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Journal of the Optical Society of America B

Bragg diffraction of an atom laser by an optical standing wave

Ying Wu, Xiaoxue Yang

Published Apr 27, 2006• 5 citations
Publisher

Abstract

We derive the exact explicit analytical expressions of incident and diffracted atom lasers and their difference in phase from the Bragg diffraction of an atom laser from an optical standing wave in the presence of two-body atomic interactions. These expressions demonstrate that two-body atomic interactions may significantly affect the Bragg diffraction of an atom laser from an optical standing wave, and they provide a convenient basis for discussing and designing the future Bragg devices of strong atom lasers.

DOI
10.1364/josab.23.000913

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We derive the exact explicit analytical expressions of incident and diffracted atom lasers and their difference in phase from the Bragg diffraction of an atom laser from an optical standing wave in the presence of two-body atomic interactions. These expressions demonstrate that two-body atomic interactions may significantly affect the Bragg diffraction of an atom laser from an optical standing wave, and they provide a convenient basis for discussing and designing the future Bragg devices of strong atom lasers.
A vector quantum field theory is developed to describe the interaction of an ultracold atomic ensemble with a laser field. The ultracold atomic ensemble is composed of either bosonic atoms or fermionic atoms. The photon exchanges between different ultracold atoms result in a long-range interatom interaction. Under appropriate conditions, such a many-body interaction leads to an effective ``Kerr-type'' nonlinearity of atomic waves. In terms of the nonlinearity, we construct a general formalism of nonlinear atom optics for an ultracold atomic beam. Applying the formalism to the diffraction of an ultracold atomic beam composed of bosonic atoms by a standing-wave laser field, we find that the many-body nonlinearity induces self-phase and cross-phase modulation of diffracted atomic waves. As a result, a standing-wave laser acts as a nonlinear atomic grating which diffracts atoms in the same way as a nonlinear periodic medium diffracts photons.
Bragg diffraction of atoms at thick standing light waves requires that the wave-matching condition is fulfilled. This usually means that the atomic beam crosses the light wave exactly at the Bragg angle. Nevertheless, our experiments also demonstrate Bragg diffraction at detuned angles if the amplitude of the standing light wave is temporally modulated with an appropriate frequency. If, on the other hand, the phase of the light wave is modulated no diffraction is observed. Both modulation processes produce frequency sidebands which set up `slowly travelling standing waves' in front of a retro-reflection mirror. Atoms are diffracted at these `almost standing' light waves in a similar way to photons at the travelling sound waves in an acousto-optic modulator. The frequency of the diffracted de Broglie waves is assumed to be shifted by the intensity modulation frequency. The different results using amplitude- and phase-modulated light waves are due to interference between the diffraction contributions of the individual frequency sidebands contained in the standing light wave.
We study theoretically the diffraction of atoms by a standing-wave light field. Conceptually the text is divided into two parts. In the first part we deal with the coherent interaction only. We use a band theoretical approach to describe the laser-atom interaction, and to characterize two-beam resonances (Dopplerons and Bragg resonances). These two-beam resonances are major candidates to develop effective atom beam splitters. We study the interaction with classical light fields as well as with quantum fields. In the second part we take incoherent processes, i.e. spontaneous emission, into account and present a numerical scheme for the solution of the generalized optical Bloch equations. This scheme is based on the split-operator technique, and we use it to study numerically the influence of spontaneous emission on the diffraction process. We compare our results with recent experimental data, and investigate the impact of spontaneous emission on the performance of two-beam resonances.
We consider the dynamical Bragg reflection of an atomic matter wave from a finite optical lattice; the resulting energy dependence of the transmittivity allows us to filter out the velocities of the incident atoms. In particular, we show how the coherence length of the incident beam can be inferred from the sharpness of the transmittivity as a function of the lattice intensity. For incident frequencies well inside the reflecting window, the interference of incident and reflected matter waves gives rise to an oscillatory density profile in front of the lattice which can be observed by means of light diffraction. The angular width of the diffracted peaks also provides information on the coherence length of the incident atomic beam.
We study up to the sixth order of Bragg deflection of metastable neon atoms from a standing light wave, corresponding to a momentum transfer of 12\ensuremath{\Elzxh}k. We derive an analytical result for the scattering probability, suitable for arbitrarily high Bragg order, and demonstrate its agreement with experimental results. We investigate the effect of velocity distribution on the Bragg process and show that overlapping diffraction orders can be resolved in velocity space. The prospect of using Bragg scattering as the optics in a Mach-Zehnder style atom interferometer with large splitting is discussed.
This chapter discusses the basic physics of atom diffraction. Starting with a short review on the diffraction of light, we describe the absorption of photons by an atom and its subsequent emission, where the atom to changes its momentum and internal state. Assuming a two-level atom, we describe the coherent interactions of atoms with light, showing its effect on the ground state of the atoms. We further illustrate how the light impacts forces on the atom that can be used for trapping it in the light field. Next, we discuss Bragg diffraction of atoms, where the internal state of an atom is unchanged after diffraction. Here the external motional state of the atom is put in a linear superposition of its movement. Finally, we describe the diffraction of atoms by Raman pulses, where the internal state of the atom is changed after diffraction, while achieving directed motion.