Ultracold Atoms In Optical Lattices Research Articles

Individually tunable tunnelling coefficients in optical lattices using local periodic driving

Abstract Ultracold atoms in optical lattices have emerged as powerful quantum simulators of translationally invariant systems with many applications in e.g. strongly-correlated and topological systems. However, the ability to locally tune all Hamiltonian parameters remains an outstanding goal that would enable the simulation of a wider range of quantum phenomena. Motivated by recent advances in quantum gas microscopes and optical tweezers, we here show theoretically how local control over individual tunnelling links in an optical lattice can be achieved by incorporating local time-periodic potentials. We propose to periodically modulate the on-site energy of individual lattice sites and employ Floquet theory to demonstrate how this provides full individual control over the tunnelling amplitudes in one dimension. We provide various example configurations realising interesting topological models such as extended Su–Schrieffer–Heeger models that would be challenging to realise by other means. Extending to two dimensions, we demonstrate that local periodic driving in a Lieb lattice engineers a two-dimensional (2D) network with fully controllable tunnelling magnitudes. In a three-site plaquette, we show full simultaneous control over the relative tunnelling amplitudes and the gauge-invariant flux piercing the plaquette, providing a clear stepping stone to building a fully programmable 2D tight-binding model. We also explicitly demonstrate how utilise our technique to generate a magnetic field gradient in 2D. This local modulation scheme is applicable to many different lattice geometries.

Holographic imaging of an array of submicron light scatterers at low photon numbers

We experimentally test a recently proposed holographic method for imaging coherent light scatterers which are distributed over a two-dimensional grid. In our setup, the scatterers consist of a back-illuminated, opaque mask with submicron-sized holes. We study how the imaging fidelity depends on various parameters of the set-up. We observe that a few hundred scattered photons per hole already suffice to obtain a fidelity of 96% to correctly determine whether a hole is located at a given grid point. The holographic method demonstrated here has a high potential for applications with ultracold atoms in optical lattices.

Scalable Multipartite Entanglement Created by Spin Exchange in an Optical Lattice.

Ultracold atoms in optical lattices form a competitive candidate for quantum computation owing to the excellent coherence properties, the highly parallel operations over spins, and the ultralow entropy achieved in qubit arrays. For this, a massive number of parallel entangled atom pairs have been realized in superlattices. However, the more formidable challenge is to scale up and detect multipartite entanglement, the basic resource for quantum computation, due to the lack of manipulations over local atomic spins in retroreflected bichromatic superlattices. In this Letter, we realize the functional building blocks in quantum-gate-based architecture by developing a cross-angle spin-dependent optical superlattice for implementing layers of quantum gates over moderately separated atoms incorporated with a quantum gas microscope for single-atom manipulation and detection. Bell states with a fidelity of 95.6(5)% and a lifetime of 2.20±0.13 s are prepared in parallel, and then connected to multipartite entangled states of one-dimensional ten-atom chains and two-dimensional plaquettes of 2×4 atoms. The multipartite entanglement is further verified with full bipartite nonseparability criteria. This offers a new platform toward scalable quantum computation and simulation.

A comparative study of deconvolution techniques for quantum-gas microscope images

Quantum-gas microscopes are used to study ultracold atoms in optical lattices at the single-particle level. In these systems atoms are localised on lattice sites with separations close to or below the diffraction limit. To determine the lattice occupation with high fidelity, a deconvolution of the images is often required. We compare three different techniques, a local iterative deconvolution algorithm, Wiener deconvolution and the Lucy–Richardson algorithm, using simulated microscope images. We investigate how the reconstruction fidelity scales with varying signal-to-noise ratio, lattice filling fraction, varying fluorescence levels per atom, and imaging resolution. The results of this study identify the limits of singe-atom detection and provide quantitative fidelities which are applicable for different atomic species and quantum-gas microscope setups.

Optimal lattice depth on lifetime of D-band ultracold atoms in a triangular optical lattice.

Ultracold atoms in optical lattices are a flexible and effective platform for quantum precision measurement, and the lifetime of high-band atoms is an essential parameter for the performance of quantum sensors. In this work, we investigate the relationship between the lattice depth and the lifetime of D-band atoms in a triangular optical lattice and show that there is an optimal lattice depth for the maximum lifetime. After loading the Bose-Einstein condensate into D band of optical lattice by shortcut method, we observe the atomic distribution in quasi-momentum space for the different evolution time, and measure the atomic lifetime at D band with different lattice depths. The lifetime is maximized at an optimal lattice depth, where the overlaps between the wave function of D band and other bands (mainly S band) are minimized. Additionally, we discuss the influence of atomic temperature on lifetime. These experimental results are in agreement with our numerical simulations. This work paves the way to improve coherence properties of optical lattices, and contributes to the implications for the development of quantum precision measurement, quantum communication, and quantum computing.

Erratum: Anyon braiding on a fractal lattice with a local Hamiltonian [Phys. Rev. A 105 , L021302 (2022)

There is a growing interest in searching for topology in fractal dimensions with the aim of finding different properties and advantages compared to the integer dimensional case. Here, we construct a local Hamiltonian on a fractal lattice whose ground state exhibits topological braiding properties. The fractal lattice is obtained from a second generation Sierpinski carpet with Hausdorff dimension 1.89. We use local potentials to trap and exchange anyons in the model, and the numerically obtained results for the exchange statistics of the anyons are close to the ideal statistics for quasiholes in a bosonic Laughlin state at half filling. For the considered system size, the energy gap is about three times larger for the fractal lattice than for a two-dimensional square lattice, and we find that the braiding results obtained on the fractal lattice are more robust against disorder. We propose a scheme to implement both fractal lattices and our proposed local Hamiltonian with ultracold atoms in optical lattices.

Probing quantum phase transition point by tuning an external anti trap.

Manipulation of ultracold atoms in optical lattices is one of the optimal ways to observe phase transitions of the Hubbard model which is useful in a variety of condensed-matter systems. Bosonic atoms in this model experience a phase transition from superfluids to Mott insulators by tuning systematic parameters. However, in conventional setups, phase transitions take place over a large range of parameters instead of one critical point due to the background inhomogeneity caused by the Gaussian shape of optical-lattice lasers. To probe the phase transition point more precisely in our lattice system, we apply a blue-detuned laser to compensate for this local Gaussian geometry. By inspecting the change of visibility, we find a sudden jump point at one particular trap depth of optical lattices, corresponding to the first appearance of Mott insulators in inhomogeneous systems. This provides a simple method to detect the phase transition point in such inhomogeneous systems. We believe it will be a useful tool for most cold atom experiments.

Few-Body Analog Quantum Simulation with Rydberg-Dressed Atoms in Optical Lattices

Most experiments with ultracold atoms in optical lattices have contact interactions and therefore operate at high densities of around one atom per site to observe the effect of strong interactions. Strong ranged interactions can be generated via Rydberg dressing, which opens up the path to exploring the physics of few interacting particles. Rather than the unit cells of a crystal, the sites of the optical lattice can now be interpreted as discretized space. This allows the study of completely new types of problems in a familiar architecture. We investigate the possibility of realizing problems akin to those found in quantum chemistry, although with a different scaling law in the interactions. Through numerical simulation, we show that simple pseudoatoms and pseudomolecules could be prepared with high fidelity in state-of-the-art experiments.Received 12 December 2022Revised 7 February 2023Accepted 22 February 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020301Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCold gases in optical latticesQuantum simulationAtomic, Molecular & OpticalQuantum Information

Quantum simulations with ultracold atoms in optical lattices: past, present and future

Quantum simulations with ultracold atoms in optical lattices: past, present and future

An accordion superlattice for controlling atom separation in optical potentials

We propose a method for separating trapped atoms in optical lattices by large distances. The key idea is the cyclic transfer of atoms between two lattices of variable spacing, known as accordion lattices, each covering at least a factor of two in lattice spacing. By coherently loading atoms between the two superimposed potentials, we can reach, in principle, arbitrarily large atom separations, while requiring only a relatively small numerical aperture. Numerical simulations of our ‘accordion superlattice’ show that the atoms remain localized to one lattice site throughout the separation process, even for moderate lattice depths. In a proof-of-principle experiment, we demonstrate the optical fields required for the accordion superlattice using acousto-optic deflectors. The method can be applied to neutral-atom quantum computing with optical tweezers, as well as quantum simulation of low-entropy many-body states. For instance, a unit-filling atomic Mott insulator can be coherently expanded by a factor of ten in order to load an optical tweezer array with very high filling. In turn, sorted tweezer arrays can be compressed to form high-density states of ultracold atoms in optical lattices. The method can also be applied to biological systems where dynamical separation of particles is required.

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.

Multifrequency optical lattice for dynamic lattice-geometry control

Ultracold atoms in optical lattices are pristine model systems with a tunability and flexibility that goes beyond solid-state analogies, e.g., dynamical lattice-geometry changes allow tuning a graphene lattice into a boron-nitride lattice. However, a fast modulation of the lattice geometry remains intrinsically difficult. Here we introduce a multi-frequency lattice for fast and flexible lattice-geometry control and demonstrate it for a three-beam lattice, realizing the full dynamical tunability between honeycomb lattice, boron-nitride lattice and triangular lattice. At the same time, the scheme ensures intrinsically high stability of the lattice geometry. We introduce the concept of a geometry phase as the parameter that fully controls the geometry and observe its signature as a staggered flux in a momentum space lattice. Tuning the geometry phase allows to dynamically control the sublattice offset in the boron-nitride lattice. We use a fast sweep of the offset to transfer atoms into higher Bloch bands, and perform a new type of Bloch band spectroscopy by modulating the sublattice offset. Finally, we generalize the geometry phase concept and the multi-frequency lattice to three-dimensional optical lattices and quasi-periodic potentials. This scheme will allow further applications such as novel Floquet and quench protocols to create and probe, e.g., topological properties.

Floquet engineering the band structure of materials with optimal control theory

We demonstrate that the electronic structure of a material can be deformed into Floquet pseudobands with arbitrarily tailored shapes. We achieve this goal with a combination of quantum optimal control theory and Floquet engineering. The power and versatility of this framework is demonstrated here by utilizing the independent-electron tight-binding description of the $\ensuremath{\pi}$ electronic system of graphene. We show several prototype examples focusing on the region around the $K$ (Dirac) point of the Brillouin zone: creation of a gap with opposing flat valence and conduction bands, creation of a gap with opposing concave symmetric valence and conduction bands (which would correspond to a material with an effective negative electron-hole mass), and closure of the gap when departing from a modified graphene model with a nonzero field-free gap. We employ time-periodic drives with several frequency components and polarizations, in contrast to the usual monochromatic fields, and use control theory to find the amplitudes of each component that optimize the shape of the bands as desired. In addition, we use quantum control methods to find realistic switch-on pulses that bring the material into the predefined stationary Floquet band structure, i.e., into a state in which the desired Floquet modes of the target bands are fully occupied, so that they should remain stroboscopically stationary, with long lifetimes, when the weak periodic drives are started. Finally, we note that although we have focused on solid state materials, the technique that we propose could be equally used for the Floquet engineering of ultracold atoms in optical lattices and for other nonequilibrium dynamical and correlated systems.

Glassy disorder-induced effects in noisy dynamics of Bose–Hubbard and Fermi–Hubbard systems

We address the effects of quenched disorder averaging in the time-evolution of systems of ultracold atoms in optical lattices in the presence of noise, imposed by an environment. For bosonic systems governed by the Bose–Hubbard Hamiltonian, we quantify the response of disorder in Hamiltonian parameters in terms of physical observables, including bipartite entanglement in the ground state, and report the existence of disorder-induced enhancement in weakly interacting cases. For systems of two-species fermions described by the Fermi–Hubbard Hamiltonian, we find similar results. In both cases, our dynamical calculations show no appreciable change in the effects of disorder from that of the initial state of the evolution. We explain our findings in terms of the statistics of the disorder in the parameters and the behaviour of the observables with the parameters.

Direct geometric probe of singularities in band structure.

A quantum system's energy landscape may have points where multiple energy surfaces are degenerate and that exhibit singular geometry of the wave function manifold, with major consequences for the system's properties. Ultracold atoms in optical lattices have been used to indirectly characterize such points in the band structure. We measured the non-Abelian transformation produced by transport directly through the singularities. We accelerated atoms along a quasi-momentum trajectory that enters, turns, and then exits the singularities at linear and quadratic band-touching points of a honeycomb lattice. Measurements after transport identified the topological winding numbers of these singularities to be 1 and 2, respectively. Our work introduces a distinct method for probing singularities that enables the study of non-Dirac singularities in ultracold-atom quantum simulators.

The manipulation of ultracold atoms of high orbitals in optical lattices

Ultracold atoms in optical lattices are a powerful tool for quantum simulation, precise measurement, and quantum computation. A fundamental problem in applying this quantum system is how to manipulate the higher bands or orbitals in Bloch states effectively. Here we mainly review our methods for manipulating high orbital ultracold atoms in optical lattices with different configurations. Based on these methods, we construct the atom-orbital qubit under nonadiabatic holonomic quantum control and Ramsey interferometry with trapped motional quantum states. Then we review the observation of the novel quantum states and the study of the dynamical evolution of the high orbital atoms in optical lattices. The effective manipulation of the high orbitals provides strong support for applying ultracold atoms in the optical lattice in many fields.

Cavity-Enhanced Optical Lattices for Scaling Neutral Atom Quantum Technologies to Higher Qubit Numbers

We demonstrate a cavity-based solution to scale up experiments with ultracold atoms in optical lattices by an order of magnitude over state-of-the-art free space lattices. Our two-dimensional optical lattices are created by power enhancement cavities with large mode waists of 489(8) $\mu$m and allow us to trap ultracold strontium atoms at a lattice depth of 60 $\mu$K by using only 80 mW of input light per cavity axis. We characterize these lattices using high-resolution clock spectroscopy and resolve carrier transitions between different vibrational levels. With these spectral features, we locally measure the lattice potential envelope and the sample temperature with a spatial resolution limited only by the optical resolution of the imaging system. The measured ground-band and trap lifetimes are 18(3) s and 59(2) s, respectively, and the lattice frequency (depth) is long-term stable on the MHz (0.1\%) level. Our results show that large, deep, and stable two-dimensional cavity-enhanced lattices can be created at any wavelength and can be used to scale up neutral-atom-based quantum simulators, quantum computers, sensors, and optical lattice clocks.

Second-order topological insulator in periodically driven optical lattices.

The higher-order topological insulator (HOTI) is a new type of topological system which has special bulk-edge correspondence compared with conventional topological insulators. In this work, we propose a scheme to realize Floquet HOTI with ultracold atoms in optical lattices. With the combination of periodically spin-dependent driving of the superlattices and a long-range coupling term, a Floquet second-order topological insulator with four zero-energy corner states emerges, whose Wannier bands are gapless and exhibit interesting bulk topology. Furthermore, the nearest-neighbor anisotropic coupling term also induced other intriguing topological phenomena, e.g. non-topologically protected corner states and topological semimetal for two different types of lattice structures respectively. Our scheme may give insight into the construction of different types of higher-order topological insulators in synthetic systems. It also provides an experimentally feasible platform to research the relations between different types of topological states and may have a wide range of applications in future.

Nonlinear Hall response in the driving dynamics of ultracold atoms in optical lattices

We propose that a nonlinear Hall response can be observed in Bloch oscillations of ultracold atoms in optical lattices under the condition of preserved time-reversal symmetry. In the short-time limit of Bloch oscillations driven by a direct current (dc) field, the nonlinear Hall current dominates, being a second-order response to the external field strength. The associated Berry curvature dipole, which is a second-order nonlinear coefficient of the driving field, can be obtained from the oscillation of atoms. In an alternating current (ac) driving field, the nonlinear Hall response has a double frequency of the driving force in the case of time-reversal symmetry.