In 1995, Chapman et al (1995 Phys. Rev. Lett. 75 2783) showed experimentally that the interference contrast in a three-grating atom interferometer does not vanish in the presence of scattering events with photons, as required by the complementarity principle. In this work, we present an analytical study of this experiment by determining the evolution of an atom's wave function along the three-grating Mach–Zehnder interferometer under the assumption that the atom is hit by a photon after passing through the first grating. The consideration of a transverse wave function in momentum representation is essential in this study. As is shown, the number of atoms transmitted through the third grating is given by a simple periodic function of the lateral shift along this grating, both in the absence and in the presence of photon scattering. Moreover, the relative contrast (laser on/laser off) is shown to be a simple analytical function of the ratio d p /λ i , where d p is the distance between atomic paths at the scattering locus and λ i the scattered photon wavelength. We argue that this dependence, being in agreement with experimental results, can be considered as showing compatibility between the wave and corpuscle properties of atoms.
In 1995, Chapman et al (1995 Phys. Rev. Lett. 75 2783) showed experimentally that the interference contrast in a three-grating atom interferometer does not vanish in the presence of scattering events with photons, as required by the complementarity principle. In this work, we present an analytical study of this experiment by determining the evolution of an atom's wave function along the three-grating Mach–Zehnder interferometer under the assumption that the atom is hit by a photon after passing through the first grating. The consideration of a transverse wave function in momentum representation is essential in this study. As is shown, the number of atoms transmitted through the third grating is given by a simple periodic function of the lateral shift along this grating, both in the absence and in the presence of photon scattering. Moreover, the relative contrast (laser on/laser off) is shown to be a simple analytical function of the ratio d p /λ i , where d p is the distance between atomic paths at the scattering locus and λ i the scattered photon wavelength. We argue that this dependence, being in agreement with experimental results, can be considered as showing compatibility between the wave and corpuscle properties of atoms.
Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied.It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase.We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event.This also explains the experimentally observed (Chapman et al 1995 Phys.Rev. Lett.75 2783) dependence of the visibility on the ratio d p /λ i = y 12 (2π/kdλ i ), where y 12 is the distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic centre-of-mass motion, d is the grating constant and λ i is the photon wavelength.Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near-field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of 'which-way' information for the interference visibility.
Here, interference visibility in a three-grating atom interferometer with presence of photon-atom scattering events is analyzed. The model considered is entirely based on the atom wave function and the effects caused on it by both scattering events and subsequent diffractions through the interferometer gratings. A functional dependence of the interference visibility on the probability distribution of transferred momentum (by the photons) to the atoms is thus found, which is used to interpret the available experimental data. Within this model there is no need, therefore, to appeal for concepts such as “which-way” information or entanglement to explain the losses, revivals and regains of quantum coherence in this type of experiments. Rather, visibility losses and revivals are explained in terms of the sudden change induced in the atomic wave function by the momentum transfer, while regains are directly related to the visibility functional dependence on the statistical distribution of transferred momentum of the sample of atoms selected after passing through the interferometer (before they are detected).
The coherence effects induced by external photons coupled to matter waves inside a Mach–Zehnder three-grating interferometer are analyzed. Alternatively to atom–photon entanglement scenarios, the model considered here only relies on the atomic wavefunction and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. Good quantitative agreement is found when comparing the results obtained from our model with the experimental data.
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=0 and t=T to diffract and recombine momentum states separated by $2\ensuremath{\hbar}k$ at t=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=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 present a three-path photon interferometer, theoretically investigate the behavior of the photon passing through it, and revisit the surprising experimental outcomes introduced by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)]. Our study shows that the ``discontinuous trajectory'' behavior of the photon results from the interference of the three propagation paths of the photon, which originate from the light source and end in the detector. If two of the three paths are adjusted in a destructive interference condition, there will be a zero probability domain in the overlap region of these two paths. However, these two paths can still individually interfere with the third path and contribute to the final output. In this condition, the discontinuous trajectory phenomenon appears. Our theory has a clear physical image and agrees with the experimental outcomes very well.
Abstract In this article we present a new representation-free formalism, which can significantly simplify the analysis of interferometers comprised of atoms moving in time-dependent linear potentials. We present a methodology for the construction of two pairs of time-dependent functions that, once determined, lead to two conditions for the closing of the interferometer, and determine the phase and the contrast of the resultant interference. Using this new formalism, we explore the dependency of the interferometer phase on the interferometer time T for different atom interferometers. By now, it is well established that light pulse atom interferometers of the type first demonstrated by Kasevich and Chu (1991 Phys. Rev. Lett. 67, 181–4; 1992 Appl. Phys. B 54, 321–32), henceforth referred to as Mach–Zehnder (MZ) atom interferometers, have a phase scaling as T 2. A few years ago, McDonald et al (2014 Europhys. Lett. 105, 63001) have experimentally demonstrated a novel type of atom interferometer, referred to as the continuous-acceleration bloch (CAB) interferometer, where the phase reveals a mixed scaling which is governed by a combination of T 2 and T 3. Moreover, we have recently proposed a different type of atom interferometer (Zimmermann et al 2017 Appl. Phys. B 123, 102), referred to as the T 3-interferometer, which has a pure T 3 scaling, as demonstrated theoretically. Finally, we conclude that the CAB interferometer can be shown to be a hybrid of the standard MZ interferometer and the T 3-interferometer.