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arXiv:1907.08910 · Physical Review Research

Realization of a deeply subwavelength adiabatic optical lattice

R. P. Anderson, Dimitrios Trypogeorgos, A. Valdés-Curiel, Qiyu Liang, J. Tao, M. Zhao, T. Andrijauskas, G. Juzeliūnas, I. B. Spielman

Published Feb 12, 2020• 48 citations
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Abstract

This paper presents a flexible sub-wavelength lattice with period divided by a factor of $N$ built from $N$ coupled atomic states, and convert the lattice to a tunable superlattice with $N$-wells arrayed within a conventional half-wavelength unit cell.

DOI
10.1103/physrevresearch.2.013149

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This paper presents a flexible sub-wavelength lattice with period divided by a factor of NNN built from NNN coupled atomic states, and convert the lattice to a tunable superlattice with NNN-wells arrayed within a conventional half-wavelength unit cell.
Recent experiments demonstrated deeply subwavelength lattices using atoms with NNN internal states Raman coupled with lasers of wavelength $\ensuremath{\lambda}$. The resulting unit cell was $\ensuremath{\lambda}/2N$ in extent, an NNN-fold reduction compared to the usual $\ensuremath{\lambda}/2$ periodicity of an optical lattice. For resonant Raman coupling, this lattice consists of NNN independent sinusoidal potentials (with period $\ensuremath{\lambda}/2$) displaced by $\ensuremath{\lambda}/2N$ from each other. We show that detuning from Raman resonance induces tunneling between these potentials. Temporally modulating the detuning couples the sss and ppp bands of the potentials, creating a pair of coupled subwavelength Rice-Mele chains. This operates as a topological charge pump that counterintuitively can give half the displacement per pump cycle of each individual Rice-Mele chain separately. We analytically describe this behavior in terms of infinite-system Chern numbers and numerically identify the associated finite-system edge states.
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.
, are versatile tools to study the dynamical and static properties of ultracold atoms. OLs with subwavelength spatial structure have been realized in recent quantum-gas experiment, offering new possibility for nonlinear and quantum control of ultracold atoms at the nano scale. Herein, we study theoretically and numerically the formation, property, and dynamics of matter-wave localized gap modes of Bose-Einstein condensates loaded in a one-dimensional nanoscale dark-state OL consisted of an array of optical subwavelength barriers. The nonlinear localized modes, in the forms of on- and off-site fundamental gap solitons, and dipole ones, are demonstrated; and we uncover that, counterintuitively, these modes exhibit always a cusplike (side peaks) mode even for a deeply subwavelength adiabatic lattice, contrary to the previously reported results in conventional deep OLs where the localized gap modes are highly confined in a single lattice cell. The (in)stability features of all the predicted localized modes are verified through the linear-stability analysis and direct perturbed simulations. Our predicted results are attainable in current ultracold atoms experiments with the cutting-edge technique, pushing the nonlinear control of ultracold atoms with short-period OLs as an enabling technology into subwavelength structures.