can be governed by changing the design parameters of the optical construction. We expect that this study may contribute to providing another unique method for fabricating spatially complicated two-dimensional nanostructures.

Phase Dependent Parity Time Symmetry in a quantum dot nanostructure

We present a diamond configuration quantum dots nanostructure trapped in two-dimensional (2D) optical lattices for the investigation of parity time (PT) symmetry. We trap quantum dots in a Gaussian density distribution to examine the PT, non-PT, and anti-PT symmetry in periodic 2D optical lattices. The variation in the relative phase of the optical beams in the quantum dots spectrum indicates either PT, anti-PT, or non-PT symmetry, resulting in an intriguing modulation of imaginary and real refractive index (RI) components. Controlling the appropriate modulation of the RI leads in PT symmetry being controlled by a single parameter, the relative phase of the optical fields. Using detuning and the coupling field of Rabi frequencies, we may determine the state of PT symmetry as well as the direction of field propagation. Coherent control of PT symmetry in 2D quantum dot nanostructure trapped in optical lattices may also have applications in 2D optical devices such as diodes, modulators and photonic transistors.

Probing site-resolved correlations in a spin system of ultracold molecules

Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in explaining fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising platform that combines several advantageous properties1-11. These include a large set of internal states with long coherence times12-17 and long-range, anisotropic interactions. These features could enable the exploration of intriguing phases of correlated quantum matter, such as topological superfluids18, quantum spin liquids19, fractional Chern insulators20 and quantum magnets21,22. Probing correlations in these phases is crucial to understanding their properties, necessitating the development of new experimental techniques. Here we use quantum gas microscopy23 to measure the site-resolved dynamics of quantum correlations of polar 23Na87Rb molecules confined in a two-dimensional optical lattice. By using two rotational states of the molecules, we realize a spin-1/2 system with dipolar interactions between particles, producing a quantum spin-exchange model21,22,24,25. We study the evolution of correlations during the thermalization process of an out-of-equilibrium spin system for both spatially isotropic and anisotropic interactions. Furthermore, we examine the correlation dynamics of a spin-anisotropic Heisenberg model engineered from the native spin-exchange model by using periodic microwave pulses26-28. These experiments push the frontier of probing and controlling interacting systems of ultracold molecules, with prospects for exploring new regimes of quantum matter and characterizing entangled states that are useful for quantum computation29,30 and metrology31.

Optical PT symmetry and PT antisymmetry in one- and two-dimensional optical lattices

Optical PT symmetry and PT antisymmetry in one- and two-dimensional optical lattices

Dimensional cross-over in self-organised super-radiant phases of ultra-cold atoms inside a cavity

We consider a condensate of ultra-cold bosonic atoms in a linear optical cavity illuminated by a two-pump configuration where each pump makes different angles with the direction of the cavity axis. We show that such a configuration allows a smooth transition from a one-dimensional quantum optical lattice configuration to a two-dimensional quantum optical lattice configuration induced by the cavity–atom interaction. Using a Holstein–Primakoff transformation, we find the atomic density profile of such a self-organised ground state in the super-radiant phase as a function of the angular orientations of the pumps in such a dynamical quantum optical lattice, and also provide an analysis of their structures in coordinate and momentum space. In the later part of the paper, we show how the corresponding results can also be qualitatively understood in terms of an extended Bose–Hubbard model in such a quantum optical lattice potential.

Fractional quantum Hall effect in optical lattices

In this research, we study the bosonic fractional quantum Hall (FQH) states in a system of ultracold bosons in a two-dimensional optical lattice in the presence of a synthetic magnetic field, described by the bosonic Harper–Hofstadter Hamiltonian. We use the cluster Gutzwiller mean-field and exact diagonalization techniques in our work. We obtain incompressible states as ground states at various filling factors similar to those of the FQH states. We focus in particular on the ν = 1/2 FQH state, and it is characterized by the two-point correlation function and the many-body Chern number. We further investigate the effect of dipolar interaction on the ν = 1/2 FQH state. We find that the dipolar interaction stabilizes the FQH state against the competing superfluid state.

The behavior of ultra-cold atoms in two-dimensional optical lattices with asymmetric periodic pinning potentials

We examine the disorder effect of the pinning potential acting on ultracold atoms in the optical lattice based on the expanded Bose–Hubbard model for soft-core bosons. Using Quantum Monte Carlo simulation with local optimal Worm algorithm, we obtain three additional crystal-like phase types at commensurate densities, ρ = 1/2, 1, and 3/2 besides two basic phases which are superfluid and Mott insulator phases as observed in the bare soft-core boson model. In the presence of disorder, the superfluid and the charge-density wave coexist in the sandwiched regions between the superfluid and the solid orders around the commensurate densities. This observation signifies our work because it has not been revealed previously in other models of the soft-core bosons.

Quantum simulation of ultracold atoms in optical lattice based on dynamical mean-field theory

With the development of atomic cooling technology and optical lattice technology, the quantum system composed of optical lattice and ultracold atomic gas has become a powerful tool for quantum simulation. The purity and highly controllable nature of the optical lattice give it a strong regulatory capability. Therefore, more complex and interesting physical phenomena can be simulated, which deepens the understanding of quantum many-body physics. In recent years, we have studied different Bose systems with strong correlations in optical lattice based on the bosonic dynamical mean-field theory, including multi-component system, high- orbit bosonic system, and long-range interaction system. In this review, we introduce the research progress of the above mentioned. Through the calculation by using bosonic dynamical mean-field theory which has been generalized to multi-component and real space versions, a variety of physical phenomena of optical crystal lattice Bose system in weak interaction intervals to strong interaction intervals can be simulated. The phase diagram of spin-1 ultracold bosons in a cubic optical lattice at zero temperature and finite temperature are drawn. A spin-singlet condensate phase is found, and it is observed that the superfluid can be heated into a Mott insulator with even (odd) filling through the first (second) phase transition. In the presence of a magnetic field, the ground state degeneracy is broken, and there are very rich quantum phases in the system, such as nematic phase, ferromagnetic phase, spin-singlet insulating phase, polar superfluid, and broken-axisymmetry superfluid. In addition, multistep condensations are also observed. Further, we calculate the zero-temperature phase diagram of the mixed system of spin-1 alkali metal atoms and spin-0 alkali earth metal atoms, and find that the system exhibits a non-zero magnetic ordering, which shows a second-order Mott insulation-superfluid phase transition when the filling number is <inline-formula><tex-math id="M1">\begin{document}$n=1$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230701_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230701_M1.png"/></alternatives></inline-formula>, and a first-order Mott insulation-superfluid phase transition when the filling number is <inline-formula><tex-math id="M2">\begin{document}$n=2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230701_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230701_M2.png"/></alternatives></inline-formula>. The two-step Mott-insulating-superfluid phase transition due to mass imbalance is also observed. In the study of long-range interactions, we first use Rydberg atoms to find two distinctive types of supersolids, and then realize the superradiant phase coupled to different orbits by controlling the reflection of the pump laser in the system coupled to the high-finesse cavity. Finally, we study the high-orbit Bose system. We propose a new mechanism of spin angular-momentum coupling with spinor atomic Bosons based on many-body correlation and spontaneous symmetry breaking in a two-dimensional optical lattice, and then study the orbital frustration in a hexagonal lattice. We find that the interaction between orbital frustration and the strong interaction results in exotic Mott and superfluid phases with spin-orbital intertwined orders.

Staggered quantum phases of dipolar bosons at finite temperatures

The extended Bose-Hubbard model with correlated tunneling exhibits staggered superfluid and supersolid quantum phases. We study finite-temperature phase transitions of quantum phases of dipolar bosons in a two-dimensional optical lattice using Gutzwiller mean-field and quantum Monte Carlo approaches. When nearest-neighbor repulsion is comparable to the on-site interaction, we find that the two topologically distinct superfluids are separated by a normal-fluid phase, while at stronger off-site interactions, density-modulated insulating quantum phases appear. We estimate the critical temperature of the staggered-superfluid to normal-fluid transition and show that this transition is of the Kosterlitz-Thouless type. Finally, we elucidate the coexistence of staggered quantum phases in the presence of an external trapping potential. Our study paves the way to observe novel staggered quantum phases in dipolar optical lattice experiments.

Two-dimensional lattice soliton and pattern formation in a cold Rydberg atomic gas with nonlocal self-defocusing Kerr nonlinearity

We propose a Rydberg-dressed atomic gas under the condition of electromagnetically induced transparency (EIT) to realize two-dimensional (2D) optical lattices and achieve nonlocal giant Kerr nonlinearity. We obtain the formation of stable 2D bright lattice solitons that result by the balance of diffraction with negative effective mass and nonlocal self-defocusing Kerr nonlinearity. Moreover, extended optical pattern formations are observed based on the modulation instability (MI). It is interesting to note that the solitons and patterns obtained are strongly influenced by the depth of the potential, the degree of nonlocality, and the strength of the Kerr nonlinearity. The results of our work provide a route for versatile control of laser patterns and solitons, which may have potential applications in optical communications and information processing.

Quantum precision measurement of two-dimensional forces with [formula omitted]-Newton stability

High-precision sensing of vectorial forces has broad impact on both fundamental research and technological applications such as the examination of vacuum fluctuations and the detection of surface roughness of nanostructures. Recent years have witnessed much progress on sensing alternating electromagnetic forces for the rapidly advancing quantum technology—orders of magnitude improvement has been accomplished on the detection sensitivity with atomic sensors, whereas such high-precision measurements for static electromagnetic forces have rarely been demonstrated. Here, based on quantum atomic matter waves confined by a two-dimensional optical lattice, we perform precision measurement of static electromagnetic forces by imaging coherent wave mechanics in the reciprocal space. The lattice confinement causes a decoupling between real-space and reciprocal dynamics, and provides a rigid coordinate frame for calibrating the wavevector accumulation of the matter wave. With that we achieve a state-of-the-art sensitivity of 2.30(8)×10-26 N/Hz. Long-term stabilities on the order of 10-28 N are observed in the two spatial components of a force, which allows probing atomic Van der Waals forces at one millimeter distance. As a further illustrative application, we use our atomic sensor to calibrate the control precision of an alternating electromagnetic force applied in the experiment. Future developments of this method hold promise for delivering unprecedented atom-based quantum force sensing technologies.