Coherent light traversing disordered media usually attains a random field both in amplitude and phase with independent Gaussian statistics and results in thermal light (associated with Bose-Einstein photon-number statistics) upon ensemble averaging. This is expected according to the central limit theorem, which dictates the addition of a large number of independent random variables leads to a normal (Gaussian) distribution. Here, we show that certain network topologies that light travels within preclude the central limit theorem and result in non-Gaussian statistics. We realize such networks in the form of evanescently-coupled waveguide arrays (photonic lattices) and obtain the photon statistics at the output by time gating and averaging over multiple realizations of disordered photonic lattices. The effect of lattice topology, however, only exists when the photonic lattice is endowed with chiral-symmetric eigenmode pairs a disorder-immune symmetry where the eigenmodes appear in pairs with oppositely signed eigenvalues and the coherent input field satisfies certain conditions. We specifically examine one-dimensional arrays of randomly coupled identical waveguides (off-diagonal disorder) arranged on linear and ring topologies. The emerging field exhibits super-thermal statistics (associated with modified Bose-Einstein photon-number statistics) only for ring lattices with even parity and linear lattices (independent of its parity), whereas input coherent fields traversing ring lattices with odd parity attain sub-thermal statistics. By controlling the relative phase of a coherent input field exciting two neighboring lattice sites, we also demonstrate a deterministic tuning of photon-number statistics, namely photon bunching, while maintaining the mean photon number fixed.
Coherent light traversing disordered media usually attains a random field both in amplitude and phase with independent Gaussian statistics and results in thermal light (associated with Bose-Einstein photon-number statistics) upon ensemble averaging. This is expected according to the central limit theorem, which dictates the addition of a large number of independent random variables leads to a normal (Gaussian) distribution. Here, we show that certain network topologies that light travels within preclude the central limit theorem and result in non-Gaussian statistics. We realize such networks in the form of evanescently-coupled waveguide arrays (photonic lattices) and obtain the photon statistics at the output by time gating and averaging over multiple realizations of disordered photonic lattices. The effect of lattice topology, however, only exists when the photonic lattice is endowed with chiral-symmetric eigenmode pairs a disorder-immune symmetry where the eigenmodes appear in pairs with oppositely signed eigenvalues and the coherent input field satisfies certain conditions. We specifically examine one-dimensional arrays of randomly coupled identical waveguides (off-diagonal disorder) arranged on linear and ring topologies. The emerging field exhibits super-thermal statistics (associated with modified Bose-Einstein photon-number statistics) only for ring lattices with even parity and linear lattices (independent of its parity), whereas input coherent fields traversing ring lattices with odd parity attain sub-thermal statistics. By controlling the relative phase of a coherent input field exciting two neighboring lattice sites, we also demonstrate a deterministic tuning of photon-number statistics, namely photon bunching, while maintaining the mean photon number fixed.
We demonstrate deterministic control over the photon-number distribution by interfering two coherent beams within a disordered photonic lattice. By sweeping a relative phase between two equal-amplitude coherent fields with Poissonian statistics that excite adjacent sites in a lattice endowed with disorder-immune chiral symmetry, we measure an output photon-number distribution that changes periodically between super-thermal and sub-thermal photon statistics upon ensemble averaging. Thus, the photon-bunching level is controlled interferometrically at a fixed mean photon-number by gradually activating the excitation symmetry of the chiral-mode pairs with structured coherent illumination and without modifying the disorder level of the random system itself.
We report measurements of Hanbury Brown and Twiss correlation of coherent light transmitted through disordered one-dimensional photonic lattices. Although such a lattice exhibits transverse Anderson localization when a single input site is excited, uniform excitation precludes its observation. By examining the Hanbury Brown--Twiss correlation for a uniformly excited disordered lattice, we observe intensity anticorrelations associated with photon antibunching---a signature of non-Gaussian statistics. Although the measured average intensity distribution is uniform, transverse Anderson localization nevertheless underlies the observed anticorrelation.
Waveguide quantum electrodynamics (WQED) offers a powerful framework for controlling light-matter interactions and realizing collective phenomena such as super- and subradiance. In general waveguide settings, the quantum dynamics spans the full Hilbert space, rendering exact theoretical treatments exponentially difficult and currently out of reach, and only a few models have exact, analytical solutions. Motivated by recent experiments, we treat the thermodynamic limit of the number of atoms, N→∞, while the homogeneous atom-waveguide coupling β→0 keeping the optical depth 4Nβ fixed. In this limit, a second order mean field method is exact, giving analytical solutions for the statistics of the photons emitted in the waveguide both for chiral and symmetric configurations starting from full inversion. As N→∞, the emission in freespace approaches that of an independent ensemble. However, until a special time, ≈1.59× the lifetime of a single-atom, we show an exponentially enhanced superradiance in the waveguide as the optical depth increases. After the special time, the emission into the waveguide exhibits subradiance. We also show that the initial shot-to-shot fluctuations in the rate of emission into the waveguide diminish in a chiral system and vanish in a symmetric system as N approaches ∞. Additionally, the equal-time second-order correlation becomes trivial, showing that finite-size effects are essential to observe the emergence of second-order coherence. Finally, going beyond the thermodynamic limit requires higher order mean field methods. Our results illustrate finite- and infinite-body collective effects in symmetric and symmetry-lacking systems.
We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs. The propagation of a classical single walker on a random graph is an important field in statistics and can be applied on many domains in nature reaching from a foraging animals over Brownian molecular motion towards the evolution of lead changes in competitive team sports. Its quantum mechanical counterpart, the Quantum Walk (QW), features genuine quantum objects to walk on a random graph and hence, leading to non-classical quantum interference, in particular when considering two or more walkers. Their great potential lies i.a. in their ability to exponentially speed up a multitude of algorithms, as for instance the data bank search algorithm from L. Grover. In this regard, photonic lattices of evanescently coupled waveguides represent an ideal platform to study QW dynamics, since they feature advantages in stability, robustness and miniaturization. Our waveguide lattices were fabricated by means the direct laser inscription technique. In doing so, three dimensional waveguide geometries are realizable, enabling the implementation of various QW graphs. Along these lines, we study QWs of entangled photon pairs in disordered lattices. There we observe Anderson co-localization, meaning that neither the individual photons nor the pair localizes, rather their distance does. It turns out that both photons tend to bunch as they will be found together in the same lattice site, implying that their original correlation remains while performing a QW in a disordered lattice. Further, we investigate QWs of non-local two-photon EPR-states in Bloch-lattices. The experimental results reveal the strong dependence of the correlation output statistics (bosonic-, anyonicor fermionic-like) on the input states' symmetry. Finally, the discrete fractional Fourier transform of quantum states is realized through a discrete QW lattice. The results demonstrate the enormous potential of waveguide lattices in the field of quantum photonics and give rise to further investigations like the Fourier suppression law.
Photonic lattices consisting of arrays of evanescently coupled waveguides fabricated with precisely controlled parameters have enabled the study of discrete optical phenomena, both classical and quantum, and the simulation of other physical phenomena governed by the same dynamics. In this dissertation, I have experimentally demonstrated transverse Anderson localization of classical light in arrays with off-diagonal coupling disorder and investigated theoretically and experimentally the propagation of entangled photon pairs through such disordered systems. I discovered a new phenomenon, Anderson co-localization, in which a spatially entangled photon pair in a correlated transversally extended state localizes in the correlation space, though neither photon localizes on its own. When the photons of a pair are in an anti-correlated state, they maintain their anti-correlation upon transmission through the disordered lattice, exhibiting Anderson anti-localization. These states were generated by use of parametric down conversion in a nonlinear crystal. The transition between the correlated and anti-correlated states was also explored by using a lens system in a configuration intermediate between imaging and Fourier transforming. In the course of this research, I discovered a curious aspect of light transmission through such disordered discrete lattices. An excitation wave of a single spatial frequency (transverse momentum) is transmitted through the system and is accompanied by another wave with the same spatial frequency but opposite sign, indicating some form of internal reflection facilitated by the disordered structure.
A cluster of recent results across quantum optics, photonics, and atom-photon interaction suggests a unifying thesis: the **photon-number statistics of the driving or probe field** — whether thermal, coherent, squeezed, or manifestly non-Gaussian — function as an active control degree of freedom that determines the character of the quantum state produced, the fidelity of a light-matter interface, and the precision ceiling of a sensing protocol, rather than merely setting a noise floor to be minimized. We synthesize five specific findings to argue this point. First, bright squeezed vacuum (BSV) light enables photon-subtraction-like operations at high intensity via above-threshold ionization, generating large-amplitude optical Schrödinger cat states whose non-Gaussian character is tunable through the detected photoelectron momentum [corpus:arxiv:2605.31160]. Second, the same BSV resource, combined with single-shot quadrature measurement, heralds macroscopic quantum superpositions in matter on ultrafast timescales, with the squeezing amplitude directly controlling the preparation speed of zero-eigenvalue Dicke states [corpus:arxiv:2605.30224]. Third, chiral light-matter coupling in slow-light photonic-crystal waveguides is not fixed by geometry alone but can be electrically inverted through the quantum-confined Stark effect, demonstrating that the local optical chirality — a mode-structure property — acts as a tunable interface parameter [corpus:arxiv:2605.30047]. Fourth, superradiant intensity correlations of order *m* ≥ 2 from *N* thermal light sources provide a Cramér–Rao bound improvement scaling as 1/*N* relative to conventional LIDAR, showing that photon-bunching statistics encode metrological information inaccessible to first-order intensity measurements [corpus:arxiv:2605.28378]. Fifth, spin noise spectroscopy reveals a quadratic density dependence of spin noise variance in warm rubidium vapor that is attributable to resonant dipole-dipole interactions, and can be quenched by suppressing the residual optical excitation that mediates those correlations [corpus:arxiv:2605.31262]. Together these results support the hypothesis that photon statistics — Gaussian or non-Gaussian, first-order or higher-order, classical or quantum — constitute a primary design variable for quantum state engineering, chiral interfaces, and precision metrology. Falsification paths for each sub-claim are identified throughout. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.28378, 2605.30047, 2605.30224, 2605.31160, 2605.31262, 2605.31442