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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Bose-Einstein condensates and quantum degenerate Ferni gases in optical lattices

M. Inguscio, Estefania de Mirandés, L. Fallani, Francesca Ferlaino, C. Fort, Jessica Lye, Giovanni Carlo Modugno, Michele Modugno, G. Roati

Published Jan 25, 2006• 0 citations
Publisher

Abstract

The physics of quantum particles in periodic potentials can be described in terms of Bloch waves and indeed many effects originally predicted for electrons moving in a lattice of ions have been observed for ultracold atoms in optical lattices. Interactions among the atoms forming the BEC are responsible for the nonlinear character of the Bloch waves, resulting in the onset of different kinds of instabilities, we have performed a detailed investigation of the stability regimes of a condensate in a moving optical lattice, separately addressing the effects and the timescales of energetic and dynamic instabilities. Spin-polarized Fermi gases are free from these effects and fundamental conduction phenomena, such as the crossover from a conducting to an insulating behaviour, the latter due to a localization of the particles in the lattice, can be observed

DOI
10.1109/cleoe.2005.1568480

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The physics of quantum particles in periodic potentials can be described in terms of Bloch waves and indeed many effects originally predicted for electrons moving in a lattice of ions have been observed for ultracold atoms in optical lattices. Interactions among the atoms forming the BEC are responsible for the nonlinear character of the Bloch waves, resulting in the onset of different kinds of instabilities, we have performed a detailed investigation of the stability regimes of a condensate in a moving optical lattice, separately addressing the effects and the timescales of energetic and dynamic instabilities. Spin-polarized Fermi gases are free from these effects and fundamental conduction phenomena, such as the crossover from a conducting to an insulating behaviour, the latter due to a localization of the particles in the lattice, can be observed
We present the results of experimental work on the dynamics of a Bose-Einstein condensate (BEC) loaded in a 1D moving optical lattice. The system is studied both in the regime of low atomic density (expanding BEC) and high atomic density (trapped BEC). In the low-density regime, the stable dynamics of the system is well-described in terms of Bloch waves. In the presence of nonlinearities, as in a high-density sample, the Bloch waves are not stable solutions of the Gross-Pitaevskii equation (GPE) and dynamical instability takes place.
Laser light isafundamental tool forthemanipulation ofBoseEinstein condensates (BECs) aswell asdegenerate Fermi gases. We havestudied bothstatic anddynamic properties ofthese quantum degenerate systems inthepresence ofa one-dimensional (ID)periodic potential created with alaser standing wave(optical lattice). Thephysics ofquantum particles inperiodic potentials canbedescribed intermsofBlochwavesandindeed many effects originally predicted forelectrons moving inalattice ofions havebeenobserved forultracold atomsinoptical lattices. Interactions amongtheatomsforming theBECareresponsible forthenonlinear character oftheBlochwaves, resulting intheonsetofdifferent kinds ofinstabilities: wehaveperformed adetailed investigation ofthestability regimes ofacondensate inamoving optical lattice, separately addressing theeffects andthetimescales ofenergetic and dynamic instabilities [1]. Spin-polarized Fermigasesarefreefromtheseeffects andfundamental conduction phenomena, suchasthecrossover fromaconducting toaninsulating behaviour, thelatter duetoalocalization ofthe particles inthelattice, canbeobserved. Wealso demonstrate aradiofrequency technique toaddress thelocalized states inaperiodic plusparabolic potential anddiscuss thepossible implications ofthis experimental procedure forthe implementation ofquantum computing. Also, inthecaseofaFerni gasinaIDoptical lattice subjected togravity, Bloch oscillations havebeenobserved forlongtimeintervals [2], suggesting apossible useofthese systems forthe measurement offorces atshort distances. We will also report asummary ofrecent observations ontheproperties ofBECsinoptical lattices withlarge spacing (10-20 ,um), wherethelongtunnelling times allow therealization ofarrays ofindependent condensates localized inthe lattice sites. Furthermore, wehavestarted theinvestigation oftheproperties ofaBECinarandom potential produced byanoptical speckle pattern, evidencing theeffects ofthedisorder inthecollective dynamics andinthedensity distribution after expansion: wediscuss theperspectives offered bythis system, also inconnection withthestudy of localization effects andwiththephenomenology ofBECsinmagnetic microtraps.
Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.
The higher-order interactions of Bose-Einstein condensate in multi-dimensional optical lattices are discussed both analytically and numerically. It is demonstrated that the effects of the higher-order atomic interactions on the sound speed and the stabilities of Bloch waves strongly depend on the lattice strength. In the presence of higher-order effects, tighter and high-dimensional lattices are confirmed to be two positive factors for maintaining the system's energetic stability, and the dynamical instability of Bloch waves can take place simultaneously with the energetic instability. In addition, we find that the higher-order interactions exhibit a long-range behavior and the long-lived coherent Bloch oscillations in a tilted optical lattice exist. Our results provide an effective way to probe the higher-order interactions in optical lattices.
Bloch band and stabilities of Bloch waves of superfluid Fermi gases in one-dimensional (1D) periodic optical lattices are discussed. Within the hydrodynamical theory and the two-mode approximation, the Bloch band structure, the energetic and dynamical instabilities of Bloch waves at the first Brilliouin zone are presented. The results show that, when the atom density is beyond a critical value, a loop structure in the Bloch band at the zone edge is developed along the BEC-BCS crossover. The Bloch band structure and the stabilities of Bloch waves are modified dramatically when the system crosses from the BEC side to the BCS side, and they can be adjusted to the required characteristics by changing the atom's interaction (with the Feshbach resonance technique), the atom density, and the lattice parameters. The analytical expressions of the critical atom density for exciting the loop structure and maintaining the stabilities of Bloch waves are obtained.
In BECs, collisions between condensate atoms give rise to a nonlinear contribution to the dynamics which is typically included as a mean-field term in the Schrodinger equation. This nonlinearity leads to a modification of well-known effects associated with matter waves in periodic potentials and adds a number of phenomena that are absent in the linear problem. We focused on the dynamics of a BEC in an accelerated optical lattice. In the linear case, this gives rise to Bloch oscillations and, above a critical acceleration, to Landau-Zener tunneling. In the nonlinear case, the probability for Landau-Zener tunneling is modified depending on the direction in which it occurs between two bands. By varying the acceleration of the optical lattice and measuring the time-dependence of the interference contrast, we were able to identify the instability regime and the characteristic time in which the dynamical instability destroys the interference pattern. Furthermore, we observed an increase in the condensate dimensions perpendicular to the lattice direction when the unstable region was reached. This indicates a mechanism whereby the longitudinal instability leads to an increase in the transverse release energy