Abstract We present an efficient approach to precisely simulate tight binding models with optical lattices, based on programmable digital-micromirror-device (DMD) techniques. Our approach consists of a subroutine of Wegner-flow enabled precise extraction of a tight-binding model for a given optical potential, and a reverse engineering step of adjusting the potential for a targeting model, for both of which we develop classical algorithms to achieve high precision and high efficiency. With renormalization of Wannier functions and high band effects systematically calibrated in our protocol, we show the tight-binding models with programmable onsite energies and tunnelings can be precisely simulated with optical lattices integrated with the DMD techniques. With numerical simulation, we demonstrate that our approach would facilitate quantum simulation of localization physics with adequate programmability and atom-based boson sampling for illustration of quantum computational advantage. We expect this approach would pave a way towards large-scale and precise programmable quantum simulations based on optical lattices.
Abstract We present an efficient approach to precisely simulate tight binding models with optical lattices, based on programmable digital-micromirror-device (DMD) techniques. Our approach consists of a subroutine of Wegner-flow enabled precise extraction of a tight-binding model for a given optical potential, and a reverse engineering step of adjusting the potential for a targeting model, for both of which we develop classical algorithms to achieve high precision and high efficiency. With renormalization of Wannier functions and high band effects systematically calibrated in our protocol, we show the tight-binding models with programmable onsite energies and tunnelings can be precisely simulated with optical lattices integrated with the DMD techniques. With numerical simulation, we demonstrate that our approach would facilitate quantum simulation of localization physics with adequate programmability and atom-based boson sampling for illustration of quantum computational advantage. We expect this approach would pave a way towards large-scale and precise programmable quantum simulations based on optical lattices.
Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local control of chemical potentials and tunnelings, and thus enable us to operate this platform digitally as a programmable quantum simulator. Here, we explore these opportunities and develop ground-state preparation algorithms for different fermionic models, based on the ability to implement both single-particle and many-body high-fidelity fermionic gates, as provided by the native FH Hamiltonian. In particular, we first design variational precompiled quantum circuits to prepare the ground state of the natively implemented FH model, with significant speedups relative to competing adiabatic protocols. Besides, the versatility of this variational approach enables us to target extended FH models, i.e., including terms that are not natively realized on the platform. As an illustration, we include next-nearest-neighbor tunnelings at finite dopings, relevant in the context of d -wave superconductivity. Furthermore, we discuss how to approximate the imaginary-time evolution using variational fermionic circuits, both as an alternative state-preparation strategy and as a subroutine for the quantum Lanczos algorithm to further improve the energy estimation. We benchmark our protocols for ladder geometries, though they can be readily applied to two-dimensional experimental setups to address regimes beyond the capabilities of current classical methods. These results pave the way for more efficient and comprehensive explorations of relevant many-body phases with existing programmable fermionic quantum simulators.
Quantum Fourier transform (QFT) is a widely used building block for quantum algorithms, whose scalable implementation is challenging in experiments. Here, we propose a protocol of quadratic QFT (QQFT) considering cold atoms confined in an optical lattice. This QQFT is equivalent to QFT in the single-particle subspace and generalizes to a many-body setting through the second quantization formalism. We show this QQFT protocol can be implemented using a programmable laser potential with the digital-micromirror-device techniques recently developed in experiments. The QQFT protocol enables programmable Hamiltonian engineering and allows quantum simulations of Hamiltonian models, which are difficult to realize with conventional approaches. The flexibility of our approach is demonstrated by performing quantum simulations of one-dimensional Poincar\'e crystal physics and two-dimensional topological flat bands, where the QQFT protocol effectively generates the required long-range tunnelings despite the locality of the cold atom system. We find the discrete Poincar\'e symmetry and topological properties in the two examples, respectively, have robustness against a certain degree of noise that is potentially existent in the experimental realization. We expect this approach would open wide opportunities for optical lattice-based programmable quantum simulations.
The implementation of spatial light modulators (SLMs) in quantum gas experiments has allowed the realization of ever more complex trapping geometries. As ultracold atoms may be sensitive to perturbations of the trapping potential at the 1% level, the high contrast ratios of digital micromirror devices are proving advantageous for use in optical trapping. Our laboratory pursues configurable traps based on the direct (nearly diffraction limited) imaging of a digital micromirror device (DMD). We achieve highly flexible potentials using commercially available microscope objectives external to our vacuum chamber that directly project the DMD to the atom plane, producing optical traps over an area of 130 μm × 200 μm, with a resolution of 630(10) nm full width at half maximum (FWHM) at 532 nm illumination. We combine these potentials with a horizontally propagating TEM00 or TEM01 Hermite-Gaussian optical sheet that provides vertical confinement. With the dynamic control enabled by the maximum full-frame rate of 20 KHz and on-board storage of <13,000 frames of the DMD, we study the transport of atoms and superfluid dynamics in configurable trapping geometries. Using the fast frame rate of the DMD we also produce intermediate grey levels that complement half-toning techniques for producing optimized grayscale patterns.
We propose a numerical method using the discrete variable representation (DVR) for constructing real-valued Wannier functions localized in a unit cell for both symmetric and asymmetric periodic potentials. We apply these results to finding Wannier functions for ultracold atoms trapped in laser-generated optical lattices. Following S. Kivelson [Phys. Rev. B 26, 4269 (1982)], for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigenstates of the position operators $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}, \stackrel{\ifmmode \hat{}\else \^{}\fi{}}{y}$, and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ restricted to single-particle Bloch functions belonging to one or more bands. To ensure that the Wannier functions are real-valued, we numerically obtain the band structure and real-valued eigenstates using a uniform Fourier grid DVR. We then show, by a comparison of tunneling energies, that the Wannier functions are accurate for both inversion-symmetric and asymmetric potentials to better than 10 significant digits when using double-precision arithmetic. The calculations are performed for an optical lattice with double-wells per unit cell with tunable asymmetry along the x axis and a single sinusoidal potential along the perpendicular directions. Localized functions at the two potential minima within each unit cell are similarly constructed, but using a superposition of single-particle solutions from the two lowest bands. We finally use these localized basis functions to determine the two-body interaction energies in the Bose-Hubbard model and show the dependence of these energies on lattice asymmetry.
Abstract A boson sampler implements a restricted model of quantum computing. It is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating ac- cording to programmable, non-interacting dynamics [1]. Here, we demonstrate a new combination of tools for implementing boson sampling using ultracold atoms in a two-dimensional, tunnel-coupled optical lattice. These tools include fast and programmable preparation of large ensembles of nearly identical bosonic atoms (99.5+0.5 −1.6% indistinguishability) by means of rearrangement with optical tweezers and high-fidelity optical cooling, propagation for variable evolution time in the lattice with low loss (5.0(2) %, independent of evolution time), and high fidelity detection of the atom positions after their evolution (typically 99.8(1) %). With this system, we study specific instances of boson sampling involving up to 180 atoms distributed among ∼ 1000 sites in the lattice. Direct verifi- cation of a given boson sampling distribution is not feasible in this regime. Instead, we introduce and perform targeted tests to determine the indistinguishability of the prepared atoms, to char- acterize the applied family of single particle unitaries, and to observe expected bunching features due to interference for a large range of atom numbers. When extended to interacting systems, our work demonstrates the core capabilities required to directly assemble ground and excited states in simulations of various Hubbard models [2, 3].
Synthetic dimension approach has emerged as a versatile and powerful technique in cold-atom toolbox for quantum simulation, serving as a complementary alternative to conventional optical lattice platforms. By mapping internal or external atomic states into discrete lattice sites, this method provides precise control over local tunneling amplitudes, phases, and on-site potentials, enabling flexible engineering of tight-binding Hamiltonians. Such capabilities have facilitated the experimental exploration of topology, synthetic gauge fields, disorder-induced phenomena, and exotic time-dependent dynamics across a range of platforms, including hyperfine and Rydberg states, momentum lattices, and harmonic-trap modes. In this review, we summarize the underlying principles of the key experimental synthetic dimension platforms, and their recent advances in quantum simulation. We also discuss the advantages and current limitations of the synthetic method, and provide a perspective on future directions, including hybrid-dimensional architectures and the study of high-dimensional many-body physics.