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Physical Review A

Direct observation of atomic localization in optical superlattices

Luca Guidoni, Philippe Verkerk

Published Mar 1, 1998• 41 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.57.r1501

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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≃70\ensuremath{\simeq}70\ensuremath≃70 \ensuremathμm\ensuremath{\mu}\mathrm{m}\ensuremathμm) have been obtained both by detecting the fluorescence and by observing the shadow of the cloud.
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 observe transitions of laser-cooled Rb between vibrational levels in subwavelength-sized optical potential wells, using high-resolution spectroscopy of resonance fluorescence. We measure the spacing of the levels and the population distribution, and find the atoms to be localized to 1/15 of the optical wavelength. We find up to 60% of the population of trapped atoms in the vibrational ground state. The dependence of the spectrum on the parameters of the optical field provides detailed information about the dynamics of laser-cooled atoms.
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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.
We explore Bragg diffraction from atomic lattices bound by light as a diagnostic tool for studying properties of optical lattices not accessible so far. A weak laser beam at a wavelength of about half the wavelength of the lattice field is diffracted from the (100) and (130) lattice planes of a Rb optical lattice. The observation of well-defined Bragg spots confirms the long-range order in optical lattices. From the acceptance angle for Bragg diffraction we deduce the range over which crystalline order is preserved. The comparison of two Bragg spots diffracted from different lattice planes allows us to directly measure the position spread of the atomic wave packets oscillating in the light-induced potential wells. By combining conventional probe transmission spectroscopy with Bragg diffraction we study the motion of atoms that are deeply bound inside the potential wells. We show experimentally and theoretically how backaction of the bound atoms on the trapping field influences the lattice constant. We develop a model for the modification of the refractive index by the highly ordered atomic medium. Based on first-order scattering theory the model explicitly includes the influence of atomic localization on the resulting lattice constant. By measuring the change of the Bragg angle, we observe a decrease of the lattice plane separation for increasing atomic density. We report experimental evidence for the correction to the refractive index due to the finite position spread of the atoms.
Ultralow temperatures produced with polarization-gradient cooling now allow atoms to be trapped in shallow optical potential wells. We present evidence for the quantized motion of atoms in a 1-D optical molasses with the observation of spontaneous Raman transitions between vibrational levels in these wells, observed in fluorescence. In addition, we discuss the features of a far off resonance trap (FORT) -- a single focus dipole force trap so far off resonance to be an essentially ground-state trap.