1D Optical Lattice Research Articles

Fractional domain walls from on-site softening in dipolar bosons

We study dipolar bosons in a 1D optical lattice and identify a region in parameter space---strong coupling but relatively weak on-site repulsion---hosting a series of stable charge-density-wave (CDW) states whose low-energy excitations, built from ``fractional domain walls,'' have remarkable similarities to those of non-Abelian fractional quantum Hall states. Here, a conventional domain wall between translated CDW's may be split by inserting strings of degenerate, but inequivalent, CDW states. Outside these insulating regions, we find numerous supersolids as well as a superfluid regime. The mentioned phases should be accessible experimentally and, in particular, the fractional domain walls can be created in the ground state using single-site addressing, i.e., by locally changing the chemical potential.

Long-Lived Dipolar Molecules and Feshbach Molecules in a 3D Optical Lattice

We have realized long-lived ground-state polar molecules in a 3D optical lattice, with a lifetime of up to 25 s, which is limited only by off-resonant scattering of the trapping light. Starting from a 2D optical lattice, we observe that the lifetime increases dramatically as a small lattice potential is added along the tube-shaped lattice traps. The 3D optical lattice also dramatically increases the lifetime for weakly bound Feshbach molecules. For a pure gas of Feshbach molecules, we observe a lifetime of greater than 20 s in a 3D optical lattice; this represents a 100-fold improvement over previous results. This lifetime is also limited by off-resonant scattering, the rate of which is related to the size of the Feshbach molecule. Individually trapped Feshbach molecules in the 3D lattice can be converted to pairs of K and Rb atoms and back with nearly 100% efficiency.

Optical magnetic resonance imaging with an ultra-narrow optical transition

We demonstrate optical magnetic resonance imaging (OMRI) of a Bose–Einstein condensate of ytterbium atoms trapped in a one-dimensional (1D) optical lattice using an ultra-narrow optical transition 1S0↔3P2 (m=−2). We developed a vacuum chamber equipped with a thin glass cell, which provides high optical access and allows a compact design of magnetic coils. A line shape of a measured spectrum of the OMRI is well described by a spatial distribution of the atoms in a 1D optical lattice with the Thomas–Fermi approximation and an applied magnetic field gradient. The observed spectrum exhibits a periodic structure corresponding to the optical lattice periodicity.

EVOLUTION OF INTERFERENCE PATTERNS OF SUPERFLUID FERMI GASES RELEASED FROM A TWO-DIMENSIONAL OPTICAL LATTICE

We study interference patterns and their time evolution of a superfluid fermionic gas released from a two-dimensional (2D) optical lattice below and above Feshbach resonance. We calculate initial distribution of many subcondensates formed in a combined potential of a parabolic trap and a 2D optical lattice in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC). By using Feynman propagator method combined with numerical simulations we investigate the interference patterns of the subcondensates for two different cases. One is when both the parabolic trap and optical lattice are switched off. In this case, interference pattern displays a main peak and many secondary peaks. The distance between these interference peaks grows as time increases. The other one is when only the 2D optical lattice is switched off. The interference pattern in this case is found to display decay and revival, and such behavior repeats periodically with increasing time. In different regimes of the BCS-BEC crossover, coherent arrays of interference patterns show different features, which can be used to characterize experimentally different properties in different superfluid regimes of the BCS–BEC crossover.

A staggered dual Mott insulator in a 3D optical lattice

We propose a novel scheme for trapping ultracold rubidium and ytterbium atoms in a three-dimensional (3D) optical lattice simultaneously, in which the two species of atoms locate on two staggered lattices with the same spatial period and have a spatial separation of 133 nm. Furthermore, we calculate the tunneling and intra- and interspecies interactions of rubidium and ytterbium atoms as a function of light intensity, and find that the mixture of quantum degenerate gases in optical lattices can exhibit more intriguing quantum phases, especially a staggered dual Mott insulator of alkali-metal and alkaline-earth metal atoms.

Estimating optical lattice alignment by RF spectroscopy

A method that uses radio frequency (RF) spectroscopy to evaluate the alignment of an optical lattice is proposed and demonstrated. A one-dimensional (1D) optical lattice is applied along the long axis of a cigar-shaped Bose-Einstein condensate (BEC) in a magnetic trap. The RF spectra of condensates with and without the optical lattice are analyzed, measured, and compared with the condition in which the lattice is misaligned with the BEC. The proposed method greatly optimizes the optical alignments of the lattices.

Topological phase in a one-dimensional interacting fermion system

We study a one-dimensional interacting topological model by means of exact diagonalization method. The topological properties are firstly examined with the existence of the edge states at half-filling. We find that the topological phases are not only robust to small repulsive interactions but also are stabilized by small attractive interactions, and also finite repulsive interaction can drive a topological non-trivial phase into a trivial one while the attractive interaction can drive a trivial phase into a non-trivial one. Next we calculate the Berry phase and parity of the bulk system and find that they are equivalent in characterizing the topological phases. With them we obtain the critical interaction strengths and construct part of the phase diagram in the parameters space. Finally we discuss the effective Hamiltonian at large-U limit and provide additional understanding of the numerical results. Our these results could be realized experimentally using cold atoms trapped in the 1D optical lattice.

Realization of discrete quantum billiards in a two-dimensional optical lattice

We propose the method for optical visualization of Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by different refractive index than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over direction of propagation for both ordered and disordered cases, exploring sensitivity of the averaged picture with respect to the beam injection position. For our finite systems the resulting patterns reminiscent the ones set in billiards and therefore we introduce a definition of discrete quantum billiard discussing the possible relevance to its well established continuous counterpart.

Antiferromagnetism and superfluidity of a dipolar Fermi gas in a two-dimensional optical lattice

In a dipolar Fermi gas, the dipole-dipole interaction between fermions can be turned into a dipolar Ising interaction between pseduospins in the presence of an AC electric field. When trapped in a 2D optical lattice, such a dipolar Fermi gas has a very rich phase diagram at zero temperature, due to the competition between antiferromagnetism and superfluidity. At half filling, the antiferromagnetic state is the favored ground state. The superfluid state appears as the ground state at a smaller filling factor. In between there is a phase-separated region. The order parameter of the superfluid state can display different symmetries depending on the filling factor and interaction strength, including d-wave ($d$), extend s-wave ($xs$), or their linear combination ($xs+i\times d$). The implication for the current experiment is discussed.

Direct Observation and Analysis of Spin Dependent Transport of Single Atoms in a 1D Optical Lattice

We have directly observed spin-dependent transport of single cesium atoms in a 1D optical lattice. A superposition of two circularly polarized standing waves is generated from two counter propagating, linearly polarized laser beams. Rotation of one of the polarizations by $\pi$ causes displacement of the $\sigma^{+}$- and $\sigma^{-}$-lattices by one lattice site. Unidirectional transport over several lattice sites is achieved by rotating the polarization back and forth and flipping the spin after each transport step. We have analyzed the transport efficiency over 10 and more lattice sites, and discussed and quantified relevant error sources.

Quantum Hall effect in a one-dimensional dynamical system

We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study the quantum Hall effect in a one-dimensional (1D) system. This reduction to 1D is very efficient computationally and would make it possible to perform experiments on the 2D quantum Hall effect using cold atoms in a 1D optical lattice.

Optical forces and optical torques on various materials arising from optical lattices in the Lorentz-Mie regime

By combining the Maxwell stress tensor with the finite-difference time-domain (FDTD) method, we calculate the optical force and optical torque on particles from optical lattices. We compare our method to the two-component method and the electrostatic approximation (ESA). We also discuss how particle's refractive index, shape, size, and the morphology of an optical lattice influence optical forces and the condition to form stable optical trapping wells. In addition to optical forces, optical torque from one dimensional (1D) optical lattice is discussed for particles having anisotropic shapes; metastable and stable equilibrium orientation states are found. A detailed understanding of the optical force and torque from optical lattices has significant implications for optical trapping, micromanipulation, and sorting of particles.

Strongly interacting bosons in a one-dimensional optical lattice at incommensurate densities

We investigate quantum phase transitions occurring in a system of strongly interacting ultracold bosons in a 1D optical lattice. After discussing the commensurate-incommensurate transition, we focus on the phases appearing at incommensurate filling. We find a rich phase diagram, with superfluid, supersolid and solid (kink-lattice) phases. Supersolids generally appear in theoretical studies of systems with long-range interactions; our results break this paradigm and show that they may also emerge in models including only short-range (contact) interactions, provided that quantum fluctuations are properly taken into account.

Finite-temperature study of bosons in a two-dimensional optical lattice

We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two-dimensional(2D) optical lattice. The scale-invariant, finite temperature state diagram is presented for the Bose-Hubbard model in terms of experimental parameters -- the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott insulator, and normal Bose liquid phases, we examine the local density, compressibility, superfluid density, and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long-range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between one-dimension and two-dimensions, while at a finite temperature, the decay is similar to that in one-dimension at a much lower temperature. The calculations reveal shortcomings of the local density approximation in describing superfluid properties of trapped bosons. We also present the finite-temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite-temperature effect in the experiment.

Simulating cyclotron-Bloch dynamics of a charged particle in a 2D lattice by means of cold atoms in driven quasi-1D optical lattices

Quantum dynamics of a charged particle in a 2D lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations (the case of vanishing electric field) and Bloch oscillations (zero magnetic field), details of which has not yet been completely understood. In the present work we suggest to study this problem by using cold atoms in optical lattices. We introduce a 1D model which can be easily realized in laboratory experiments with quasi 1D optical lattices and show that this model captures many features of the cyclotron-Bloch dynamics of the quantum particle in 2D square lattices.

Extracting density–density correlations from in situ images of atomic quantum gases

We present a complete recipe to extract the density–density correlations and the static structure factor of a two-dimensional (2D) atomic quantum gas from in situ imaging. Using images of non-interacting thermal gases, we characterize and remove the systematic contributions of imaging aberrations to the measured density–density correlations of atomic samples. We determine the static structure factor and report the results on weakly interacting 2D Bose gases, as well as strongly interacting gases in a 2D optical lattice. In the strongly interacting regime, we observe a strong suppression of the static structure factor at long wavelengths.

Spontaneous Demagnetization of a Dipolar Spinor Bose Gas in an Ultralow Magnetic Field

We study the spinor properties of S = 3 (52)Cr condensates, in which dipole-dipole interactions allow changes in magnetization. We observe a demagnetization of the Bose-Einstein condensate (BEC) when the magnetic field is quenched below a critical value corresponding to a phase transition between a ferromagnetic and a nonpolarized ground state, which occurs when spin-dependent contact interactions overwhelm the linear Zeeman effect. The critical field is increased when the density is raised by loading the BEC in a deep 2D optical lattice. The magnetization dynamics is set by dipole-dipole interactions.

Resolved Atomic Interaction Sidebands in an Optical Clock Transition

We report the observation of resolved atomic interaction sidebands (ISB) in the (87)Sr optical clock transition when atoms at microkelvin temperatures are confined in a two-dimensional optical lattice. The ISB are a manifestation of the strong interactions that occur between atoms confined in a quasi-one-dimensional geometry and disappear when the confinement is relaxed along one dimension. The emergence of ISB is linked to the recently observed suppression of collisional frequency shifts. At the current temperatures, the ISB can be resolved but are broad. At lower temperatures, ISB are predicted to be substantially narrower and useful spectroscopic tools in strongly interacting alkaline-earth gases.

Statistically induced phase transitions and anyons in 1D optical lattices

Anyons--particles carrying fractional statistics that interpolate between bosons and fermions--have been conjectured to exist in low-dimensional systems. In the context of the fractional quantum Hall effect, quasi-particles made of electrons take the role of anyons whose statistical exchange phase is fixed by the filling factor. Here we propose an experimental setup to create anyons in one-dimensional lattices with fully tuneable exchange statistics. In our setup, anyons are created by bosons with occupation-dependent hopping amplitudes, which can be realized by assisted Raman tunnelling. The statistical angle can thus be controlled in situ by modifying the relative phase of external driving fields. This opens the fascinating possibility of smoothly transmuting bosons via anyons into fermions and of inducing a phase transition by the mere control of the particle statistics as a free parameter. In particular, we demonstrate how to induce a quantum phase transition from a superfluid into an exotic Mott-like state where the particle distribution exhibits plateaus at fractional densities.

Stable Fulde-Ferrell-Larkin-Ovchinnikov pairing states in two-dimensional and three-dimensional optical lattices

We present the study of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states in the $p$-orbital bands in both two and three-dimensional optical lattices. Due to the quasi one-dimensional band structure which arises from the unidirectional hopping of the orthogonal $p$-orbitals, the pairing phase space is not affected by spin imbalance. Furthermore, interactions build up high dimensional phase coherence which stabilizes the FFLO states in 2D and 3D optical lattices in a large parameter regime in phase diagram. These FFLO phases are stable with imposing the inhomogeneous trapping potential. Their entropies are comparable to those of the normal states at finite temperatures.