Higher-order Intensity Correlations Research Articles

Anisotropic and heterogeneous dynamics in an aging colloidal gel.

We investigate the out-of-equilibrium dynamics of a colloidal gel obtained by quenching a suspension of soft polymer-coated gold nanoparticles close to and below its gelation point using X-ray Photon Correlation Spectroscopy (XPCS). A faster relaxation process emergent from the localized motions of the nanoparticles reveals a dynamically-arrested network at the nanoscale as a key signature of the gelation process. We find that the slower network dynamics is hyperdiffusive with a compressed exponential form, consistent with stress-driven relaxation processes. Specifically, we use direction-dependent correlation functions to characterize the anisotropy in dynamics. We show that the anisotropy is greater for the gel close to its gelation point than at lower temperatures, and the anisotropy decreases as the gel ages. We quantify the anisotropic dynamical heterogeneities emergent in such a stress-driven dynamical system using higher order intensity correlations, and demonstrate that the aging phenomenon contributes significantly to the properties evaluated by the fluctuations in the intensity correlations. Our results provide important insights into the structural origin of the emergent anisotropic and cooperative heterogeneous dynamics, and we discuss analogies with previous work on other soft disordered systems.

Directional Dicke Subradiance with Nonclassical and Classical Light Sources.

We investigate Dicke subradiance of N≥2 distant quantum sources in free space, i.e., the spatial emission patterns of spontaneously radiating noninteracting multilevel atoms or multiphoton sources, prepared in totally antisymmetric states. We find that the radiated intensity is marked by a full suppression of spontaneous emission in particular directions. In resemblance to the analogous, yet inverted, superradiant emission profiles of N distant two-level atoms prepared in symmetric Dicke states, we call the corresponding emission patterns directional Dicke subradiance. We further derive that higher-order intensity correlations of the light emitted by statistically independent thermal light sources display the same directional Dicke subradiant behavior and show that it stems from the same interference phenomenon as in the case of quantum sources. We finally present measurements of directional Dicke subradiance for N=2,…,5 distant thermal light sources corroborating the theoretical findings.

Precision estimation of source dimensions from higher-order intensity correlations

An important topic of interest in imaging is the construction of protocols that are not diffraction limited. This can be achieved in a variety of ways, including classical superresolution techniques or quantum entanglement-based protocols. Here, we consider superresolving imaging in the far field using higher-order intensity correlations. We show that third and fourth order correlations can improve upon the first and second order correlations that are traditionally used in classical optics and Hanbury Brown and Twiss type experiments. The improvement is achieved entirely by post-processing of the data. As a demonstrator, we simulate the far field intensity distribution of a circular aperture that emits thermal light and use maximum likelihood estimation to determine the radius of the aperture. We compare the achieved precision to the Cram\'er-Rao lower bound and find that the variance of measurements for the third and fourth order correlation functions are indeed closer to the Cram\'er-Rao bound than that of the second order correlation function. The method presented here is general, and can be used for all kinds of incoherent emitters, geometries, and types of noise.

Hanbury Brown–Twiss Interferometry at a Free-Electron Laser

We present measurements of second- and higher-order intensity correlation functions (so-called Hanbury Brown-Twiss experiment) performed at the free-electron laser (FEL) FLASH in the non-linear regime of its operation. We demonstrate the high transverse coherence properties of the FEL beam with a degree of transverse coherence of about 80% and degeneracy parameter of the order 10(9) that makes it similar to laser sources. Intensity correlation measurements in spatial and frequency domain gave an estimate of the FEL average pulse duration of 50 fs. Our measurements of the higher-order correlation functions indicate that FEL radiation obeys Gaussian statistics, which is characteristic to chaotic sources.

Localization of photon bunching with thermal light

We propose an experimental scheme in which two orthogonally polarized thermal light beams with antisymmetrical wavefronts are overlapped. The experimental results demonstrate that this setup can focus the beam in two-photon and multiphoton correlation measurements. The focused ``two-photon'' spot possesses subwavelength resolution, surpassing the classical diffraction limit. Since the experimental setup consists of only two right-angle-mirror devices without the help of lenses, the two-photon focusing effect does not apparently rely on the beam focusing. Physically, the phenomenon signifies that the photon bunching can be localized within a very small region through two-photon interference in contrast to the conventional Hanbury Brown\char21{}Twiss effect of thermal light. In the higher-order intensity correlation measurement, the multiphoton bunching can be limited within a very small central region while the background is greatly suppressed.

High-visibility, high-order lensless ghost imaging with thermal light

High-visibility Nth-order ghost imaging with thermal light has been realized by recording only the intensities in two optical paths in a lensless setup. It is shown that the visibility is dramatically enhanced as the order N increases, but longer integration times are required owing to the increased fluctuations of higher-order intensity correlation functions. It is also demonstrated that the required integration time for a good image depends on the partition ratio of the intensities on the two detectors and the complexity of the object.

High-visibility intensity interference and ghost imaging with pseudo-thermal light

We consider higher-order intensity correlations in thermal light and show that they can be used for observing high-visibility interference of the Hanbury Brown–Twiss-type as well as high-visibility ghost imaging. Experimental results are obtained for third- and fourth-order intensity interference, by processing images made with a digital photographic camera.

Measuring intensity correlations with a two-element superconducting nanowire single-photon detector

Second-order intensity correlation measurements were made using a two-element superconducting nanowire single photon detector (SNSPD) without the need for an optical beam splitter. This approach can be used to obtain a $50\text{\penalty1000-\hskip0pt}\mathrm{ps}$ full width at half maximum timing resolution over a wide range of visible and near-infrared wavelengths and can be extended to measure higher-order intensity correlations. Measurements of the second-order intensity correlation of a pulsed laser and an InGaAs quantum dot were made using both a two-element SNSPD and a conventional Hanbury Brown--Twiss interferometer to demonstrate the accuracy and advantages of the multielement SNSPD.

Maser Emission in Astrophysical Plasmas: 2003 Robert Ellery Lecture

AbstractThere are three distinct types of ‘coherent emission’ in astrophysical plasmas: plasma emission (e.g. in solar radio bursts), electron cyclotron maser emission (e.g. in Jupiter's radio bursts), and pulsar radio emission. The development and current status of our understanding of coherent emission is reviewed, concentrating on plasma emission and electron cyclotron maser emission for which there is direct information on the distributions of electrons that produce the radiation. A generic model for a coherent emission process involves a maser generating radiation in a natural mode of the ambient plasma, and operating near marginal stability. A specific coherent emission mechanism involves the form of free energy to drive the maser, a pump that provides the free energy, and the plasma instability that leads to wave growth. The nature of coherence and its measurement through higher order intensity correlations are discussed.

Quasi-elastic light scattering for intermittent dynamics

Dynamic light-scattering techniques provide noninvasive probes of diverse media such as colloidal suspensions, granular materials, and foams. Traditional analysis relies on the Gaussian properties of the scattering process found in most experimental situations and uses second-order intensity-correlation functions. This approach fails in the presence of, among other things, the collective intermittent dynamics found in systems such as granular materials. By extending the existing formalism and introducing higher-order intensity-correlation functions, we show how to detect and quantify the intrinsic dynamics and switching statistics of intermittent processes. We then explore two systems: (1) an auger-driven granular column for which the granular dynamics are controlled and the formalism is tested and (2) a granular heap whose dynamics are a priori unknown but may, now, be characterized.

Coulomb wave function corrections for n-particle Bose–Einstein correlations

The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is a solution of the n-body Coulomb Schrodinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose–Einstein correlation functions of similarly charged particles and remove a systematic error as big as 100% from higher-order multi-particle Bose–Einstein correlation functions.

Coulomb wave function corrections for

The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is solution of the n-body Coulomb Schr\"odinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose-Einstein correlation functions of similarly charged particles and remove a systematic error as big as 100% from higher-order multi-particle Bose-Einstein correlation functions.

Quantum jumps in a coherently driven Raman system

Early results of Agarwal and Jha [Z. Phys. B 35, 391 (1979)] are used to examine the question of quantum jumps in a Raman (\ensuremath{\Lambda}) system driven by two coherent fields. We discuss both short-time (${\ensuremath{\gamma}}_{1}$t\ensuremath{\lesssim}1) and long-time (${\ensuremath{\gamma}}_{2}$t\ensuremath{\approxeq}1) behavior of the intensity correlations assuming that the Stokes transition is very weak, ${\ensuremath{\gamma}}_{2}$\ensuremath{\ll}${\ensuremath{\gamma}}_{1}$. We calculate the counting statistics of the dark periods using the higher-order intensity correlations. The results differ from those obtained using arguments based on population trapping which predict only a very rare ``jump'' event. The intermittence in fluorescence produced by a coherently driven \ensuremath{\Lambda} system is interpreted in terms of an equivalent two-state Markov process.

Time factorization of the higher-order intensity correlation functions in the theory of resonance fluorescence

The intensity correlation functions $\mathrm{Tr}{\ensuremath{\rho}(0){s}^{+}(t){s}^{+}(t+{\ensuremath{\tau}}_{1})\ensuremath{\cdots}{s}^{+}(t+{\ensuremath{\Sigma}}_{i=1}^{n}{\ensuremath{\tau}}_{i}){s}^{\ensuremath{-}}(t+{\ensuremath{\Sigma}}_{i=1}^{n}{\ensuremath{\tau}}_{i})\ensuremath{\cdots}{s}^{\ensuremath{-}}(t+{\ensuremath{\tau}}_{1}){s}^{\ensuremath{-}}(t)}$ associated with a two-level atom undergoing Markovian dynamics [${s}^{\ifmmode\pm\else\textpm\fi{}}(t)$ being the spin-\textonehalf{} operators for the atom] are shown to factorize in the form $f(t){\ensuremath{\Pi}}_{i=1}^{n}g({\ensuremath{\tau}}_{i})$ with $f(t)$ [$g(t)$] giving the probability of finding the atom in the excited state when initially it is in the state $\ensuremath{\rho}(0)$ [ground state].

Effects of higher-order intensity correlations in photoelectron time-interval distributions

Series expansions of photoelectron time-interval distributions in terms of correlation and moment functions are used to investigate the effect of higher-order intensity correlations. Two cases are considered: light modulated by gaussian and by squared-gaussian noise. For gaussian modulated light fluctuations the use of correlation functions was preferred to the use of moment functions, because of better convergence of the series expansions. For light intensities modulated by squared-gaussian noise the series expansions may even diverge, depending on variance and correlation time of the light intensity fluctuations. In the domain of convergence first-, second- and third-order approximations are derived from the series expansions and it is shown that even at low mean photoelectron counting rate the third-order correlation function cannot be neglected. Theoretical expressions for the half-open time-interval distributions are experimentally verified. Light signals with the desired statistical character were obtained by modulation of the current of a light emitting diode with a gaussian or a squared-gaussian noise signal.

Third- and Higher-Order Intensity Correlation in Laser Light

Third- and Higher-Order Intensity Correlation in Laser Light