Photon correlations and cross-correlations of light scattered by a regular structure of strongly driven atoms are investigated. At strong driving, the scattered light separates into distinct spectral bands, such that each band can be treated as independent, thus extending the set of observables. We focus on second-order intensity-intensity correlation functions in two- and multi-atom systems. We demonstrate that for a single two-photon detector as, e.g., in lithography, increasing the driving field intensity leads to an increased spatial resolution of the second-order two-atom interference pattern. We show that the cross-correlations between photons emitted in the spectral sidebands violate Cauchy-Schwartz inequalities, and that their emission ordering cannot be predicted. Finally, the results are generalized for multi-particle structures, where we find results different from those in a Dicke-type sample.
We calculate the intensity-field correlations in the light scattered by N cold atoms driven by a quasi-resonant laser field. Fundamental differences occur if the atomic state is an entangled single-excitation state or a coherent factorized state. We provide analytic expressions for the two-time field and intensity correlation functions for the timed Dicke state and the quasi-Bloch state. The comparison with multi-atom simulations shows good agreement between numerical and analytic solutions.
In the context of the quantum-mechanical description of single-molecule surface-enhanced Raman scattering, intensity-field correlation measurements of photons emitted from a plasmonic cavity are explored, theoretically, using the technique of conditional homodyne detection. The inelastic interplay between plasmons and vibrations of a diatomic molecule placed inside the cavity can be manifested in phase-dependent third-order fluctuations of the light recorded by the aforesaid technique, allowing us to reveal signatures of non-classicality (indicatives of squeezing) of the outgoing Raman photons…
The interplay between the superradiant emission of a cloud of cold two-level atoms and the radiation pressure force is discussed. Using a microscopic model of coupled atomic dipoles driven by an external laser, the radiation field and the average radiation pressure force are derived. A relation between the far-field scattered intensity and the force is derived, using the optical theorem. Finally, the scaling of the sample scattering cross section with the parameters of the system is studied.
We predict a new spatial quantum correlation in light propagating through a multiple scattering random medium. The correlation depends on the quantum state of the light illuminating the medium, is infinite range, and dominates over classical mesoscopic intensity correlations. The spatial quantum correlation is revealed in the quantum fluctuations of the total transmission or reflection through the sample and should be readily observable experimentally.
We study theoretically how multiple scattering of light in a disordered medium can spontaneously generate quantum correlations. In particular we focus on the case where the input state is Gaussian and characterize the correlations between two arbitrary output modes. As there is not a single all-inclusive measure of correlation, we characterise the output correlations with three measures: intensity fluctuations, entanglement, and quantum discord. We found that, while a single mode coherent state input can not produce quantum correlations, any other Gaussian input will produce them in one form o…
In this paper we show that the scattered field of a bichromatically driven V-type three-level atom exhibit asymmetry and large violation of classical bounds in amplitude-intensity correlations. These features result from the noncommutativity of amplitude and intensity field operators, and the strong non-Gaussian fluctuations in this system. The amplitude-intensity correlations of resonance fluorescence, with its large third-order fluctuations, describe the nonclassical features of the emitted field more accurately than the second-order measure related to squeezing. Spectra and variances of the…
An explicit expression is given for the correlation function of blinking systems, i.e. systems exhibiting light and dark periods in their fluorescence. We show through the example of terrylene in a crystalline host that it is possible to determine by means of this explicit expression photo-physical parameters, like Einstein coefficients and the mean light and dark periods by a simple fit. In addition we obtain further parameters like the frequency of the various intensity periods and the probability density of photons scattered off the host crystal. It turns out that this approach is simpler a…
We propose a method for measuring the temperature of fermionic atoms in an optical lattice potential from the intensity of the scattered light in the far-field diffraction pattern. We consider a single-component gas in a tightly-confined two-dimensional lattice, illuminated by far off-resonant light driving a cycling transition. Our calculations show that thermal correlations of the fermionic atoms generate fluctuations in the intensity of the diffraction pattern of light scattered from the atomic lattice array and that this signal can be accurately detected above the shot noise using a lens t…
The advent of accelerator-driven free-electron lasers (FEL) has opened new avenues for high-resolution structure determination via diffraction methods that go far beyond conventional x-ray crystallography methods. These techniques rely on coherent scattering processes that require the maintenance of first-order coherence of the radiation field throughout the imaging procedure. Here we show that higher-order degrees of coherence, displayed in the intensity correlations of incoherently scattered x-rays from an FEL, can be used to image two-dimensional objects with a spatial resolution close to o…
When a pump beam is propagating through a silicon nanophotonic waveguide, a very small fraction of the light is scattered to other frequencies. At very low intensity, the amount of scattered light is proportional to the power of the pump beam. We show that the scattering intensity increases linearly within the temperature range 300-575 K and that the photon flux decreases as the inverse of the frequency detuning ν over the investigated bandwidth 0.4 THz < |ν| < 2.5 THz. The simplest interpretation of these observations is that the pump beam is scattered on a 1 dimensional thermal bath of excit…
We observe interference in the light scattered from trapped $^{40}$Ca$^+$ ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three and four ions in a harmonic trap. Control of the trapping potential allows…
We present an experimental study of a four beam optical lattice using the light scattered by the atoms in the lattice. We use both intensity correlations and observations of the transient behavior of the scattering when the lattice is suddenly switched on. We compare results for 3 different configurations of the optical lattice. We create situations in which the Lamb-Dicke effect is negligible and show that, in contrast to what has been stated in some of the literature, the damping rate of the 'coherent' atomic oscillations can be much smaller than the inelastic photon scattering rate.
In a recent Letter (Phys. Rev. Lett. \textbf{98}, 083601 (2007), arXiv:cond-mat/0610804), O. Assaf and E. Akkermans claim that the angular correlations of the light intensity scattered by a cloud of cold atoms with internal degeneracy (Zeeman sublevels) of the ground state overcome the usual Rayleigh law. More precisely, they found that they become exponentially large with the size of the sample. In what follows, we will explain why their results are wrong and, in contrary, why the internal degeneracy leads to lower intensity correlations.
Established x-ray diffraction methods allow for high-resolution structure determination of crystals, crystallized protein structures or even single molecules. While these techniques rely on coherent scattering, incoherent processes like Compton scattering or fluorescence emission -- often the predominant scattering mechanisms -- are generally considered detrimental for imaging applications. Here we show that intensity correlations of incoherently scattered x-ray radiation can be used to image the full 3D structure of the scattering atoms with significantly higher resolution compared to convent…
We report on theoretical and numerical study of propagation of atomic beams crossing a detuned standing-wave laser beam in the geometric optics limit. The interplay between external and internal atomic degrees of freedom is used to manipulate the atomic motion along the optical axis by light. By adjusting the atom-laser detuning, we demonstrate how to focus, split and scatter atomic beams in a real experiment. The novel effect of chaotic scattering of atoms at a regular near-resonant standing wave is found numerically and explained qualitatively. Some applications of the effects found are disc…
Collective off resonant scattering of coherent light by a cold gas induces long-range interactions via interference of light scattered by different particles. In a 1D configuration these interactions grow particularly strong for particles trapped along an optical nanofiber. We show that there exists a threshold pump laser intensity, above which the gas can be found in a crystalline, selfsustained order. In the nonabsorbing regime we determine the critical condition for the onset of order as well as the forms of particle density and scattered field patterns along the fiber above threshold. Surp…
We present a new method to obtain the first-order temporal correlation function, $g^{(1)} (τ)$, of the light scattered by an assembly of point-like quantum scatterers, or equivalently its spectral power distribution. This new method is based on the mirror-assisted backscattering interferometric setup. The contrast of its angular fringes was already linked in the past to the convolution of $g^{(1)} (τ)$ 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 waveplate to the interferometer in a sp…
A cloud of cold N two-level atoms driven by a resonant laser beam shows cooperative effects both in the scattered radiation field and in the radiation pressure force acting on the cloud center-of-mass. The induced dipoles synchronize and the scattered light presents superradiant and/or subradiant features. We present a quantum description of the process in terms of a master equation for the atomic density matrix in the scalar, Born-Markov approximations, reduced to the single-excitation limit. From a perturbative approach for weak incident field, we derive from the master equation the effectiv…
We report a combined experimental and theoretical simulation of multiply scattered light dynamics in an ultracold gas of 85Rb atoms. Measurements of the spectral dependence of the time-decay of the scattered light intensity, following pulsed excitation with near resonance radiation, reveals that the decay for long times is nearly exponential, with a decay constant that is largely independent of detuning from resonance. Monte Carlo simulations of the multiple scattering process show that, for large detunings, near resonance scattering of Fourier components of the excitation pulse plays a signif…
We show how to calculate the first- and second-order statistics of the scattered fields for an arbitrary intensity coherent state light field interacting with a two-level system in a waveguide geometry. Specifically, we calculate the resonance fluorescence from the qubit, using input-output formalism. We derive the transmission and reflection coefficients, and illustrate the bunching and anti-bunching of light that is scattered in the forward and backward directions, respectively. Our results agree with previous calculations on one- and two-photon scattering as well as those that are based on …
We analyze the light scattered by a single InAs quantum dot interacting with a resonant continuous-wave laser. High resolution spectra reveal clear distinctions between coherent and incoherent scattering, with the laser intensity spanning over four orders of magnitude. We find that the fraction of coherently scattered photons can approach unity under sufficiently weak or detuned excitation, ruling out pure dephasing as a relevant decoherence mechanism. We show how spectral diffusion shapes spectra, correlation functions, and phase-coherence, concealing the ideal radiatively-broadened two-level…
We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without an optical access to a single site) and pair …
We theoretically study the propagation of light through a cold atomic medium, where the effects of motion, laser intensity, atomic density, and polarization can all modify the properties of the scattered light. We present two different microscopic models: the "coherent dipole model" and the "random walk model", both suitable for modeling recent experimental work done in large atomic arrays in the low light intensity regime. We use them to compute relevant observables such as the linewidth, peak intensity and line center of the emitted light. We further develop generalized models that explicitl…
