Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate

Abstract

We study experimentally superradiant Rayleigh scattering from a Bose-Einstein condensate (BEC) in a new parameter regime where pump depletion and the exchange of photons between the endfire modes are important. Through experiments and simulations we show that collective atom light coupling leads to the self-organized formation of dynamic Bragg gratings within the sample. These gratings lead to an efficient back-scattering of pump photons and optical resonator structures within the BEC.PACS numbers: 03.75. Nt,37.10.Vz,42.50.Gy With its extremely high optical depth and unique coherence properties, a Bose Einstein condensate provides an ideal object on which to study collective light scattering with the goal of generating and probing light-atom correlations. Superradiant light scattering (SLS) from ultra-cold atomic ensembles has been recognized as a method to generate entangled atoms and photons due to the fact that the interaction Hamiltonian has the generic form of a parametric amplifier H ∝â †b † , where correlations based on momentum conservation arise in the case of Rayleigh scattering [1], and angular momentum in the case of Raman processes [2]. Entanglement in the ultra-low gain regime of such an interaction, when far less than one atom-photon excitation pair is generated on average, forms the basis for a quantum repeater [3] and has been studied extensively [4]. Here, we are interested in the high gain -superradiant -regime where the detection of entanglement requires in general the measurement of both the phase and amplitude of the light and matter waves at the sub-shot noise level. While this is typically hampered by the lack of an atomic analogue to homodyne detection of light, a recent proposal claims entanglement may be detected by just counting photons and atoms [5]. Nonetheless, the full dynamics of coupled matter and light waves where one does not place limitations on the depletion of either the condensate or input light, and where propagation effects are considered, remain important issues if such correlations and entanglement are to be made useful resources.To this end, we explore superradiant Rayleigh scattering from a trapped, cigar shaped BEC as the pump detuning is varied while the single particle scattering rate R is kept constant. In this way, we investigate the effect of the detuning of the pump beam in the process, and move between the case where the pump beam remains essentially undepleted by the scattering, to the situation where superradiant scattering is 'clamped' by a lack of photons in the pump beam. Crucial to these dynamics is the structure that builds up along the long axis of the condensate, demonstrating characteristics from 'Dicke' superradiance from extended samples [6,7,8], a fact recognized recently both experimentally [9, 10] and theoretically [11,12,13,14]. Contrary to most earlier experimental work on the subject [9,15,16, 17], we end-pump along * hilliard@nbi.dk the long axis with a beam mode-matched to the transverse cross-section of the BEC in order to optimize the...

High Order Momentum States by Light Wave Scattering

“…Therefore, the frequency difference between the beams can be controlled precisely. Furthermore, to avoid the reflection from the glass tube and formation of Bragg scattering in the experiment, the pump beam can actually deviate a few degrees from the long axis, as shown in the experiments (Fallani et al, 2005;Hilliard et al, 2008;Li, Zhou et al, 2008).…”

“…Because the above traditional superradiant-scattering configuration involves many atomic side modes coupled together, to simplify it, we chose another configuration where a pump beam travels along the long axis of the BEC. This scheme is widely studied in photon echo (Piovella et al, 2003), decoherence (Fallani et al, 2005), spatial distribution effects and self-organized formation of dynamic gratings (Hilliard et al, 2008). Since the pulse length is far longer than the initial spontaneous process (Zobay & Nikolopoulos, 2006), we choose the semi-classical theory which can well describe the experimental results (Bar-Gill et al, 2007;Yang et al, 2008;Zobay & Nikolopoulos, 2006).…”

“…Since the BEC is tightly constrained in its short axis (x,ŷ) in the present superradiance setup and the Fresnel number of the optical field is around 1, one dimensional approximation is usually used (Bar-Gill et al, 2007;Hilliard et al, 2008;Inouye et al, 1999;Li, Zhou et al, 2008). We expand the wavefunction of the condensate ψ(r, t) in momentum space,…”

Anisotropy ins-wave Bose-Einstein condensate collisions and its relationship to superradiance

“…Anisotropies are less surprising in a wave context. The process of optically pumped superradiance [27][28][29][30][31][32][33][34][35], which occurs when an elongated atomic cloud is illuminated with light, exhibits strong anisotropies which can be explained in terms of an anisotropic gain medium.…”

Information-Recycling Beam Splitters for Quantum Enhanced Atom Interferometry

“…superradiance transition [15][16][17][18][19][20][21], in which the initial population ofÊ 2 is set to zero, and the population transfer between j1i and j2i is driven by the absorption of a photon fromÊ 1 , and the spontaneous emission of a photon intoÊ 2 . A small ''seed'' of atoms in j2i, which could be populated via a conventional Raman transition, stimulates the transfer such that the majority of photons are emitted into a single mode.…”