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Physical Review A

Realization of bichromatic optical superlattices

Axel Görlitz, Toshiya Kinoshita, Theodor W. Hänsch, Andreas Hemmerich

Published Jun 4, 2001• 33 citations
Publisher

Abstract

We present the experimental realization of optical superlattices created by exposing laser cooled ${}^{85}\mathrm{Rb}$ atoms to a bichromatic standing-wave light field. The two light frequencies are tuned close to the ${D}_{1}$ and ${D}_{2}$ lines of ${}^{85}\mathrm{Rb}.$ The total optical potential seen by the atoms exhibits a modulation at the spatial beat period of the two light fields in addition to the typical periodicity on the scale of an optical wavelength. The bichromatic light field cools the atoms into the superlattice potential, resulting in a density modulation on a macroscopic scale. We have observed the density modulation directly in one- and three-dimensional superlattice configurations using an absorption imaging technique.

DOI
10.1103/physreva.64.011401

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We present the experimental realization of optical superlattices created by exposing laser cooled 85Rb{}^{85}\mathrm{Rb}85Rb atoms to a bichromatic standing-wave light field. The two light frequencies are tuned close to the D1{D}_{1}D1​ and D2{D}_{2}D2​ lines of 85Rb.{}^{85}\mathrm{Rb}.85Rb. The total optical potential seen by the atoms exhibits a modulation at the spatial beat period of the two light fields in addition to the typical periodicity on the scale of an optical wavelength. The bichromatic light field cools the atoms into the superlattice potential, resulting in a density modulation on a macroscopic scale. We have observed the density modulation directly in one- and three-dimensional superlattice configurations using an absorption imaging technique.
We report the results of an experimental study on the interaction of cooled cesium atoms with the optical field of two standing waves having different wavelengths (852 and 894 nm) and opposite circular polarizations. The spatial modulation of the superposition of the two optical potentials and the polarization properties of this configuration are expected to produce cooling of the atoms and a spatial modulation of their density with the periodicity of the beat of the two wavelengths. We performed temperature measurements of the cesium sample and observed the density distribution of the atoms for several configurations of the standing wave by means of time-of-flight absorption imaging and fluorescence imaging techniques. Experimentally we could not observe a pronounced density modulation on the length scale of the superperiod. Reasons for this are revealed by a one-dimensional numerical simulation including the complexity of the full Zeeman structure of the cesium atoms. That simulation reproduces the experimental results for the temperatures and spatial confinement.
We present direct experimental evidence for the localization of atoms cooled and trapped in a three- dimensional optical superlattice. As in the case of solid-state superlattices, we are able to tailor the characteristics of the optical potential wells. In particular, we impose a long-range modulation to the depth of the potential wells whose size remains in the optical wavelength range. The cooling mechanism in this configuration accumulates the atoms in the deepest wells. Images of the resulting separated denser atomic planes (distance $\ensuremath{\simeq}70$ $\ensuremath{\mu}\mathrm{m}$) have been obtained both by detecting the fluorescence and by observing the shadow of the cloud.
I describe the theory and construction of a new bichromatic optical superlattice to study the pairing and thermodynamics of spin frac12\\frac{1}{2}frac12-up and spin frac12\\frac{1}{2}frac12-down atoms in periodic double well potentials. Our bichromatic lattice contains lambda1=1064\\lambda_1=1064lambda1​=1064 nm and lambda2=532\\lambda_2=532lambda2​=532 nm standing wave lattices. With tunable depth and relative phase between the two lattices, periodic double well potentials of arbitrary local symmetry can be constructed. I present the first systematic experimental study of a two-component ultracold 6^66Li atomic Fermi gas in a single color 1064 nm lattice, which is continuously tuned from 2D to quasi-2D. A system is 2D if it is free to move in two dimensions while tightly confined in the third direction, such that only the ground state is occupied. Conversely, it is quasi-2D if higher states in the tightly confined direction are also occupied. I describe both radio frequency spectra and radial cloud profiles measured under identical conditions for each regime. Our results confirm predictions that the mean-field theory is not valid throughout the 2D to quasi-2D dimensional crossover. We also clarify that there is no transition between 2D and quasi-2D systems. I also present the first study of pairing in a periodic double well potential. A Green's function method is developed to compute the pairing energies in the lattice. Although further understanding of the results are needed, I provide some preliminary rf spectra measurements supporting the theoretical approach and implying the existence of two types of pairing.
Ultracold atoms in optical lattices provide a versatile platform for studying many-body physics in a defect-free system with tunable parameters. For the analog quantum simulation of the Fermi-Hubbard model, fermionic atoms take on the role of the valence electrons and optical lattices provide the periodic potential in place of the solid-state crystal. The dynamics in the system are described by the tunneling amplitude t between neighboring lattice sites and the interaction energy U of two particles occupying the same lattice site. With the depth of the optical lattices and an external magnetic field, both parameters can be tuned to access a wide range of regimes. Two superimposed lattices with different lattice periods form an optical superlattice, where the most common configuration is a bichromatic superlattice with lattice periods different by a factor of two. Depending on the lattice depths and the relative phase of the lattices, the bichromatic superlattice potential ranges from an array of weakly-coupled double wells to a continuous lattice potential with a staggered energy offset. We developed a calibration technique for measuring the depth of an optical lattice with local resolution. The band structure of the optical lattice is probed by modulating the lattice depth and exciting the atoms to higher bands. However, compared to resolving the band occupations in a time-of-flight measurement, we further excite the atoms to an untrapped band to deplete the optical lattice along equipotential lines where the modulation frequency is resonant with the local band transitions. From the profile of the lattice depth, we obtain the calibration factor for the power regulation, the waist of the underlying lattice beams and the position of the lattice axis. This technique combines several calibration measurements, thereby reducing the measurement time and enabling an automation of the lattice alignment. For the bichromatic superlattice we realized an active stabilization of the superlattice phase that enables long-term measurements with a precise control over the superlattice phase. The instability of the superlattice phase is a result of the different refractive indices for the two lattices in air and the optical elements along the optical path. Using environmental sensors, we monitor the temperature, the pressure, and the relative humidity to apply the expected correction to the superlattice phase. The stabilized superlattice phase enabled the investigation of Floquet-driven double wells by modulating the energy offset through the superlattice phase. We used a near-resonant driving frequency with respect to the interaction energy to enhance the pair-tunneling amplitude in doubly-occupied double wells compared to static double wells and compared to the tunneling amplitude in singly-occupied double wells.
The long range goal of this project was the creation of nanostructures using light fields to manipulate atoms. By passing an atomic beam through one or more standing wave light fields, it is possible to create modulations in the atomic density having periods which are a fraction of the period of the standing wave light fields. Patterns having periods as small as lambda/10 were observed using optical masks and clear evidence for matter-wave effects were established. Several theoretical methods for achieving sub-lambda matter wave patterns were developed, Moreover it was shown that it is possible to create optical lattices having reduced periodicity using Raman transitions in a novel atom-field geometry Experiments were carried out in both magneto-optical traps and atomic beams. In both experimental set-ups, pulsed standing wave optical fields were used to excite the atoms. At some later time the atoms were probed by a traveling wave field, revealing the spatial patterns that had evolved as a result of the atom-field interaction.