Collective atomic recoil in a moving Bose-Einstein condensate: From superradiance to Bragg scattering

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio

Phys. Rev. A 71, 033612 – Published 8 March 2005

Abstract

We present the results of an experiment on light scattering from an elongated Bose-Einstein condensate (BEC) interacting with a far-off-resonant pump laser. By collective atomic recoil lasing (CARL) a coherent superposition of two atomic wave packets with different momenta is created. Varying the intensity of a weak counterpropagating laser beam we observe the transition from the pure superradiant regime to the Bragg scattering regime, where Rabi oscillations in a two-level system are observed. The process is limited by the decoherence between the two atomic wave packets. In the superradiant regime the experiment gives evidence of a contribution to decoherence which depends on the initial velocity of the condensate. The system is described by the CARL-BEC model, which is a generalization of the Gross-Pitaevskii model to include the self-consistent evolution of the scattered field and a phase-diffusion decoherence process, which accounts for the observed damping.

Received 10 March 2004

DOI:https://doi.org/10.1103/PhysRevA.71.033612

Authors & Affiliations

L. Fallani^1,2,*, C. Fort^1,2, N. Piovella^1,3, M. Cola^1,3, F. S. Cataliotti^1,4, M. Inguscio^1,2, and R. Bonifacio^1,3

¹INFM and European Laboratory for Non-Linear Spectroscopy (LENS), via Nello Carrara 1, I-50019 Sesto Fiorentino (Firenze), Italy
²Dipartimento di Fisica, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Firenze), Italy
³Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy
⁴INFM-MATIS, Scuola Superiore di Catania, Dipartimento di Fisica, Università di Catania, via Santa Sofia 64, I-95124 Catania, Italy

^*Electronic address: fallani@lens.unifi.it

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Vol. 71, Iss. 3 — March 2005

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Images

Figure 1
Schematics of superradiant light scattering from a Bose-Einstein condensate. An elongated BEC with momentum ${\vec{p}}_{0}$ is illuminated by a far-off-resonant laser beam (pump beam) with frequency $ω$ and wave vector $\vec{k}$ directed along its axial direction. After backscattering of photons with ${\vec{k}}_{s c} ≃ - \vec{k}$ and the subsequent recoil of atoms, a matter-wave grating forms, due to the quantum interference between the two momentum components ${\vec{p}}_{0}$ and ${\vec{p}}_{0} + 2 ℏ \vec{k}$ of the wave function of the condensate. The effect of this grating is to further scatter the incident light in a self-amplifying process.Reuse & Permissions
Figure 2
Sketch of the experimental procedure. The condensate may be set into motion by a sudden displacement of the magnetic trap center (A). When the condensate reaches the desired momentum $p_{0}$ we switch off the magnetic trap and flash the atoms with far-off-resonance laser light (pump and seed beams) directed along the condensate symmetry axis (B). After an expansion time (28 ms) allowing a complete separation of the momentum components $p_{0}$ and $p_{0} + 2 ℏ k$ , we take an absorption image of the atoms (C).Reuse & Permissions
Figure 3
Time evolution of the population in the original momentum state $p_{0} = 0$ for a BEC interacting with an off-resonant pump beam and a counterpropagating weak seed beam (resonant with the Bragg transition $ω - ω_{s} = 4 ω_{R}$ ) for different seed beam intensities $I_{s} = η I$ . The laser detuning and intensity are 15 GHz and $0.9 W ∕ {cm}^{2}$ , respectively. As the seed intensity decreases (from top to bottom) the response of the system goes from the Bragg scattering regime to the pure superradiant regime. The solid lines are obtained from the numerical integration of Eqs. (12, 13, 14).Reuse & Permissions
Figure 4
(Left) Time evolution of the atomic population in the original momentum state $p_{0}$ (open circles) and in the recoiled state $p_{0} + 2 ℏ k$ (solid circles) for different pulse durations. The solid line is a fit with the hyperbolic tangent (20) predicted by the theoretical model. The initial momentum $p_{0}$ of the condensate is set to $- ℏ k$ (top), 0 (center), and $+ ℏ k$ (bottom). (Right) Plots of the expanded atomic density profile after interaction with a $250 − μ s$ -long pump pulse. The peak on the left corresponds to the initial momentum state $p_{0}$ and the peak on the right corresponds to the state $p_{0} + 2 ℏ k$ . The laser detuning and intensity are 13 GHz and $1.35 W ∕ {cm}^{2}$ , respectively.Reuse & Permissions
Figure 5
Decoherence rate as a function of the initial momentum $p_{0}$ of the condensate. The solid line is a fit of the experimental data with a parabola centered in $p_{0} = - ℏ k$ , as expected from the theoretical model [see Eq. (16)].Reuse & Permissions

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