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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Dynamic diffraction of atoms in the recoil-dominated regime

Péter Horák, Klaus M. Gheri, Helmut Ritsch

Published Jun 1, 1996• 0 citations
Publisher

Abstract

We study the dynamic diffraction of atoms by a standing light wave in the limit where the recoil shift is much larger than the atomic linewidth. We demonstrate the appearance of a damped Pendellosung as well as anomalous transmission, which is equivalent to optical pumping into dark superpositions of the same internal atomic state with different external momenta. As an example, we discuss the case of metastable He coupled to the ground state via an anti-Stokes - Raman transition. We show that besides leading to a very narrow velocity selection for the deflected atoms, this effect could, in principle, be used to build a large-angle coherent beamsplitter and a large-area interferometer for metastable helium. We calculate the signal contrast and flux including initial velocity spread and decoherence through spontaneous emission for such an interferometer.

DOI
10.1088/1355-5111/8/3/020

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We study the dynamic diffraction of atoms by a standing light wave in the limit where the recoil shift is much larger than the atomic linewidth. We demonstrate the appearance of a damped Pendellosung as well as anomalous transmission, which is equivalent to optical pumping into dark superpositions of the same internal atomic state with different external momenta. As an example, we discuss the case of metastable He coupled to the ground state via an anti-Stokes - Raman transition. We show that besides leading to a very narrow velocity selection for the deflected atoms, this effect could, in principle, be used to build a large-angle coherent beamsplitter and a large-area interferometer for metastable helium. We calculate the signal contrast and flux including initial velocity spread and decoherence through spontaneous emission for such an interferometer.
We have used an echo-type atom interferometer that manipulates laser-cooled atoms in a single ground state to investigate the effect of light scattering from pulsed and continuous-wave light. The interferometer uses two off-resonant standing-wave pulses applied at times t=0t=0t=0 and t=Tt=Tt=T to diffract and recombine momentum states separated by $2\ensuremath{\hbar}k$ at t=2Tt=2Tt=2T. Matter wave interference is associated with the formation of a density grating with period $\ensuremath{\lambda}/2$ in the vicinity of this echo time. The grating contrast is measured by recording the intensity of coherently backscattered light. The interferometer is perturbed by an additional pulse applied at $t=2T\ensuremath{-}\ensuremath{\delta}T$ or by continuous-wave background light. If the additional pulse is a standing wave, the momentum states interfering at t=2Tt=2Tt=2T are displaced and the grating contrast can be completely recovered due to constructive interference. In this case, the contrast shows a periodic modulation at the atomic recoil frequency as a function of $\ensuremath{\delta}T$. In a recent work, it was shown that the atomic recoil frequency can be measured easily and precisely when using coherence functions to model the signal shape. This paper provides an alternative description of the signal shape through an analytical calculation of echo formation in the presence of an additional standing-wave pulse. Using this treatment, it is possible to model the effects of spontaneous emission and spatial profile of the laser beam on the signal shape. Additionally, the theory predicts scaling laws as a function of the pulse area and the number of additional standing-wave pulses. These scaling laws are investigated experimentally and can be exploited to improve precision measurements of the atomic recoil frequency. We also show that coherence functions can be used to make a direct measurement of the populations of momentum states associated with the ground state under conditions where the Doppler-broadened velocity distribution of the sample is much larger than the recoil velocity. These measurements are consistent with Monte Carlo wave-function simulations. If the additional pulse is a traveling wave, we find that the grating contrast measured as a function of $\ensuremath{\delta}T$ can be modeled by a quasiperiodic coherence function as in previous experiments that utilized atomic beams. In this work, we investigate the dependence of the photon scattering rate on the intensity and detuning of the traveling wave. We also study the effects of perturbing the interferometer with continuous-wave light and find that the dependence of the photon scattering rate on the intensity and detuning of the perturbing field is consistent with expectations.
We investigate the diffraction of a three-level atom from a "walking" light wave composed of counterpropagating traveling waves of different frequencies. The coupling of the two nondegenerate internal ground states by means of an off-resonant Raman transition resonantly couples the initial external momentum state to only one other momentum state. This happens even in the Raman-Nath regime, where the interaction time is short enough that momentum transfer is not constrained by phase-matching conditions. The final momentum state depends on the initial internal state of the atom and the relative directions of the two traveling waves. By using multiple diffraction regions, this process can be used to coherently split a beam of atoms into two beams that are widely separated in momentum space. This type of beam splitter would be useful in the building an atom interferometer.
We have observed both diffractive and diffusive regimes in the transfer of momentum to an atomic beam by a standing-wave radiation field. The momentum transfer was measured by passing a well-collimated beam of sodium atoms through a focused standing-wave laser waist. A narrow velocity distribution beam was obtained by utilizing a supersonic expansion and a two-state system was realized by optically pumping the beam prior to the interaction. The transverse momentum transferred to the atomic beam by the radiation field was measured by scanning a detector downstream from the interaction. The overall momentum resolution of the apparatus is less than the momentum of a single photon. The transition from diffractive to diffusive behavior is associated with an increase in the average number of spontaneous decays occurring during the interaction. In the diffractive regime, spontaneous decay is insignificant and momentum transfer proceeds by pairs of absorption/stimulated emission processes. This produces momentum exchange quantized in even multiples of photon momentum, the so-called Kapitza-Dirac effect; the deflection patterns show oscillatory structure. In the diffusive regime, spontaneous decay is important and causes fluctuations in the radiative forces. In addition, the recoil distribution associated with spontaneous decay results in a washing out of the diffraction peaks associated with stimulated processes, resulting in a smooth deflection pattern.
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.
The diffraction of a coherent, stationary, beam of atoms from a standing wave of light is considered. Particular attention is paid to long interaction times for which the motion of the atoms inside the light field must be taken into account. This is the regime of dynamical diffraction, and is treated within the framework of a set of differential difference equations due to Raman and Nath. The popular Raman-Nath approximation, in which the kinetic energy imparted to the atoms by the light wave is ignored, is no longer valid and the full equations must be solved. When the interaction between the atoms and the light is very weak then few beams are produced. To describe spontaneous emission from the atom one can invoke a complex potential as a model for dissipation. If the atom beam is obliquely incident one finds anomalously high transmission close to the Bragg angles which is the physical manifestation of degeneracies in non-Hermitian matrices. The classical limit is approached when the atom-light interaction is strong, producing many beams. The classical dynamics (geometrical rays) reveal that the farfield intensity pattern is dominated by caustics. These proliferate with increasing interaction distance. Two methods are presented for analytically treating the semiclassical limit of the wave mechanics. The first begins with W.K.B. solutions to the continuised Raman-Nath equations. Mapping onto parabolic cylinder functions removes the spurious divergences of the W.K.B. solutions, giving eigenvectors which are uniformly valid for all scattering angles and may be summed to give the wavefunction. The second method transforms the original W.K.B. eigensum, using the Poisson summation formula, giving a new sum, each term of which has classical significance. This method shows that wave theory decorates the classical caustics with an Airy function intensity profile, as predicted by catastrophe theory.
We have measured the diffraction of metastable helium atoms by a transmission grating with a period of 500 nm. The atomic beam is derived from a supersonic nozzle by adiabatic gas expansion with a velocity ratio v/Δv 20; with the nozzle cooled to liquid nitrogen temperature, the corresponding de Broglie wave length of the helium atoms is 1.08 Å. We have observed diffraction peaks up to the third order with a good signal-to-noise ratio. The position and the height of the different orders are in satisfactory agreement with the measured grating shape and the mean velocity in the atomic beam. As was pointed out previously, such transmission gratings offer one way to realize an atom-wave interferometer.1 In this context, our results demonstrate that an efficient diffraction can also be obtained with excited-state atoms: Here the use of metastable rare-gas atoms is of special interest because they are easy to handle and can be detected on almost zero background. As an alternative to the use of transmission gratings in matter-wave interferometry, we also discuss a simple double-slit arrangement that may provide another approach to the study of atomic interference phenomena.