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Annual Meeting Optical Society of America

Atomic scattering in quantum fields: standing wave versus traveling waves

P. Meystrel, Bruce W. Shore, Stig Stenholm

Published Jan 1, 1990• 0 citations
Publisher

Abstract

Atoms undergo two types of momentum changes as they pass across a near-resonant standing wave. First, their transverse momentum spreads. Second, if the atoms cross the field at an angle, they undergo Bragg scattering from the periodic structure provided by the wave. Classically, this behavior can be understood in terms of traveling waves: the atom catalyzes the transfer of momentum from one traveling wave to the other, thereby changing its own transverse momentum. In the quantum regime, however, there is an essential difference between scattering by two running waves and by a standing wave. With running waves, we can in principle know which of the two waves has exchanged a unit of momentum with the atom. In contrast, a standing wave is an inseparable quantum unit whose average momentum remains zero at all times. This unity is imposed by the fixed mirrors that establish the standing wave. These act as infinite sinks of momentum. Quantum mechanics forbids one even in principle to determine, via a field measurement from which traveling wave the atom picked up its momentum. To demonstrate this point, we discuss the diffraction and deflection of an atom in both a standing wave and a superposition of two counter-propagating running waves.

DOI
10.1364/oam.1990.fh6

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Atoms undergo two types of momentum changes as they pass across a near-resonant standing wave. First, their transverse momentum spreads. Second, if the atoms cross the field at an angle, they undergo Bragg scattering from the periodic structure provided by the wave. Classically, this behavior can be understood in terms of traveling waves: the atom catalyzes the transfer of momentum from one traveling wave to the other, thereby changing its own transverse momentum. In the quantum regime, however, there is an essential difference between scattering by two running waves and by a standing wave. With running waves, we can in principle know which of the two waves has exchanged a unit of momentum with the atom. In contrast, a standing wave is an inseparable quantum unit whose average momentum remains zero at all times. This unity is imposed by the fixed mirrors that establish the standing wave. These act as infinite sinks of momentum. Quantum mechanics forbids one even in principle to determine, via a field measurement from which traveling wave the atom picked up its momentum. To demonstrate this point, we discuss the diffraction and deflection of an atom in both a standing wave and a superposition of two counter-propagating running waves.
We compare the scattering of an atom by two different quantized standing-wave configurations. The first one is established in a cavity by a pair of fixed mirrors. The other consists of two independent counterpropagating traveling waves, as could occur in a ring configuration. We show that in the quantum regime (of small photon numbers) atoms are scattered differently by a true standing wave than by a superposition of two counterpropagating waves of equal amplitudes and opposite directions. This behavior is a manifestation of momentum conservation. In the case of traveling waves each wave depletes its momentum independently, whereas the standing wave that is fixed in space acts as a potentially infinite sink or source for momentum.
We study the diffraction of quantum-degenerate fermionic atoms off of quantized light fields in an optical cavity. We compare the case of a linear cavity with standing-wave modes to that of a ring cavity with two counterpropagating traveling wave modes. It is found that the dynamics of the atoms strongly depends on the quantization procedure for the cavity field. For standing waves, no correlations develop between the cavity field and the atoms. Consequently, standing-wave Fock states yield the same results as a classical standing wave field while coherent states give rise to a collapse and revivals in the scattering of the atoms. In contrast, for traveling waves the scattering results in quantum entanglement of the radiation field and the atoms. This leads to a collapse and revival of the scattering probability even for Fock states. The Pauli exclusion principle manifests itself as an additional dephasing of the scattering probability.
We discuss two possible processes that may lead to unidirectional momentum transfer to atoms from a near-resonant standing-wave light field. The first is Bragg scattering of the matter waves from the tilted light grating—this process leaves the atoms unexcited. The second is a multiphoton (Doppleron) process in which the atom, by sequential absorption/emission of photons from/into the two traveling-wave components of the standing wave (which appear at different frequencies owingto the motion of the atom in the field), can complete the energy resonance condition for excitation to its excited state. Detailed consideration of the inteferring process of spontaneous emission and experimental factors such as the interplay among interaction length, angular collimation of the standing wave, and transit-time frequency broadening of the light frequency show that the two processes are both potentially observable but under considerably different experimental conditions.
The diffraction of sodium atoms from a standing wave of near-resonant light is studied as a function of the atomic velocity component along the k vector of the wave. A simple theory is presented which quantitatively predicts the observed diffraction patterns and the decrease of the rms momentum transfer to the atoms with increasing velocity. This decrease results from the dephasing between the two counterpropagating traveling waves due to the first-order Doppler shift. In addition, these measurements have resolved the previous discrepancy between theory and experiment concerning the overall momentum transferred by a standing wave.
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.