Analysis of Kapitza-Dirac diffraction patterns beyond the Raman-Nath regime

Abstract

Abstract:We study Kapitza-Dirac diffraction of a Bose-Einstein condensate from a standing light wave for a square pulse with variable pulse length but constant pulse area. We find that for sufficiently weak pulses, the usual analytical short-pulse prediction for the Raman-Nath regime continues to hold for longer times, albeit with a reduction of the apparent modulation depth of the standing wave. We quantitatively relate this effect to the Fourier width of the pulse, and draw analogies to the Rabi dynamics of a coupled two-state system. Our findings, combined with numerical modeling for stronger pulses, are of practical interest for the calibration of optical lattices in ultracold atomic systems.

Collinear Four-Wave Mixing of Two-Component Matter Waves

“…The KD pulse duration (25 s) and the lattice depth V a for atoms of type jai (6 E R , where E R ¼ @ 2 k 2 L =2m is the recoil energy), are chosen such that half of the jai population is diffracted into jAE2i, while higher orders remain largely unpopulated. By analyzing single-component diffraction patterns [20], we have determined the lattice depths for each component, confirming that atoms of type jbi experience < 5% of the lattice depth seen by the jai atoms. On their own, the jbi atoms therefore are not affected by the lattice pulse, as shown in Fig.…”

“…1(a). The pulse induces Kapitza-Dirac (KD) diffraction [19,20] producing recoiling jai atoms in both positive and negative momentum modes jAE2i jAE2@k L i where k L ¼ 2= L , while the jbi atoms remain unaffected. Subsequently, as illustrated in Fig.…”

Observation of diffraction phases in matter-wave scattering

“…Due to the position operatorẑ, e ±ikẑ can be described as a momentum shift operator: e ±ikẑ |p = |p ±hk [2]. In the momentum representation, the periodical potential V (ẑ), apart from a constant term, can be written in an operator form aŝ V = U 0 4 dp(|p + 2hk p| + |p − 2hk p|), which explicitly shows the momentum change 2hk of an atom scattered by the standing wave [25]. This process is accomplished by absorbing a photon from one of the laser beams and emitting it into the counterpropagating one.…”

High Order Momentum States by Light Wave Scattering

“…In the Bragg regime, the potential height introduced by the standing wave is restrained below 4E R and that leads to the difficulty of generating higher order momentum states. In the Raman-Nath regime, the intensity of the standing wave is not limited so that higher order momentum states can be generated symmetrically (Gadway et al, 2009;Sapiro et al, 2009b). However the pulse duration has to be short enough to neglect the atomic motion, so the momentum states can not be predicted in this regime if the pulse duration is slightly longer.…”