1D Optical Lattice Research Articles

Density-Density Correlation Spectra of Ultracold Bosonic Gas Released from a Deep 1D Optical Lattice.

Density-density correlation analysis is a convenient diagnostic tool to reveal the hidden order in the strongly correlated phases of ultracold atoms. We report on a study of the density-density correlations of ultracold bosonic atoms which were initially prepared in a Mott insulator (MI) state in one-dimensional optical lattices. For the atomic gases released from the deep optical lattice, we extracted the normalized density-density correlation function from the atomic density distributions of freely expanded atomic clouds. Periodic bunching peaks were observed in the density-density correlation spectra, as in the case of higher-dimensional lattices. Treating the bosonic gas within each lattice well as a subcondensate without quantum tunneling, we simulated the post-expansion density distribution along the direction of the 1D lattice, and the calculated density-density correlation spectra agreed with our experimental observations.

Expansion of strongly interacting dipolar bosons in 1D optical lattices

Expansion of strongly interacting dipolar bosons in 1D optical lattices

Clock-Line-Mediated Sisyphus Cooling.

We demonstrate subrecoil Sisyphus cooling using the long-lived ^{3}P_{0} clock state in alkaline-earth-like ytterbium. A 1388-nm optical standing wave nearly resonant with the ^{3}P_{0}→^{3}D_{1} transition creates a spatially periodic light shift of the ^{3}P_{0} clock state. Following excitation on the ultranarrow clock transition, we observe Sisyphus cooling in this potential, as the light shift is correlated with excitation to ^{3}D_{1} and subsequent spontaneous decay to the ^{1}S_{0} ground state. We observe that cooling enhances the loading efficiency of atoms into a 759-nm magic-wavelength one-dimensional (1D) optical lattice, as compared to standard Doppler cooling on the ^{1}S_{0}→^{3}P_{1} transition. Sisyphus cooling yields temperatures below 200nK in the weakly confined, transverse dimensions of the 1D optical lattice. These lower temperatures improve optical lattice clocks by facilitating the use of shallow lattices with reduced light shifts while retaining large atom numbers to reduce the quantum projection noise. This Sisyphus cooling can be pulsed or continuous and is applicable to a range of quantum metrology applications.

Observation of optical rogue waves in 2D optical lattice

Observation of optical rogue waves in 2D optical lattice

2D Exotic Optical Lattice via a Digital‐Coding Circular Airy Beam

Optical lattices have been widely used from classical to quantum physics. The tunable and scalable fabrication of lattices would be of great significance in lattice‐based multipartite applications. This work demonstrates first that a circular Airy beam (CAB), which has the peculiar properties of self‐healing and abrupt autofocusing, can be used to generate two‐dimensional (2D) optical lattices in propagation when encoded by a programmable spatial mask, resulting in the formation of large‐scale and tunable optical lattices with both axis and axial symmetry, and even high‐orbital kaleidoscope shapes. The efficient diffraction of CAB during the spatial crosstalk with the mask enables the realization of tunable lattices with rich periodicity and complexity. The study shows a flexible method to manipulate lattices with large‐scale and versatile structures for potential applications in integrated and scalable optical and photonic devices.

Accessing Position Space Wave Functions in Band Structure Calculations of Periodic Systems─A Generalized, Adapted Numerov Implementation for One-, Two-, and Three-Dimensional Quantum Problems.

In this work, a generalized, adapted Numerov implementation capable of determining band structures of periodic quantum systems is outlined. Based on the input potential, the presented approach numerically solves the Schrödinger equation in position space at each momentum space point. Thus, in addition to the band structure, the method inherently provides information about the state functions and probability densities in position space at each momentum space point considered. The generalized, adapted Numerov framework provided reliable estimates for a variety of increasingly complex test suites in one, two, and three dimensions. The accuracy of the proposed methodology was benchmarked against results obtained for the analytically solvable Kronig-Penney model. Furthermore, the presented numerical solver was applied to a model potential representing a 2D optical lattice being a challenging application relevant, for example, in the field of quantum computing.

Many-body quantum chaos in stroboscopically-driven cold atoms

In quantum chaotic systems, the spectral form factor (SFF), defined as the Fourier transform of two-level spectral correlation function, is known to follow random matrix theory (RMT), namely a ‘ramp’ followed by a ‘plateau’ in late times. Recently, a generic early-time deviation from RMT, so-called the ‘bump’, was shown to exist in random quantum circuits as toy models for many-body quantum systems. We demonstrate the existence of ‘bump-ramp-plateau’ behavior in the SFF for a number of paradigmatic and stroboscopically-driven 1D cold-atom models: spinless and spin-1/2 Bose-Hubbard models, and nonintegrable spin-1 condensate with contact or dipolar interactions. We find that the scaling of the many-body Thouless time tTh —the onset of RMT—, and the bump amplitude are more sensitive to variations in atom number than the lattice size regardless of the hyperfine structure, the symmetry classes, or the choice of driving protocol. Moreover, tTh scaling and the increase of the bump amplitude in atom number are significantly slower in spinor gases than interacting bosons in 1D optical lattices, demonstrating the role of locality. We obtain universal scaling functions of SFF which suggest power-law behavior for the bump regime in quantum chaotic cold-atom systems, and propose an interference measurement protocol.

Two-dimensional anisotropic vortex–bright soliton and its dynamics in dipolar Bose–Einstein condensates in optical lattice

We study construction and dynamics of two-dimensional (2D) anisotropic vortex–bright (VB) soliton in spinor dipolar Bose–Einstein condensates confined in a 2D optical lattice (OL), with two localized components linearly mixed by the spin–orbit coupling and long-range dipole–dipole interaction (DDI). It is found that the OL and DDI can support stable anisotropic VB soliton in the present setting for arbitrarily small value of norm N. We then present a new method via examining the mean square error of norm share of bright component to implement stability analysis. It is revealed that one can control the stability of anisotropic VB soliton only by adjusting OL depth for a fixed DDI. In addition, the dynamics of the anisotropic VB soliton was studied by applying the kick to them. The mobility of the single kicked VB soliton is Rabbi-like oscillation. However, for the collision dynamics of two kicked anisotropic VB solitons, their properties mainly depend on their initial distance and OL, and they can realize the transition from the bright component to the vortex component. Our work may provide a convenient way to prepare and manipulate anisotropic VB soliton in high-dimensional space.

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.

Degenerate Raman sideband cooling of K40 atoms

We report on the implementation of degenerate Raman sideband cooling of $^{40}$K atoms. The scheme incorporates a 3D optical lattice, which confines the atoms and drives the Raman transitions. The optical cooling cycle is closed by two optical pumping beams. The wavelength of the laser beams forming the lattice is close to the D$_2$ atomic transition, while the optical pumping is operated near the D$_1$ transition. With this cooling method, we achieve temperature of $\sim$$1\mu$K of a cloud with $\sim$$10^7$ atoms. This corresponds to a phase space density of $\ge$$10^{-3}$. Moreover, the fermionic ensemble is spin polarized to conditions which are favorable for subsequent evaporative cooling. We study the dependence of the cooling scheme on several parameters, including the applied magnetic field, the detuning, duration, and intensity profile of the optical pumping beams. Adding this optical cooling stage to current Fermi gas experiments can improve the final conditions and increase the data rate.

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.

Hierarchical dimensional crossover of an optically-trapped quantum gas with disorder

Dimensionality serves as an indispensable ingredient in any attempt to formulate low-dimensional physics, and studying the dimensional crossover at a fundamental level is challenging. The purpose of this work is to study the hierarchical dimensional crossovers, namely the crossover from three dimensions (3D) to quasi-2D and then to 1D. Our system consists of a 3D Bose–Einstein condensate trapped in an anisotropic 2D optical lattice characterized by the lattice depths V 1 along the x direction and V 2 along the y direction, respectively, where the hierarchical dimensional crossover is controlled via V 1 and V 2. We analytically derive the ground-state energy, quantum depletion and the superfluid density of the system. Our results demonstrate the 3D-quasi-2D-1D dimensional crossovers in the behavior of quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.

Three-color reflections in one-dimensional ordered and disordered atomic lattices with trapped N-type cold atoms.

Investigating and controlling light propagation in one-dimensional (1D) ordered and disordered atomic lattices is critical both fundamentally and for applications. In this study, cold atoms are trapped in 1D optical lattice and driven to the four-level N configuration. In each period, the atoms exhibit a Gaussian density distribution with the average atomic density N0 (1 + Δk). When the random number Δk = 0 (the atomic density Nk(z)) corresponding to an ordered 1D atomic lattice, there are three reflection regions of high reflectivity located in two EIT windows and one large detuning range. However, the atomic density may increase (N k+(z) with Δk > 0) or decrease (N k-(z) with Δk < 0) owing to the imperfect manufacturing process or random distribution of atoms corresponding to a disordered atomic lattice. The results show that the width and height of reflections can be raised (reduced) by the increased (decreased) ratio of N k+(z)/N k (z) (N k-(z)/N k (z)) with the random distribution of lattice cells with N k+(z) (N k-(z)). When a cluster of disordered lattice cells with N k+(z) and N k-(z) is located at the front or tail of the atomic lattice, reflection symmetry can be broken. However, the symmetry and robustness can be well preserved with the random fluctuation of the average atomic density in each lattice cell.

Discrete vortex quantum droplets

We analyze the existence and characteristics of discrete vortex quantum droplets with intrinsic topological charges S of up to 5 in two-component Bose-Einstein condensates in a deep two-dimensional (2D) optical lattice. The 2D discrete Gross-Pitaevskii equation with a Lee-Huang-Yang (LHY) correction term is used to model the condensate, which incorporates local contact interactions and LHY corrections induced by quantum fluctuations. The characteristics of vortical modes with S = 1 and S = 2 are studied in detail. The chemical potential μ and peak density ρmax of the modes are calculated as functions of the norm N. The μ−N curves of on-site-centered and off-site-centered modes with the same number of lattice sites are nearly identical. We make an analysis and reach a conclusion consistent with these simulation results. This system contains a nontrivial type of vortex mode known as the mixed-vortex mode, in which the two components have the same density pattern and different topological charges. To the best of our knowledge, we are the first to report vortex modes with isomorphic density patterns and heteromorphic vortices in the field of quantum droplets.

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.

Measuring Correlations from the Collective Spin Fluctuations of a Large Ensemble of Lattice-Trapped Dipolar Spin-3 Atoms

We perform collective spin measurements to study the buildup of two-body correlations between ≈10^{4} spin s=3 chromium atoms pinned in a 3D optical lattice. The spins interact via long range and anisotropic dipolar interactions. From the fluctuations of total magnetization, measured at the standard quantum limit, we estimate the dynamical growth of the connected pairwise correlations associated with magnetization. The quantum nature of the correlations is assessed by comparisons with analytical short- and long-time expansions and numerical simulations. Our Letter shows that measuring fluctuations of spin populations for s>1/2 spins provides new ways to characterize correlations in quantum many-body systems.

Field deployable atomics package for an optical lattice clock

An atomics package is the heart of any atom based quantum sensing device. Here we report on the realisation of a field deployable atomics package for alkaline earth atoms, e.g. Sr or Yb. In terms of size (∼121 L), weight (<75 kg) and power (∼320 W), it is the smallest package to date which is designed to load Sr atoms into an optical lattice. It consists of an ultra-high vacuum assembly (<4 L), lasers, magnetic field coils & optics required for cooling & trapping as well as a module for imaging & detection. The package can routinely produce ultra cold and dense samples of 1.6 × 105 88Sr atoms trapped in a 1D optical lattice in less than a second. Its robustness has been demonstrated by conducting two transportation campaigns within out-of-the-lab environments. This advancement will have impact not only on transportable optical clock development but also will influence the wider areas of quantum science and technologies, particularly requiring field deployable cold atom based quantum sensors.

Single-particle excitations and metal-insulator transition of ultracold Fermi atoms in one-dimensional optical lattice with spin-orbit coupling

The dynamic structure factors reflecting the excitation spectra were investigated in a one-dimensional (1D) optical lattice with a spin-orbit coupling (SOC) effect. The results reveal that the single-particle excitations of both the density and spin dynamical structure factors are strongly reconstructed and split owing to the SOC effect, and a hat-like excitation band appears in the high-binding-energy region. The hat-like excitation band of the density dynamical structure factor exhibits an arc form, and has a pocket in the spin dynamical structure factor. In particular, only a gapless single-particle excitation point is left for both the density dynamical structure factor and the spin dynamical structure factor when the SOC strength reaches a critical point at half-filling. A stronger SOC strength causes the gapless excitation points to disappear, which indicates that the metal-insulator transition occurs. The metal-insulator transition only appears in half-filling and lightly doped regimes.

Seconds-Scale Coherence on Nuclear Spin Transitions of Ultracold Polar Molecules in 3D Optical Lattices.

Ultracold polar molecules (UPMs) are emerging as a novel and powerful platform for fundamental applications in quantum science. Here, we report characterization of the coherence between nuclear spin levels of ultracold ground-state sodium-rubidium molecules loaded into a 3D optical lattice with a nearly photon scattering limited trapping lifetime of 9(1)seconds. After identifying and compensating the main sources of decoherence, we achieve a maximum nuclear spin coherence time of T_{2}^{*}=3.3(6) s with two-photon Ramsey spectroscopy. Furthermore, based on the understanding of the main factor limiting the coherence of the two-photon Rabi transition, we obtain a Rabi line shape with linewidth below 0.8Hz. The simultaneous realization of long lifetime and coherence time, and ultrahigh spectroscopic resolution in our system unveils the great potentials of Ultracold polar molecules in quantum simulation, computation, and metrology.

Direct reconstruction of the band structure of a one-dimensional optical lattice with thermal atoms

We report on a simple method to reconstruct the band structure of a 1D optical lattice using a thermal cloud with a momentum spread of about two-photon recoils. We image the momentum distribution of a thermal cloud exposed to a standing wave potential using time-of-flight absorption images and observe unique features. With the support of numerical calculations, we explain their appearance and show how they can be used to reconstruct the full band-structure directly. While this can serve as a precise lattice depth calibration tool, we additionally propose a method to estimate the lattice depth in a single-shot manner.