Periodic Optical Potential Research Articles

Quantum rotor description of the bosonic superfluid–Mott insulator transition in optical lattices

AbstractThe physics of the Bose–Hubbard (BH) model is the subject of intensive studies in recent years, since it has been realized that BH Hamiltonian can be applied to systems of cold atoms confined in periodic optical lattice potential, where the effects on interactions are strongly enhanced. Our aim is to extend the widely used mean‐field treatment of the superfluid–Mott insulator (SF–MI) transition in the BH model. Our method also improves the strong‐coupling expansion that works well only for sufficiently large insulating gap. The key point of the approach is to consider the representation of strongly interacting bosons as particles with attached U(1) gauge group flux tubes, which constitutes the quantum rotor description. The effective action formalism allows us to cast the problem in terms of the phaseonly action and obtain an analytical formulas for critical lines. Finally, we calculate the zero‐temperature SF–MI phase diagrams for three‐dimensional BH model and compare our results with the outcome of numerical Monte Carlo simulations. We found a very good agreement for the quantitative results regarding the details of the lobe in the phase diagrams showing the quantum transition from superfluid to the Mott insulating phase (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DIRTY BOSONS: TWENTY YEARS LATER

A concise and somewhat personal review of the problem of superfluidity and quantum criticality in regular and disordered interacting Bose systems is given, concentrating on general features and important symmetries that are exhibited in different parts of the phase diagram, and that govern the different possible types of critical behavior. A number of exact results for various insulating phase boundaries, which may be used to constrain the results of numerical simulations, can be derived using large rare region type arguments. The nature of the insulator-superfluid transition is explored through general scaling arguments, exact model calculations in one dimension, numerical results in two dimensions, and approximate renormalization group results in higher dimensions. Experiments on 4 He adsorbed in porous Vycor glass, on thin film superconductors, and magnetically trapped atomic vapors in a periodic optical potential are used to illustrate many of the concepts.

Atomic Landau-Zener Tunneling in Fourier-Synthesized Optical Lattices

We report on an experimental study of quantum transport of atoms in variable periodic optical potentials. The band structure of both ratchet-type asymmetric and symmetric lattice potentials is explored. The variable atom potential is realized by superimposing a conventional standing wave potential of lambda/2 spatial periodicity with a fourth-order multiphoton potential of lambda/4 periodicity. We find that the Landau-Zener tunneling rate between the first and the second excited Bloch band depends critically on the relative phase between the two spatial lattice harmonics.

Stationary Classical Chaos of Trapped Two-ComponentBose–Einstein Condensates in 1-D OpticalLattice Potentials

We study the nonlinear dynamics of two-component Bose–Einsteincondensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross–Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.

Molecular transport in pulsed optical lattices

This paper presents an overview of our recent theoretical and experimental work investigating the application of deep, periodic optical dipole potentials (optical lattices) produced by intense pulsed optical fields for the transport of neutral molecular gases. Our review outlines the deceleration of molecules in a molecular beam to create slow cold molecules and also acceleration for production of hyperthermal molecular beams with velocities in excess of 10 km/s for material processing. We describe how bulk motion can be induced in a gas by a traveling optical lattice, even when the gas is not fully trapped by the lattice. In all these cases energy and momentum can be deposited from laser radiation that is not resonant with any internal states. When significant numbers of gas collisions occur during the lattice/laser pulse, gas heating accompanied by the formation of gas jets in free space and bulk drift in a capillary can be induced. Finally, we describe a new nonintrusive laser diagnostic method for measurement of gas properties based on analysis of light scattered from density perturbations induced by lattices.

Hydrodynamics of Superfluid Bose Gases in an Optical Lattice at Finite Temperatures

Starting from an effective action for the order parameter field, we derive a coupled set of generalized hydrodynamic equations for a Bose condensate in an optical lattice at finite temperatures. Using the linearized hydrodynamic equations, we study the microscopic mechanism of the Landau instability due to the collisional damping process between the condensate and noncondensate atoms. It is shown that the Landau criterion for the stability of a superfluid in a uniform system is modified due to the presence of the periodic optical lattice potential.

Fourier synthesis of optical potentials for atomic quantum gases

We demonstrate a scheme for the Fourier synthesis of periodic optical potentials with asymmetric unit cells for atoms. In a proof of principle experiment, an atomic Bose-Einstein condensate is exposed to either symmetric or sawtooth-like asymmetric potentials by superimposing a conventional standing wave potential of $\lambda/2$ spatial periodicity with a fourth-order lattice potential of $\lambda/4$ periodicity. The high periodicity lattice is realized using dispersive properties of multiphoton Raman transitions. Future applications of the demonstrated scheme could range from the search for novel quantum phases in unconventionally shaped lattice potentials up to dissipationless atomic quantum ratchets.

Controlling the motion of cold molecules with deep periodic optical potentials

The application of optical forces has allowed unprecedented control over the motion of atoms leading to laser cooling and trapping1 and Bose–Einstein condensation2. More recently, the manipulation of cold neutral polar molecules using electrostatic fields has been used to create slow cold molecules in the laboratory frame3. Here, we report on the controlled manipulation of molecules using deep periodic optical lattice potentials (22 K) created by intense optical fields (1011 W cm−2). By using the oscillatory motion of nitric oxide molecules in these potentials, we have demonstrated rapid deceleration or acceleration in a molecular beam to well-defined velocities on a length scale of less than 535 nm. We reduce the kinetic energy of the molecules in a cold molecular beam by up to 50% in a single laser pulse (5.8 ns) demonstrating precise control of molecular-beam velocity and a new method for creating slow cold molecules using optical fields.

Micropropulsion devices based on molecular acceleration by pulsed optical lattices

The ability of a traveling periodic optical potential to increase the thrust and specific impulse of microthrusters is investigated. Two flow regimes, high density and low density, are considered. The thrust from a micronozzle, with a stagnation pressure of 1atm and temperature of 300K, can be increased by more than an order of magnitude. These conditions can be achieved for a constant velocity lattice, produced by two near counterpropagating optical fields that are focused into the nozzle throat. A propulsion system that operates in low-density regime and is driven by molecules trapped by an accelerating optical lattice is proposed. It is shown that such a system has a potential to achieve a specific impulse of thousands of seconds.

Cold Atom Dynamics in a Quantum Optical Lattice Potential

We study a generalized cold atom Bose-Hubbard model, where the periodic optical potential is formed by a cavity field with quantum properties. On the one hand, the common coupling of all atoms to the same mode introduces cavity-mediated long-range atom-atom interactions, and, on the other hand, atomic backaction on the field introduces atom-field entanglement. This modifies the properties of the associated quantum phase transitions and allows for new correlated atom-field states, including superposition of different atomic quantum phases. After deriving an approximative Hamiltonian including the new long-range interaction terms, we exhibit central physical phenomena at generic configurations of few atoms in few wells. We find strong modifications of population fluctuations and next-nearest-neighbor correlations near the phase transition point.

Dissipation-Induced Symmetry Breaking in a Driven Optical Lattice

We analyze the atomic dynamics in an ac driven periodic optical potential which is symmetric in both time and space. We experimentally demonstrate that in the presence of dissipation the symmetry is broken, and a current of atoms through the optical lattice is generated as a result.

Nonadiabatic dynamics of a Bose-Einstein condensate in an optical lattice

We study the nonequilibrium dynamics of a Bose-Einstein condensate that is split in a harmonic trap by turning up a periodic optical lattice potential. We evaluate the dynamical evolution of the phase coherence along the lattice and the number fluctuations in individual lattice sites within the stochastic truncated Wigner approximation when several atoms occupy each site. We show that the saturation of the number squeezing at high lattice strengths, which was observed in recent experiments by Orzel et al. [Science 291, 2386 (2001)] can be explained by the nonadiabaticity of the splitting.

Structural Phase Transitions of Vortex Matter in an Optical Lattice

We consider the vortex structure of a rapidly rotating trapped atomic Bose-Einstein condensate in the presence of a corotating periodic optical lattice potential. We observe a rich variety of structural phases which reflect the interplay of the vortex-vortex and vortex-lattice interactions. The lattice structure is very sensitive to the ratio of vortices to pinning sites and we observe structural phase transitions and domain formation as this ratio is varied.

From the superfluid to the Mott regime and back: triggering a non-trivial dynamics in an array of coupled condensates

We consider a system formed by an array of Bose–Einstein condensates trapped in a harmonic potential with a superimposed periodic optical potential. Starting from the boson field Hamiltonian, appropriate to describe a dilute gas of bosonic atoms, we reformulate the system dynamics within the Bose–Hubbard model scenario. Then we analyse the effective dynamics of the system when the optical-potential depth is suddenly varied according to a procedure applied in many of the recent experiments on superfluid–Mott transition in Bose–Einstein condensates. Initially the condensate array generated in a weak optical potential is assumed to be in the superfluid ground state which is well described in terms of coherent states. At a given time, the optical-potential depth is suddenly increased and, after a waiting time, it is quickly decreased so that the initial depth is restored. We compute the system-state evolution and show that the potential jump brings on an excitation of the system, incorporated in the final condensate wavefunctions, whose effects are analysed in terms of two-site correlation functions and of on-site population oscillations. Also we show how too long a waiting time can destroy completely the coherence of the final state, making it unobservable.

Patterned loading of a Bose-Einstein condensate into an optical lattice

We have developed a technique to control the placement of atoms in an optical lattice by using a superlattice comprising two separately manipulated, periodic optical potentials with commensurate periods. We demonstrate selective loading of Bose-condensed ${}^{87}\mathrm{Rb}$ atoms into every third site of a one-dimensional optical lattice. Our technique provides atoms with wide separation yet tight confinement, useful properties for neutral-atom implementations of quantum computing. Interference of atoms released from the optical lattice and optical Bragg reflection from the atoms reveal the tight confinement and wide separation provided by the patterned filling.

Effective-mass analysis of Bose-Einstein condensates in optical lattices: Stabilization and levitation

We investigate the time evolution of a Bose-Einstein condensate in a periodic optical potential. Using an effective mass formalism, we study the equation of motion for the envelope function modulating the Bloch states of the lattice potential. In particular, we show how the negative effective-mass affects the dynamics of the condensate.

Macroscopic dynamics of a trapped Bose-Einstein condensate in the presence of 1D and 2D optical lattices.

The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data.

Coherent control of atom dynamics in an optical lattice

On the basis of a simple exactly solvable model we discuss the possibilities for state preparation and state control of atoms in a periodic optical potential. In addition to the periodic potential a uniform force with an arbitrary time dependence is applied. The method is based on a formal expression for the full evolution operator in the tight-binding limit. This allows us to describe the dynamics in terms of operator algebra, rather than in analytical expansions.

Quantum chaos for cold atoms in an optical lattice with a tilted harmonic trap

We show how ultracold (sub-µK temperature) atoms in a one-dimensional periodic optical potential with a harmonic trap can provide a new quantum chaotic system that is accessible to experiment. Provided that the harmonic potential varies slowly over a lattice period, the optical lattice has well defined energy bands. The energy-wavevector dispersion curves define an effective Hamiltonian that can be used to calculate classical orbits for atoms confined to a single band. We show that tilting the harmonic trap relative to the optical lattice induces a controllable transition from stable regular motion to classical chaos. The onset of chaos strongly delocalizes the atom orbits and should be manifest in both the classical and quantum properties of the trapped atoms. We also consider how the transition to chaos might affect the collective time-dependent dynamics of interacting atoms in Bose-Einstein condensates.

Quantum chaotic electron transport in superlattices

We introduce semiconductor superlattices as a new type of quantum chaotic system that is accessible to experiment. In contrast to previous physical systems that have been used to study quantum chaos, the classical Hamiltonian for the superlattices has an intrinsically quantum–mechanical origin. For low electric fields, superlattices have well-defined minibands which originate from the quantum–mechanical coupling of electron states in a periodic array of potential wells. The energy-wave-vector dispersion curves define an effective Hamiltonian that can be used to calculate semiclassical orbits for electrons confined to a single miniband. We show that applying a tilted magnetic field induces a controllable transition from stable regular motion to strong classical chaos. The onset of chaos delocalizes both the classical orbits and the corresponding quantum wave functions, and is therefore expected to produce a sharp increase in the current flow measured in electron transport experiments. We show that magnetically confined atoms in a periodic optical potential exhibit similar chaotic dynamics at ultra-low (μK) temperatures.