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Physical Review A

Subharmonic resonances in high-order wave mixing in the quantized atomic motion in a one-dimensional optical lattice

J. P. Lopez, A. J. F. de Almeida, J. W. R. Tabosa

Published Mar 14, 2018• 0 citations
Publisher

Abstract

We report on the observation of subharmonic resonances in high-order wave mixing associated with the quantized vibrational levels of atoms trapped in a one-dimensional optical lattice created by two intense nearly counterpropagating coupling beams. These subharmonic resonances, occurring at $\ifmmode\pm\else\textpm\fi{}1/2$ and $\ifmmode\pm\else\textpm\fi{}1/3$ of the frequency separation between adjacent vibrational levels, are observed through phase-match angularly resolved six- and eight-wave mixing processes. We investigate how these resonances evolve with the intensity of the incident probe beam, which couples with one of the coupling beams to create anharmonic coherence gratings between adjacent vibrational levels. Our experimental results also show evidence of high-order processes associated with coherence involving nonadjacent vibrational levels. Moreover, we also demonstrate that these induced high-order coherences can be stored in the medium and the associated optical information retrieved after a controlled storage time.

DOI
10.1103/physreva.97.033821

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We report on the observation of subharmonic resonances in high-order wave mixing associated with the quantized vibrational levels of atoms trapped in a one-dimensional optical lattice created by two intense nearly counterpropagating coupling beams. These subharmonic resonances, occurring at \ifmmode±\else\textpm\fi1/2\ifmmode\pm\else\textpm\fi{}1/2\ifmmode±\else\textpm\fi1/2 and \ifmmode±\else\textpm\fi1/3\ifmmode\pm\else\textpm\fi{}1/3\ifmmode±\else\textpm\fi1/3 of the frequency separation between adjacent vibrational levels, are observed through phase-match angularly resolved six- and eight-wave mixing processes. We investigate how these resonances evolve with the intensity of the incident probe beam, which couples with one of the coupling beams to create anharmonic coherence gratings between adjacent vibrational levels. Our experimental results also show evidence of high-order processes associated with coherence involving nonadjacent vibrational levels. Moreover, we also demonstrate that these induced high-order coherences can be stored in the medium and the associated optical information retrieved after a controlled storage time.
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We use a method based on optical coherent transients to study the vibrational coherence lifetimes of atoms trapped in the potential wells of a near-resonant optical lattice in the oscillating regime. The dependence of the positions and widths of the vibrational Raman resonances of the coherent transient spectra on the intensity, detuning, and geometry of the lattice beams is investigated and the results are compared with theoretical predictions. It is shown that the principal source of broadening of the vibrational Raman resonances is the anharmonicity of the light-shift potential wells. We also perform time-resolved measurements of the vibrational excitation of atoms equilibrating in an optical lattice.
In this thesis, I report on experiments with cold 85Rb atoms in a far-detuned one-dimensional optical lattice. These experiments are focused on creating efficient coupling between the quantized vibrational states of atoms in the optical lattice, on controlling and maintaining coherence between the vibrational states, and on developing a spectroscopy method to characterize the decay of coherence. First, I present an experimental study of the application of simple and compound pulses consisting of time-dependent spatial translations to coupling vibrational states of ultracold 85Rb atoms in the optical\nlattice. Experimental results show that a square pulse consisting of lattice displacements and a delay is more efficient than single-step and Gaussian pulses. The square pulse can be seen as an example of coherent control. Numerical calculations are in strong agreement with the experimental results. In addition, it is shown numerically that the vibrational state coupling due to such lattice manipulations is more efficient in shallow lattices than in deep lattices, in which the coupling probability approaches the harmonic\noscillator limit. Next, the effectiveness of these pulses in reviving oscillations of atoms in vibrational superposition states using a pulse-echo technique is examined. Experimental results show that the square and Gaussian pulses result in higher echo amplitudes than the single-step pulse. These echo amplitudes are an order of magnitude larger than the echo amplitudes observed previously for the motional states of atoms in optical lattices.\nWith the aim of the optimized square echo pulse, echo amplitude is measured at much\nlonger times, where a surprising coherence freeze (plateau) is observed. To investigate \nmechanisms responsible for the observed echo decay and the coherence freeze, we developed\na new two-dimensional pump-probe spectroscopy technique to monitor the evolution of frequency-frequency correlations in the system, a necessary input for understanding the decay of coherence. Through this 2D technique, we have characterized the temporal decay of frequency memory and through our simulations we find that coherence freeze is related to the shape of this memory loss function. This technique is general in that it can be applied in a variety of quantum information candidate systems to probe the nature of their decoherence.
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A subharmonic resonance occurs on irradiation of a three-level (\ensuremath{\Lambda}) system by two bichromatic fields when an integer multiple of the common frequency difference matches the Raman detuning between the two lower levels. The occurrence of these multiphoton resonances requires saturation of the Raman transition. The three-level model is applied in order to understand recent experimental studies of subharmonic Raman resonances between vibrational states of optically trapped atoms. I explain the difference between these resonances and the well-known velocity-tuned (Doppleron) resonances in two-level atoms by considering a two-state model with the excited state eliminated. I finally point out a Sisyphus cooling mechanism that is entirely dependent on an additional relaxation of the Raman coherence, comparable to collision-induced resonances.
We report the observation of the first six subharmonic resonances of the Rabi frequency in the absorption of a 100% amplitude-modulated laser beam by a two-level atom. The amplitude-modulated field is formed by combining two separate cw lasers; one is held fixed in frequency, and the other, of equal amplitude, is scanned in frequency. We present data and theory for several values of the detuning between the fixed field and the atomic resonance. The experimental results are in good agreement with theory.