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arXiv:2108.01437 · Physical Review A

Mirror-assisted backscattering interferometry to measure the first-order correlation function of the light emitted by quantum scatterers

Pablo Gabriel Santos Dias, Marcia Frómeta Fernández, P. H. N. Magnani, Klara Theophilo, Mathilde Hugbart, Ph. W. Courteille, R Teixeira

Published Nov 22, 2021• 0 citations
arXivHTMLPDF

Abstract

We present a method to obtain the first-order temporal correlation function, ${g}^{(1)}(\ensuremath{\tau})$, of the light scattered by an assembly of pointlike quantum scatterers, or equivalently its spectral power distribution. This method is based on the mirror-assisted backscattering interferometric setup. The contrast of its angular fringes was already linked to the convolution of ${g}^{(1)}(\ensuremath{\tau})$ for different Rabi frequencies taking into account the incoming spatial intensity profile of the probe beam, but we show here that by simply adding a half wave plate to the interferometer in a specific configuration, the fringe contrast becomes ${g}^{(1)}(\ensuremath{\tau})$ of the light scattered by atoms, which are now all subjected to the same laser intensity. This method has direct application to obtaining the saturated spectrum of quantum systems. We discuss some nontrivial aspects of this interferometric setup and propose an analogy with a double Mach-Zehnder interferometer.

DOI
10.1103/physreva.104.053716

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We present a method to obtain the first-order temporal correlation function, g(1)(\ensuremathτ){g}^{(1)}(\ensuremath{\tau})g(1)(\ensuremathτ), of the light scattered by an assembly of pointlike quantum scatterers, or equivalently its spectral power distribution. This method is based on the mirror-assisted backscattering interferometric setup. The contrast of its angular fringes was already linked to the convolution of g(1)(\ensuremathτ){g}^{(1)}(\ensuremath{\tau})g(1)(\ensuremathτ) for different Rabi frequencies taking into account the incoming spatial intensity profile of the probe beam, but we show here that by simply adding a half wave plate to the interferometer in a specific configuration, the fringe contrast becomes g(1)(\ensuremathτ){g}^{(1)}(\ensuremath{\tau})g(1)(\ensuremathτ) of the light scattered by atoms, which are now all subjected to the same laser intensity. This method has direct application to obtaining the saturated spectrum of quantum systems. We discuss some nontrivial aspects of this interferometric setup and propose an analogy with a double Mach-Zehnder interferometer.
In front of a mirror, the radiation of weakly driven large disordered clouds presents an interference fringe in the backward direction, on top of an incoherent background. Although strongly driven atoms usually present little coherent scattering, we show here that the mirror-assisted version can produce high contrast fringes, for arbitrarily high saturation parameters. The contrast of the fringes oscillates with the Rabi frequency of the atomic transition and the distance between the mirror and the atoms, due to the coherent interference between the carrier and the Mollow sidebands of the saturated resonant fluorescence spectrum emitted by the atoms. The setup thus represents a powerful platform to study the spectral properties of ensembles of correlated scatterers.
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 present the first calculation of coherent backscattering with inelastic scattering by saturated atoms. We consider the scattering of a quasi-monochromatic laser pulse by two distant atoms in free space. By restricting ourselves to scattering of two photons, we employ a perturbative approach, valid up to second order in the incident laser intensity. The backscattering enhancement factor is found to be smaller than two (after excluding single scattering), indicating a loss of coherence between the doubly scattered light emitted by both atoms. Since the undetected photon carries information about the path of the detected photon, the coherence loss can be explained by a which-path argument, in analogy with a double-slit experiment.
In this theoretical paper, we investigate coherence properties of the near-resonant light scattered by two atoms exposed to a strong monochromatic field. To properly incorporate saturation effects, we use a quantum Langevin approach. In contrast to the standard optical Bloch equations, this method naturally provides the inelastic spectrum of the radiated light induced by the quantum electromagnetic vacuum fluctuations. However, to get the right spectral properties of the scattered light, it is essential to correctly describe the statistical properties of these vacuum fluctuations. Because of the presence of the two atoms, these statistical properties are not Gaussian: (i) the spatial two-points correlation function displays a specklelike behavior and (ii) the three-points correlation function does not vanish. We also explain how to incorporate in a simple way propagation with a frequency-dependent scattering mean-free path, meaning that the two atoms are embedded in an average scattering dispersive medium. Finally we show that saturation-induced nonlinearities strongly modify the atomic scattering properties and, as a consequence, provide a source of decoherence in multiple scattering. This is exemplified by considering the coherent backscattering configuration where interference effects are blurred by this decoherence mechanism. This leads to a decrease of the so-called coherent backscattering enhancement factor.
The spatial coherence of an atomic wavepacket can be detected in scattered photons, even when the center-of-mass motion is in the quantum coherent superposition of two distant, nonoverlapping wavepackets. Spatial coherence manifests itself in the power spectrum of the emitted photons, whose spectral components can exhibit interference fringes as a function of the emission angle. The contrast and the phase of this interference pattern provide information about the quantum state of the center of mass of the scattering atom.
We present a calculation of coherent backscattering with inelastic scattering by saturated atoms. We consider the scattering of a quasimonochromatic laser pulse by two distant atoms in free space. By restricting ourselves to scattering of two photons, we employ a perturbative approach, valid up to second order in the incident laser intensity. The backscattering enhancement factor is found to be smaller than two (after excluding single scattering), indicating a loss of coherence between the doubly scattered light emitted by both atoms. Since the undetected photon carries information about the path of the detected photon, the coherence loss can be explained by a which-path argument, in analogy with a double-slit experiment.