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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Echo response of ensemble of cooled atoms in optical lattices

S. O. Elyutin, Andrei I. Maimistov

Published Apr 20, 2004• 0 citations
Publisher

Abstract

We have observed numerically a quantum mechanical probability current echo response generated by an ensemble of the drops of Bose-Einstein condensates (BEC) loaded in the cells of optical dual lattice. Echo was excited with the pulses of two-photon optical radiation due to Raman scattering. Echo temporal form and the role of inhomogeneous broadening are discussed.

DOI
10.1117/12.561025

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Coherent responses of resonance atom layer to short optical pulse excitation are numerically considered. The inhomogeneous broadening of one-photon transition, the near dipole-dipole interaction, and the substrate dispersion are involved in analysis. Under certain intensity of incident pulses, a strong coherent interaction in the form of sharp spikes of superradiation is observed in transmitted radiation. The Lorentz field correction and the substrate dispersion weaken the effect, providing additional spectral shifts. Specific features of photon echo in the form of multiple echoes to a double or triple pulse excitation in the presence ofnear dipole-dipole interaction is discussed.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 3, 2006•1 citation
We have observed numerically a quantum mechanical probability current echo response generated by an ensemble of the drops of Bose-Einstein condensates (BEC) loaded in the cells of optical dual lattice. Echo was excited with the pulses of two-photon optical radiation due to Raman scattering. Echo temporal form and the role of inhomogeneous broadening are discussed.
The dynamics of an ultracold dilute boson gas in an optical lattice is described in the framework of the Bose-Hubbard model in which the parameters of the system are controlled by light. Within this model, an ensemble of Bose-Einstein condensates trapped in cells of a double optical lattice generates an echo response in the quantum-mechanical probability current. The echo signal is excited by biharmonic radiation pulses under two-photon (Raman) resonance conditions. The time profile of the echo signal and the role played by the inhomogeneous broadening and the interaction of atoms in the formation of the boson echo are discussed.
A time-dependent perturbational approach is used to study the Raman echo generated by an inhomogeneous ensemble of three-level atomic systems in the Λ configuration. The sixth-order perturbative solution for coherence between the two lower states contains eight echo terms that are visualized with double Feynman diagrams. The echo is interpreted as a response of the ensemble to six short single-frequency optical pulses whose timing satisfies a special condition. Nonperturbative numerical simulation confirms the predictions of the perturbation analysis about the main characteristics of the echo. When the excitation pulses vary adiabatically with respect to fast optical coherence decay the echo amplitude depends on interference of the eight terms. A computational scheme developed for the higher-order perturbative analysis is also discussed.
In this thesis, I study the properties of cold neutral atoms, including Bose-Einstein condensates (BEC), inside periodic light-shift potentials created by optical lattices. In the first part, a new optical-lattice scheme, employing Raman transitions, hereafter referred to as a Raman Optical Lattice (ROL), is investigated. This optical lattice possesses a novel sub-Doppler cooling mechanism and a reduced periodicity. Both theoretical and experimental results con¯rm these two characteristics of the ROL. In the second half of the thesis, instead of thermal atoms, optical lattices are loaded with condensate atoms. Our BEC apparatus and the procedure towards forming a BEC are described in detail. After the achievement of the BEC, a 1D far-detuned optical lattice is applied to the BEC. A number of phenomena are observed, including Kapitza-Dirac diffraction, thermal atom interference, atom interferometry, Bloch oscillations, and a superfluid to Mott-insulator transition. Finally a brief discussion about future work is given.
The development of ultracold atom technology has enabled precise investigations on the quantum dynamics of quantum gases. Recently, inspired by experimental advancement, the SU(1,1)\text{SU}(1,1)SU(1,1) echo, akin to the well-known SU(2)\text{SU}(2)SU(2) spin echo, was proposed for the single-component Bose-Einstein condensate (BEC). In this paper, we investigate the possibility of quantum echo in the more intricate two-component BEC by fully exploiting its underlying symmetry, which is the Lie group Sp(4,R)\text{Sp}(4,R)Sp(4,R). We demonstrate that quantum echo can occur for the two-component BEC by applying a driving protocol consisting of two steps in each period. The first step can be any Bogoliubov Hamiltonian, while the second step is a Hamiltonian with interactions turned off, which plays a similar role as the $\ensuremath{\pi}$ pulse in spin echo. We confirm our theoretical results with numerical calculations for different examples of the two-component BEC. We further consider the effect of interactions between the excited boson modes on the quantum echo process and discuss the possible experimental implementation of this quantum echo.
Coherent responses of resonance atom layer to short optical pulse excitation are numerically considered. The inhomogeneous broadening of one-photon transition, the local field effect, and the substrate dispersion are involved into analysis. For a certain intensity of incident pulses a strong coherent interaction in the form of sharp spikes of superradiation is observed in transmitted radiation. The Lorentz field correction and the substrate dispersion weaken the effect, providing additional spectral shifts. Specific features of photon echo in the form of multiple responses to a double or triple pulse excitation is discussed.
Coherent responses of resonance atom layer to short optical pulse excitation are numerically considered. The inhomogeneous broadening of one-photon transition, the near dipole-dipole interaction, and the substrate dispersion are involved in analysis. Under certain intensity of incident pulses, a strong coherent interaction in the form of sharp spikes of superradiation is observed in transmitted radiation. The Lorentz field correction and the substrate dispersion weaken the effect, providing additional spectral shifts. Specific features of photon echo in the form of multiple echoes to a double or triple pulse excitation in the presence ofnear dipole-dipole interaction is discussed.