1D Optical Lattice Research Articles

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.

Controllable three-dimensional electrostatic lattices for manipulation of cold polar molecules

Engineering many-body systems of particles in lattices has attracted intense interest in the last few decades, thanks to their promising applications such as in quantum computation or topological matter. While lattices of different dimensions have been demonstrated with magnetic and/or optical fields, little work has been done upon three-dimensional (3D) electrostatic lattices to tame polar molecules. Here, we propose a 3D electrostatic lattice consisting of periodically distributed square-patterned electrodes in space, whose potentials reach tens of millikelvin and can be controlled easily. Detailed analysis and Monte Carlo simulations indicate that ${\mathrm{ND}}_{3}$ molecules in its $|J,KM\ensuremath{\rangle}=|1,\ensuremath{-}1\ensuremath{\rangle}$ state can be effectively trapped and evaporatively cooled. In addition, replacing the electrodes with different patterns enables realizing 3D electric lattices with new topological geometry (e.g., honeycomb or kagome). As a natural extension of the 3D optical and magnetic lattices, the 3D electrostatic lattice offers intriguing perspectives for cold chemistry, quantum simulation, and precision metrology.

Superfluid to Mott-insulator transition in a one-dimensional optical lattice

Bose–Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ∼ 13.7 E r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.

Manipulating and measuring single atoms in the Maltese cross geometry.

Background: Optical microtraps at the focus of high numerical aperture (high-NA) imaging systems enable efficient collection, trapping, detection and manipulation of individual neutral atoms for quantum technology and studies of optical physics associated with super- and sub-radiant states. The recently developed "Maltese cross" geometry (MCG) atom trap uses four in-vacuum lenses to achieve four-directional high-NA optical coupling to single trapped atoms and small atomic arrays. This article presents the first extensive characterisation of atomic behaviour in a MCG atom trap. Methods: We employ a MCG system optimised for high coupling efficiency and characterise the resulting properties of the trap and trapped atoms. Using current best practices, we measure occupancy, loading rate, lifetime, temperature, fluorescence anti-bunching and trap frequencies. We also use the four-directional access to implement a new method to map the spatial distribution of collection efficiency from high-NA optics: we use the two on-trap-axis lenses to produce a 1D optical lattice, the sites of which are stochastically filled and emptied by the trap loading process. The two off-trap-axis lenses are used for imaging and single-mode collection. Correlations of single-mode and imaging fluorescence signals are then used to map the single-mode collection efficiency. Results:We observe trap characteristics comparable to what has been reported for single-atom traps with one- or two-lens optical systems. The collection efficiency distribution in the axial and transverse directions is directly observed to be in agreement with expected collection efficiency distribution from Gaussian beam optics. Conclusions: The multi-directional high-NA access provided by the Maltese cross geometry enables complex manipulations and measurements not possible in geometries with fewer directions of access, and can be achieved while preserving other trap characteristics such as lifetime, temperature, and trap size.

Nonlocal Correlation and Entanglement of Ultracold Bosons in the 2D Bose–Hubbard Lattice at Finite Temperature

AbstractThe temperature‐dependent behavior emerging in the vicinity of the superfluid (SF) to Mott‐insulator (MI) transition of interacting bosons in a 2D optical lattice, described by the Bose–Hubbard model is investigated. The equilibrium phase diagram at finite‐temperature is computed using the cluster mean‐field (CMF) theory including a finite‐cluster‐size‐scaling. The SF, MI, and normal fluid (NF) phases are characterized as well as the transition or crossover temperatures between them are estimated by computing physical quantities such as the superfluid fraction, compressibility and sound velocity using the CMF method. It is found that the nonlocal correlations included in a finite cluster, when extrapolated to infinite size, leads to quantitative agreement of the phase boundaries with quantum Monte Carlo (QMC) results as well as with experiments. Moreover, it is shown that the von Neumann entanglement entropy within a cluster corresponds to the system's entropy density and that it is enhanced near the SF–MI quantum critical point (QCP) and at the SF–NF boundary. The behavior of the transition lines near this QCP, at and away from the particle‐hole (p–h) symmetric point located at the Mott‐tip, is also discussed. The results obtained by using the CMF theory can be tested experimentally using the quantum gas microscopy method.

Floquet Solitons and Dynamics of Periodically Driven Matter Waves with Negative Effective Mass.

We experimentally study the dynamics of weakly interacting Bose-Einstein condensates of cesium atoms in a 1D optical lattice with a periodic driving force. After a sudden start of the driving, we observe the formation of stable wave packets at the center of the first Brillouin zone (BZ) in momentum space, and we interpret these as Floquet solitons in periodically driven systems. The wave packets become unstable when we add a trapping potential along the lattice direction, leading to a redistribution of atoms within the BZ. The concept of a negative effective mass and the resulting changes to the interaction strength and effective trapping potential are used to explain the stability and the time evolution of the wave packets. We expect that similar states of matter waves exist for discrete breathers and other types of lattice solitons in periodically driven systems.

Strongly interacting two-component coupled Bose gas in optical lattices

Two-component coupled Bose gas in a 1D optical lattice is examined. In addition to the postulated Mott insulator and superfluid phases, multiple bosonic components manifest spin degrees of freedom. Coupling of the components in the Bose gas leads to substantial changes in the previously observed spin phases, giving rise to a new effective spin Hamiltonian and unraveling remarkable spin correlations. The system in the absence of coupling exhibits ferromagnetic and nonferromagnetic spin phases for on-site intracomponent interaction stronger than intercomponent interaction. Upon introduction of coupling, the phase transition switches from first to second order. For comparable on-site inter- and intracomponent interactions, with coupling, instead of one, two spin phases emerge with a second-order phase transition. Exact diagonalization and variational Monte Carlo with stochastic minimization on the entangled-plaquette state bestow a unique and enhanced perspective on the system beyond the scope of a mean-field treatment.

Quantum Simulating the Electron Transport in Quantum Cascade Laser Structures

AbstractUltracold fermionic atoms are proposed to be used in 1D optical lattices to quantum simulate the electronic transport in quantum cascade laser (QCL) structures. The competition between the coherent tunneling among (and within) the wells and the dissipative decay at the basis of lasing is discussed. In order to validate the proposed simulation scheme, such competition is quantitatively addressed in a simplified 1D model. The existence of optimal relationships between the model parameters is shown, maximizing the particle current, the population inversion (or their product), and the stimulated emission rate. This substantiates the concept of emulating the QCL operation mechanisms in cold‐atom optical lattice simulators, laying the groundwork for addressing open questions, such as the impact of electron–electron scattering and the origin of transport‐induced noise, in the design of new‐generation QCLs.

Manipulating and measuring single atoms in the Maltese cross geometry

Background: Optical microtraps at the focus of high numerical aperture (high-NA) imaging systems enable efficient collection, trapping, detection and manipulation of individual neutral atoms for quantum technology and studies of optical physics associated with super- and sub-radiant states. The recently developed “Maltese cross” geometry (MCG) atom trap uses four in-vacuum lenses to achieve four-directional high-NA optical coupling to single trapped atoms and small atomic arrays. This article presents the first extensive characterisation of atomic behaviour in a MCG atom trap. Methods: We employ a MCG system optimised for high coupling efficiency and characterise the resulting properties of the trap and trapped atoms. Using current best practices, we measure occupancy, loading rate, lifetime, temperature, fluorescence anti-bunching and trap frequencies. We also use the four-directional access to implement a new method to map the spatial distribution of collection efficiency from high-NA optics: we use the two on-trap-axis lenses to produce a 1D optical lattice, the sites of which are stochastically filled and emptied by the trap loading process. The two off-trap-axis lenses are used for imaging and single-mode collection. Correlations of single-mode and imaging fluorescence signals are then used to map the single-mode collection efficiency. Results: We observe trap characteristics comparable to what has been reported for single-atom traps with one- or two-lens optical systems. The collection efficiency distribution in the axial and transverse directions is directly observed to be in agreement with expected collection efficiency distribution from Gaussian beam optics. Conclusions: The multi-directional high-NA access provided by the Maltese cross geometry enables complex manipulations and measurements not possible in geometries with fewer directions of access, and can be achieved while preserving other trap characteristics such as lifetime, temperature, and trap size.

Transverse confinement of electron beams in a 2D optical lattice for compact coherent x-ray sources

Compact coherent x-ray sources have been the focus of extensive research efforts over the past decades. As a result, several novel schemes like optical and nano-undulators for generating x-ray emissions in ‘table-top’ setups are proposed, developed, and assessed. Despite the extensive efforts in the past decades, there exists no operational FEL based on optical or electromagnetic undulators. By combining the particle confinement capability of optical cavities with wiggling motion inside an optical undulator, this paper proposes a new concept for making a compact coherent x-ray source. The full-wave solution of first-principle equations based on finite-difference time-domain and particle-in-cell is performed to simulate inverse-Compton scattering (ICS) off both free and confined electrons. It is shown that the strong space-charge effect in a low-energy electron beam (5 MeV) is the main obstacle in acquiring coherent gain through the ICS mechanism with a 10 micrometer laser. Subsequently, it is shown that by confining the electron beam at the field nodes of an optical cavity, the space-charge effect is compensated, and additionally, the ultrahigh charge density enables high FEL-gain at confinement spots. The full-wave numerical simulations predict enhancement of about three orders of magnitude in the radiation efficiency when ICS is carried out with confined electrons compared to free electrons. These theoretical results show promising potential as a new scheme for implementing a compact coherent x-ray source.

Optical Vortices: 3D Optical Vortex Lattices (Ann. Phys. 7/2021)

In article number 2100114, Denis Ikonnikov and co-workers report the results of Fresnel diffraction of light beams with a topological charge on a 2D regular amplitude transparency mask. The cover illustrates the complex optical field behind the grating, representing all 3D lattice of optical vortices, which is formed owing to the Talbot effect. These results are confirmed by the experimental reconstruction of all 3D optical vortex lattices. It is shown that the optical vortices are created and annihilated during light propagation behind the mask with the preservation of the total topological charge. The 3D optical vortex lattices are considered to be promising for transport and manipulation of multiple micro-objects.

Metal and insulator states of SU(6) × SU(2) clusters of fermions in one-dimensional optical lattices

We studied the behavior of mixtures of 173Yb (with symmetry up to SU(6)) and 171Yb (up to SU(2)) fermionic isotopes loaded in one-dimensional (1D) optical lattices. To do so, we solved the Schrödinger equation describing different systems using a diffusion Monte Carlo technique. We considered continuous Hamiltonians in which the interactions between atoms of different species (isotopes and/or spins) were modeled by contact potentials with parameters derived from their experimental scattering lengths. This implies that we can find both attractive and repulsive interactions between fermion pairs in the same cluster. The strength of those interactions can be changed by varying the transverse confinement, leading to different cluster behaviors. Only balanced clusters, i.e. with the same number of 173Yb and 171Yb atoms were considered. We found that the standard state for these clusters is a metallic-like one with different populations of 173Yb–171Yb molecule-like pairs in each optical lattice potential well. However, for big enough clusters, insulator-like states are also possible.

Two-dimensional optical gap solitons and vortices in a coherent atomic ensemble loaded on optical lattices

Coherent atomic systems, e.g., resonantly cold atomic gases within which electromagnetically induced transparency (EIT) operates, have recently received great attention, because of their remarkable scientific properties and pivotal implications. Light behavior in such systems governed by various potentials is a new and interesting research focus, but missing literally report on two-dimensional (2D) localized gap modes in coherent atomic systems loaded on optical lattices. We survey such issue in a coherent atomic gas inside where the EIT turns on, trapped by 2D optical lattices—constituted by counter-propagating far-detuned Stark laser fields, in the framework of nonlinear Schrödinger equation derived from Maxwell-Bloch equations. Using the linear stability analysis and direct perturbed evolution we address the formation, property, and stability of 2D localized gap modes of two types, gap solitons and gap vortices, in forbidden band gaps of the underlying linear Bloch-wave spectrum. The former mode is fundamental gap solitons, and the latter belongs to higher-order gap solitons with embedded topological charge. Our results are helpful not only for in-depth understanding of soliton dynamics in coherent atomic ensemble loaded on periodic potentials, but also for laying the groundwork for forthcoming applications in optical communications and quantum information processing.

3D Optical Vortex Lattices

AbstractFresnel diffraction of light beams with a topological charge on a 2D regular amplitude transparency mask is studied. Numerical predictions show that the 3D optical lattices of optical vortices can be formed using the Talbot effect, with these predictions confirmed by the experimental reconstruction of all 3D optical vortex lattices. The periodicity of the 3D optical vortex lattices is determined by the light wavelength and periodicity of a transparency mask. Furthermore, it is shown that the optical vortices are created and annihilated during light propagation behind the mask with the preservation of the total topological charge. The 3D optical vortex lattices are considered to be tolerant to the perturbations induced by trapped particles caused by the features of the Talbot effect. The 3D optical vortex lattices open new possibilities for light–matter interactions and the related applications.

A comparison of trapping the rubidium atoms in optical and magnetic lattices

In this paper, the critical parameters of quantum phase transition from the superfluid to the Mott insulator phase are studied for three-dimensional traps in 2D optical lattices and permanent magnetic lattices for trapping the 87Rb atoms. Using the harmonic oscillator wave function approximation, the on-site interaction U, the hopping matrix element J and the ratio J/U are calculated to determine the quantum phase transition point analytically. In a magnetic lattice two components of the external magnetic field B 1x and B 1y had been considered for studying quantum phase transition. Here, B 1z as the z- direction component of the bias magnetic field is also considered for further control of the magnetic lattice parameters. In addition, an optical lattice constructed from the interference of two pairs of orthogonal counter-propagating laser beams is investigated. In both optical and magnetic lattices, the ratio J/U and the critical point of the quantum phase transition can be calculated by variation of the potential barrier height between traps. Comparison of optical lattices with permanent magnetic lattices shows that in the critical point of quantum phase transition the potential barrier height of the magnetic potential is higher than that of the optical trap which suggests that the magnetic microtraps are deeper and more stable than the optical traps in similar structures.

Preparation of one-dimensional chains and dense cold atomic clouds with a high numerical aperture four-lens system

We report the efficient and fast ($\sim 2\mathrm{Hz}$) preparation of randomly loaded 1D chains of individual $^{87}$Rb atoms and of dense atomic clouds trapped in optical tweezers using a new experimental platform. This platform is designed for the study of both structured and disordered atomic systems in free space. It is composed of two high-resolution optical systems perpendicular to each other, enhancing observation and manipulation capabilities. The setup includes a dynamically controllable telescope, which we use to vary the tweezer beam waist. A D1 $\Lambda$-enhanced gray molasses enhances the loading of the traps from a magneto-optical trap. Using these tools, we prepare chains of up to $\sim 100$ atoms separated by $\sim 1 \mathrm{\mu m}$ by retro-reflecting the tweezer light, hence producing a 1D optical lattice with strong transverse confinement. Dense atomic clouds with peak densities up to $n_0 = 10^{15}\:\mathrm{at}/\mathrm{cm}^3$ are obtained by compression of an initial cloud. This high density results into interatomic distances smaller than $\lambda/(2\pi)$ for the D2 optical transitions, making it ideal to study light-induced interactions in dense samples.

Interorbital interactions in an SU(2)⊗SU(6) -symmetric Fermi-Fermi mixture

We characterize inter- and intraisotope interorbital interactions between atoms in the 1S0 ground state and the 3P0 metastable state in interacting Fermi-Fermi mixtures of 171Yb and 173Yb. We perform high-precision clock spectroscopy to measure interaction-induced energy shifts in a deep 3D optical lattice and determine the corresponding scattering lengths. We find the elastic interaction of the interisotope mixtures 173Yb_e-171Yb_g and 173Yb_g-171Yb_e to be weakly attractive and very similar, while the corresponding two-body loss coefficients differ by more than two orders of magnitude. By comparing different spin mixtures we experimentally demonstrate the SU(2)xSU(6) symmetry of all elastic and inelastic interactions. Furthermore, we measure the spin-exchange interaction in 171Yb and confirm its previously observed antiferromagnetic nature.

A battery-powered floating current source of 100 A for precise and fast control of magnetic field

In various leading-edge ultracold atom experiments in fields such as quantum simulation, quantum computing, and quantum precision measurement, precise and fast control of the magnetic field is important and a current source with a low noise level and high control bandwidth is required. Conventional commercial current sources, even the expensive ones, may not meet the requirements. Here, we present a battery-powered current source (BPCS) solution that has a maximum output of 100 A with a root-mean-square noise of about only 0.35 mA (integrated from 1 Hz to 3 MHz) and a control bandwidth of about 10 kHz. The large output current is sourced from a lead-acid battery, a fluxgate current sensor is used to detect the output current, and fast feedback regulation is done by using an insulated-gate bipolar transistor under the control of an analog proportional-integral controller. The battery power method eliminates the switching noise. A prepulse method is applied to shorten the settling time when the current steps down from a high level to a low level that is close to zero. These features make the BPCS a suitable analog-controlled floating current source for cold-atom experiments such as the preparation of a single 2D quantum gas and optical lattice atomic clocks.

Tensor monopoles and the negative magnetoresistance effect in optical lattices

We propose that a kind of four-dimensional (4D) Hamiltonians, which host tensor monopoles related to quantum metric tensor in even dimensions, can be simulated by ultracold atoms in the optical lattices. The topological properties and bulk-boundary correspondence of tensor monopoles are investigated in detail. By fixing the momentum along one of the dimensions, it can be reduced to an effective three-dimensional model manifesting with a nontrivial chiral insulator phase. Using the semiclassical Boltzmann equation, we calculate the longitudinal resistance against the magnetic field $B$ and find the negative relative magnetoresistance effect of approximately $ -B^{2} $ dependence when a hyperplane cuts through the tensor monopoles in the parameter space. We also propose an experimental scheme to realize this 4D Hamiltonian by introducing an external cyclical parameter in a 3D optical lattice. Moreover, we show that the quantum metric tensor and Berry curvature can be detected by applying an external drive in the optical lattices.

Thermal bosons in 3d optical lattices via tensor networks

Ultracold atoms in optical lattices are one of the most promising experimental setups to simulate strongly correlated systems. However, efficient numerical algorithms able to benchmark experiments at low-temperatures in interesting 3d lattices are lacking. To this aim, here we introduce an efficient tensor network algorithm to accurately simulate thermal states of local Hamiltonians in any infinite lattice, and in any dimension. We apply the method to simulate thermal bosons in optical lattices. In particular, we study the physics of the (soft-core and hard-core) Bose–Hubbard model on the infinite pyrochlore and cubic lattices with unprecedented accuracy. Our technique is therefore an ideal tool to benchmark realistic and interesting optical-lattice experiments.