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arXiv:1302.2120 · Physical Review A

Continued-fraction analysis of dressed systems: Application to periodically driven optical lattices

T. Zanon-Willette, Emeric de Clercq, E. Arimondo

Published Feb 27, 2013• 1 citation
arXivHTMLPDF

Abstract

Radio-frequency quantum engineering of spins is based on the dressing by a nonresonant electromagnetic field. Radio-frequency dressing occurs also for the motion of particles, electrons, or ultracold atoms, within a periodic spatial potential. The dressing, producing a renormalization and also a freeze of the system energy, is described by different approaches: dressed atom, magnetic resonance semiclassical treatment, and continued-fraction solution of the Schr\"odinger equation. A comparison between these solutions points out that the semiclassical treatment, to be denoted as the $S$ solution, represents the most convenient tool to evaluate the tunneling renormalization of ultracold atoms.

DOI
10.1103/physreva.87.023424

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Radio-frequency quantum engineering of spins is based on the dressing by a nonresonant electromagnetic field. Radio-frequency dressing occurs also for the motion of particles, electrons, or ultracold atoms, within a periodic spatial potential. The dressing, producing a renormalization and also a freeze of the system energy, is described by different approaches: dressed atom, magnetic resonance semiclassical treatment, and continued-fraction solution of the Schr"odinger equation. A comparison between these solutions points out that the semiclassical treatment, to be denoted as the SSS solution, represents the most convenient tool to evaluate the tunneling renormalization of ultracold atoms.
A Zeeman-insensitive optical clock atomic transition is engineered when nuclear spins are dressed by a nonresonant radio-frequency field. For fermionic species as (87)Sr, (171)Yb, and (199)Hg, particular ratios between the radio-frequency driving amplitude and frequency lead to "magic" magnetic values where a net cancelation of the Zeeman clock shift and a complete reduction of first-order magnetic variations are produced within a relative uncertainty below the 10(-18) level. An Autler-Townes continued fraction describing a semiclassical radio-frequency dressed spin is numerically computed and compared to an analytical quantum description including higher-order magnetic field corrections to the dressed energies.
We present a semiclassical solution for a Zeeman-split, optically pumped, spin-\textonehalf{} system interacting with a strong radio-frequency field. The method of solution presented here is based upon a matrix continued-fraction expansion, and can explain any resonance phenomena which occur for arbitrary geometrical configurations of the pumping beam or the rf field polarization axis. Theoretical predictions of line shapes for some cases are reported and discussed. The solution can also explain some deviations of the observed Bloch-Siegert shift at high rf power from the behavior predicted by a previous semiclassical theory, which can account for simple geometrical configurations only.
Dressed states are eigenstates of the full Hamiltonian which also includes the interaction of the atoms with the driving field. From this point of view, photons of the field interacting with the atom externally induce quantum coherence, and thus modify the inherent properties of atomic system, such as Mollow triplets in the resonance fluorescence spectrum. Because of the rigorous requirement on the ratio of driving strength to the intrinsic linewidth, the associated demonstrations in neutral atoms are restricted to optical dressing in a cavity quantum electrodynamics system and microwave dressing in the Rydberg excitation. Here, we report the realization of coherent dressing of a ground state driven by a radio-frequency magnetic field in an antirelaxation coated warm vapor cell. We reveal the properties of the radio-frequency dressed states, a linear scaling in the resonance splitting, and the improved resonance linewidth. Such a system is robust to the variation of detection frequency and atom number and is able to determine the driving frequency. It thus may emerge as a unique and versatile tool in quantum metrology, for instance, rf atomic magnetometry in a large detection frequency range. Published by the American Physical Society 2024
Ultracold atomic gases in periodic potentials are powerful platforms for exploring quantum physics in regimes dominated by many-body effects as well as for developing applications that benefit from quantum mechanical effects. Further advances face a range of challenges including the realization of potentials with lattice constants smaller than optical wavelengths as well as creating schemes for effective addressing and manipulation of single sites. In this paper we propose a dressed-based scheme for creating periodic potential landscapes for ultracold alkali atoms with the capability of overcoming such difficulties. The dressed approach has the advantage of operating in a low-frequency regime where decoherence and heating effects due to spontaneous emission do not take place. These results highlight the possibilities of atom-chip technology in the future development of quantum simulations and quantum technologies, and provide a realistic scheme for starting such an exploration.
We show how it is possible to more than double the on-site interaction energy of neutral atoms in optical potentials by the technique of radio-frequency (rf) dressing, while maintaining interwell dynamics. We calculate Bose-Hubbard parameters for rf-dressed optical lattices and arrays of rf-dressed dipole traps. We show that decreasing the distance between wells, by the interpolation of wells confining different mF{m}_{F}mF​ states, increases the interaction energy more than decreasing the height of the classically forbidden region between existing wells. The schemes we propose have negligible Landau-Zener losses caused by atomic motion; this was a dominant effect in the first experimental demonstration of the modification of an optical potential by radio-frequency dressing.