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arXiv:physics/9810028 · Physical Review A

Matter-wave interference using two-level atoms and resonant optical fields

B. Dubetsky, P. R. Berman

Published Mar 1, 1999• 8 citations
arXivHTMLPDF

Abstract

A theory of matter-wave interference is developed in which resonant, standing-wave optical fields interact with an ensemble of two-level atoms. If effects related to the recoil the atoms undergo on absorbing or emitting radiation are neglected, the total atomic density is spatially uniform. However, when recoil effects are included, spatial modulation of the atomic density can occur for times that are greater than or comparable to the inverse recoil frequency. In this regime, the atoms exhibit matter-wave interference that can be used as the basis of a matter-wave atom interferometer. Two specific atom-field geometries are considered, involving either one or two field-interaction zones. For each geometry, the recoil-induced spatial modulation of the total atomic density is calculated. In contrast to the normal Talbot and Talbot-Lau effects, the spatially modulated density is nota periodic function of time, owing to spontaneous emission; however, after a sufficiently long time, the contribution from spontaneous processes no longer plays a role and the periodicity is restored. With a suitable choice of observation time and field strengths, the spatially modulated atomic density serves as an indirect probe of the distribution of spontaneously emitted radiation.

DOI
10.1103/physreva.59.2269

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A theory of matter-wave interference is developed in which resonant, standing-wave optical fields interact with an ensemble of two-level atoms. If effects related to the recoil the atoms undergo on absorbing or emitting radiation are neglected, the total atomic density is spatially uniform. However, when recoil effects are included, spatial modulation of the atomic density can occur for times that are greater than or comparable to the inverse recoil frequency. In this regime, the atoms exhibit matter-wave interference that can be used as the basis of a matter-wave atom interferometer. Two specific atom-field geometries are considered, involving either one or two field-interaction zones. For each geometry, the recoil-induced spatial modulation of the total atomic density is calculated. In contrast to the normal Talbot and Talbot-Lau effects, the spatially modulated density is nota periodic function of time, owing to spontaneous emission; however, after a sufficiently long time, the contribution from spontaneous processes no longer plays a role and the periodicity is restored. With a suitable choice of observation time and field strengths, the spatially modulated atomic density serves as an indirect probe of the distribution of spontaneously emitted radiation.
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 consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.
The long range goal of this project was the creation of nanostructures using light fields to manipulate atoms. By passing an atomic beam through one or more standing wave light fields, it is possible to create modulations in the atomic density having periods which are a fraction of the period of the standing wave light fields. Patterns having periods as small as lambda/10 were observed using optical masks and clear evidence for matter-wave effects were established. Several theoretical methods for achieving sub-lambda matter wave patterns were developed, Moreover it was shown that it is possible to create optical lattices having reduced periodicity using Raman transitions in a novel atom-field geometry Experiments were carried out in both magneto-optical traps and atomic beams. In both experimental set-ups, pulsed standing wave optical fields were used to excite the atoms. At some later time the atoms were probed by a traveling wave field, revealing the spatial patterns that had evolved as a result of the atom-field interaction.
A theory of pump-probe spectroscopy is developed in which optical fields drive two-photon Raman transitions between ground states of an ensemble of three-level atoms. Effects related to the recoil the atoms undergo as a result of their interactions with the fields are fully accounted for in this theory. The linear absorption coefficient of a weak probe field in the presence of two pump fields of arbitrary strength is calculated. For subrecoil cooled atoms, the spectrum consists of eight absorption lines and eight emission lines. In the limit that ${\ensuremath{\chi}}_{1}\ensuremath{\ll}{\ensuremath{\chi}}_{2},$ where ${\ensuremath{\chi}}_{1}$ and ${\ensuremath{\chi}}_{2}$ are the Rabi frequencies of the two pump fields, one recovers the absorption spectrum for a probe field interacting with an effective two-level atom in the presence of a single pump field. However, when ${\ensuremath{\chi}}_{1}\ensuremath{\gtrsim}{\ensuremath{\chi}}_{2},$ new interference effects arise that allow one to selectively turn on and off some of these recoil-induced resonances.
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We discuss the concept of an all-optical and ionizing matter-wave interferometer in the time domain. The proposed setup aims at testing the wave nature of highly massive clusters and molecules, and it will enable new precision experiments with a broad class of atoms, using the same laser system. The propagating particles are illuminated by three pulses of a standing ultraviolet laser beam, which detaches an electron via efficient single-photon absorption. Optical gratings may have periods as small as 80 nm, leading to wide diffraction angles for cold atoms and to compact setups even for very massive clusters. Accounting for the coherent and the incoherent parts of the particle–light interaction, we show that the combined effect of phase and amplitude modulation of the matter waves gives rise to a Talbot–Lau-like interference effect with a characteristic dependence on the pulse delay time.