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arXiv:2011.12830 · Physical Review A

p -band stability of an ultracold-atom gas in an anharmonic optical-lattice potential with large energy scales

Mateusz Łącki

Published May 4, 2021• 0 citations
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Abstract

Using an optical potential with subwavelength resolution in the form of sharp $\ensuremath{\delta}$-like peaks, potential landscapes are created with increased anharmonicity in placement of lattice band energies and more favorable energy scales. In particular, this makes the ultracold atom $p$-band gas more stable. The article outlines the details of the construction and discusses the $p$-band stability in a canonical cosine optical lattice potential, double-well potential, and a combination of a classical cosine potential with dark state peaked potential.

DOI
10.1103/physreva.103.053301

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Using an optical potential with subwavelength resolution in the form of sharp \ensuremathδ\ensuremath{\delta}\ensuremathδ-like peaks, potential landscapes are created with increased anharmonicity in placement of lattice band energies and more favorable energy scales. In particular, this makes the ultracold atom ppp-band gas more stable. The article outlines the details of the construction and discusses the ppp-band stability in a canonical cosine optical lattice potential, double-well potential, and a combination of a classical cosine potential with dark state peaked potential.
We propose to use subwavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the subwavelength manipulation and strong light-matter interaction associated with nanoplasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed.
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.
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We study the formation and collision-aided decay of an ultracold atomic Bose-Einstein condensate in the first excited band of a double-well two-dimensional optical lattice with weak harmonic confinement in the perpendicular zzz direction. This lattice geometry is based on an experiment by Wirth et al. [Nat. Phys. 7, 147 (2010)]. The double well is asymmetric, with the local ground state in the shallow well nearly degenerate with the first excited state of the adjacent deep well. We compare the band structure obtained from a tight-binding model with that obtained numerically using a plane-wave basis. We find the tight-binding model to be in quantitative agreement for the lowest two bands, in qualitative agreement for the next two bands, and inadequate for even higher excited bands. The bandwidths of the excited bands are much larger than the harmonic-oscillator energy spacing in the zzz direction. We then study the thermodynamics of a noninteracting Bose gas in the first excited band. We estimate the condensate fraction and critical temperature Tc{T}_{c}Tc​ as functions of the lattice parameters. For typical atom numbers, the critical energy kBTc{k}_{B}{T}_{c}kB​Tc​, with kB{k}_{B}kB​ the Boltzmann constant, is larger than the excited bandwidths and harmonic-oscillator energy. Using conservation of total energy and atom number, we show that the temperature increases after the lattice transformation. Finally, we estimate the time scale for a two-body collision-aided decay of the condensate as a function of the lattice parameters. The decay involves two processes, the dominant one in which both colliding atoms decay to the ground band, and the second involving excitation of one atom to a higher band. For this estimate, we have used tight-binding wave functions for the lowest four bands and numerical estimates for higher bands. The decay rate rapidly increases with lattice depth, but close to the critical temperature, it stays smaller than the tunneling rate between the sss and ppp orbitals in adjacent wells.
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