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Physical Review A

Theoretical analysis of velocity-selective Raman transitions

Kathryn A. Moler, David S. Weiss, Mark A. Kasevich, Steven Chu

Published Jan 1, 1992• 222 citations
Publisher

Abstract

This paper analyzes the use of Raman transitions to select a narrow velocity distribution of atoms. We determine the evolution of the atomic wave function comprised of both the internal state and the external momentum of the atom in the presence of two counterpropagating laser beams. The effects of a single \ensuremath{\pi} pulse, two separated Ramsey \ensuremath{\pi}/2 pulses, and a sequence of four \ensuremath{\pi}/2 pulses are analyzed.

DOI
10.1103/physreva.45.342

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Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Jun 1, 1996•0 citations
This paper analyzes the use of Raman transitions to select a narrow velocity distribution of atoms. We determine the evolution of the atomic wave function comprised of both the internal state and the external momentum of the atom in the presence of two counterpropagating laser beams. The effects of a single \ensuremath{\pi} pulse, two separated Ramsey \ensuremath{\pi}/2 pulses, and a sequence of four \ensuremath{\pi}/2 pulses are analyzed.
It is known [1-3], that the samples of atoms with a velocity spread much lower than the recoil velocity uR= ħk/M (k is the wave number of exciting light field, M is the mass of atom) can be obtained by use of velocity selection with stimulated Raman transitions. A theoretical analysis of the velocity selection method is presented in [2,3]. So, it was shown in [2] that the formation of such narrow velocity structures is performed not only by the counterpropagating, but also by co-propagating light waves. This fact allows to form the two-dimensional velocity distribution of the widths δvx,y « uR by the velocity selection technique using laser configuration as in Fig. 1b.
The coherent control of atomic wave packets in multiple momentum dimensions is a central challenge in Raman atom optics and a key requirement for multidimensional atom interferometry. In this paper, a momentum-basis theoretical framework is developed for two-dimensional Raman interactions. We formulate the atom-laser interaction for two-dimensional Raman beams and obtain the effective two-level ground-state Hamiltonian after adiabatic elimination of the excited states. The resulted Hamiltonian is constructed on the reachable momentum-state lattice and includes AC Stark shifts, intra-dimensional Raman couplings, and cross-dimensional Raman coupling terms, thereby describing multidimensional Raman dynamics beyond a simple superposition of independent single-dimensional models. The framework is used to analyze the principles and operating conditions of two-dimensional atom interferometry. Cross-dimensional Raman coupling and sequential reverse Raman transitions are identified as the main mechanisms that redistribute atoms into non-target momentum states and reduce the contrast of atomic interferometer fringe. Experimentally, Ramsey fringes are observed in a cold-atom fountain interferometer, with a contrast of 14.8%14.8\%14.8% at an interrogation time of T=10 msT=10~{\rm ms}T=10 ms, in good agreement with the theoretical calculation. The conditions required for velocity-sensitive multidimensional atom interferometry are further clarified, including detuning control, velocity-class selection, and suppression of undesired inter-dimensional transitions. This work provides a theoretical and experimental basis for multidimensional Raman atom interferometry.
Sodium atoms prepared in hyperfine ground-state 11 > are driven to the other ground-state hyperfine level 12> when two laser beams nearly resonant with an optical transition have a frequency difference equal to the ground-state hyperfine splitting. When the two laser beams are counterpropagating, conservation of momentum between the atom and the light field requires that the atom acquire a velocity kick ~22 ħk/m during the 11> and 12> transition (~6 cm/sec in our experiment). When the lasers are detuned far from the optical transition, spontaneous emission from the intermediate optical level becomes negligible, and the atom behaves as a two-level system coupled to a resonant rf driving field. We have created an interferometer by applying a π/2-π-π/2 Raman pulse sequence: a first π/2 pulse coherently splits the atomic wave packet by putting it in a superposition of states 11> and 12>, a second π pulse occurring a time Δt later redirects each wave packet and a final π/2 pulse recombines the wave packets at time 2Δt. We have observed wave packet interference for wave packet separations of 2.4 mm and, by using the interferometer as an accelerometer, have measured the atom’s acceleration due to gravity to 3 parts in 106.
Velocity-selective Raman transitions are widely used in atom interferometers to prepare atomic ensembles with narrowly defined momentum distributions. However, differential light shifts between atomic energy levels generate velocity distributions that are correlated with the Raman beam intensity, and therefore with the position of the atoms within the laser beam. We show that these spatially inhomogeneous velocity distributions interact with detuning-dependent systematic effects in a Bragg diffraction-based simultaneous conjugate Ramsey-Bordé interferometer. These interactions can induce systematic phase shifts of order 10 milliradians in the interferometer phase. We further identify a "magic" detuning for velocity selection and show that operating at this detuning suppresses the systematic phase shift. Magic velocity selection eliminates systematic errors arising from correlations between atom velocity and position, facilitating high-resolution atom interferometry experiments targeting sub-part-per-billion accuracy.