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arXiv:1203.0894 · Physical Review A

Raman scattering of atoms from a quasicondensate in a perturbative regime

Tomasz Wasak, Jan Chwedeńczuk, Paweł Zin, Marek Trippenbach

Published Oct 22, 2012• 6 citations
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Abstract

Using the perturbative approach, it is demonstrated that the widths of the density and second-order correlation function of atoms scattered from a quasicondensate in a Raman process are sensitive to the phase fluctuations induced by the nonzero temperature of the mother cloud. It is also shown how these widths evolve during expansion of the halo of scattered atoms. It is also argued that if the Raman scattering is preceded by expansion of the mother cloud, the density of atoms widens substantially, while the second-order correlation function remains practically unchanged. These results are useful for planning future Raman scattering experiments and indicate the degree of spatial resolution of atom-position measurements necessary to detect the temperature dependence of the quasicondensate. All the calculations are performed using experimental parameters of a metastable ${}^{4}$He${}^{*}$ quasicondensate of the Palaiseau group.

DOI
10.1103/physreva.86.043621

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Using the perturbative approach, it is demonstrated that the widths of the density and second-order correlation function of atoms scattered from a quasicondensate in a Raman process are sensitive to the phase fluctuations induced by the nonzero temperature of the mother cloud. It is also shown how these widths evolve during expansion of the halo of scattered atoms. It is also argued that if the Raman scattering is preceded by expansion of the mother cloud, the density of atoms widens substantially, while the second-order correlation function remains practically unchanged. These results are useful for planning future Raman scattering experiments and indicate the degree of spatial resolution of atom-position measurements necessary to detect the temperature dependence of the quasicondensate. All the calculations are performed using experimental parameters of a metastable 4{}^{4}4He∗{}^{*}∗ quasicondensate of the Palaiseau group.
We consider elastic scattering of atoms from elongated clouds taking into account an effective, finite duration of the collision due to the expansion of the condensates. We also include the quasicondensate nature of the degenerate quantum gas, due to a finite temperature of the system. We evaluate the pair-correlation function measured experimentally in Kheruntsyan et al. [Phys. Rev. Lett. 108, 260401 (2012)] and show that the finite duration of the collision is an important factor determining the properties of the correlations. Our analytic calculations are in agreement with the measurements. The analytical model we provide, useful for identifying physical processes that influence the correlations, is relevant for experiments with nonclassical pairs of atoms.
We measure the two-point density correlation function of freely expanding quasicondensates in the weakly interacting quasi-one-dimensional (1D) regime. While initially suppressed in the trap, density fluctuations emerge gradually during expansion as a result of initial phase fluctuations present in the trapped quasicondensate. Asymptotically, they are governed by the thermal coherence length of the system. Our measurements take place in an intermediate regime where density correlations are related to near-field diffraction effects and anomalous correlations play an important role. Comparison with a recent theoretical approach described by Imambekov et al. yields good agreement with our experimental results and shows that density correlations can be used for thermometry of quasicondensates.
We study, within the framework of the classical-field approximation, the density correlations of a weakly interacting expanding Bose gas for the whole range of temperatures across the Bose-Einstein condensation threshold. We focus on elongated quasi-one-dimensional systems where there is a huge discrepancy between the existing theory and experimental results [A. Perrin et al., Nat. Phys. 8, 195 (2012)]. We find that the density correlation function is not reduced for temperatures below the critical one as it is predicted for the ideal gas or for a weakly interacting system within the Bogoliubov approximation. This behavior of the density correlations agrees with the above-mentioned experiment with the elongated system. Although the system was much larger than that studied here, we believe that the behavior of the density correlation function found there is quite generic. Our theoretical study indicates also large density fluctuations in the trap in the quasicondensate regime where only phase fluctuations were expected. We argue that the enhanced density fluctuations can originate in the presence of interactions in the system, or more precisely in the presence of spontaneous dark solitons in the elongated gas at thermal equilibrium.
A method for detecting the internal characteristic (including density, velocity and temperature) distribution of cold atom clouds is reported in this paper. During the detection process, the spatial resolution of the cold atom cloud is achieved at sub-mm by precisely adjusting the spatial position of the Raman laser beam. Meanwhile, to minimize the impact of frequency and intensity fluctuations in the Raman laser on measurement results, we propose to utilize a differential atomic interferometer to suppress common-mode noise, thereby enhancing measurement accuracy. This method enables precise detection of the internal structure of cold atom clouds, providing a reference for in-depth studies of atom cloud properties.
The temperature effect on the resonance Raman scattering from molecules is investigated. Considering a total system consisting of a molecular system, a heat bath, and the weak radiation field, a general expression for the relaxation processes is derived utilizing the Liouville operator technique for the time evolution of the density matrix of the total system. By using the perturbation method with respect to the radiation and matter up to second order, rate constants for zero photon (radiationless processes), one-photon and two-photon processes are derived after taking the long time limit in the Markoff approximation. Assuming a weak interaction between the molecular system and heat bath, a temperature-dependent resonance Raman scattering cross section is formulated in the adiabatic basis set for the molecular systems. In the displaced harmonic oscillator model, we obtain an analytical expression for the temperature-dependent Raman scattering cross section for the multimode case, which is suitable for both weak coupling and strong coupling cases. Analytical expressions for the Stokes and anti-Stokes bands of the jth order vibrational transition in the one oscillator model can easily be obtained from the general expression for the resonance Raman scattering cross section derived. An approximate Stokes to anti-Stokes ratio is given up to the second order of the dimensionless displacement Δ. The resonance Raman scattering cross section and the excitation energy profiles are numerically calculated as a function of physical constant such as temperature, molecular vibrational frequency and Δ. It is shown that the excitation profiles of the anti-Stokes band of the jth order vibrational transition have the similar envelope of the corresponding Stokes band shifted by jh/ω. The inverse Raman effect which is closely related to the ordinary Raman effect is also discussed.
We analyze density-density correlations of expanding clouds of weakly interacting two-dimensional Bose gases below and above the Berezinskii-Kosterlitz-Thouless transition, with particular focus on short-time expansions. During time-of-flight expansion, phase fluctuations of the trapped system translate into density fluctuations, in addition to the density fluctuations that exist in situ. We calculate the correlations of these fluctuations both in real space and in momentum space and derive analytic expressions in momentum space. Below the transition, the correlation functions show an oscillatory behavior, controlled by the scaling exponent of the quasicondensed phase, due to constructive interference. We argue that this can be used to extract the scaling exponent of the quasicondensate experimentally. Above the transition, the interference is rapidly suppressed when the atoms travel an average distance beyond the correlation length. This can be used to distinguish the two phases qualitatively.