Mesoscopic Regime Research Articles

Mesoscopic ultrafast nonlinear optics—the emergence of multimode quantum non-Gaussian physics

Over the last few decades, nonlinear optics has become significantly more nonlinear, traversing nearly a billionfold improvement in energy efficiency, with ultrafast nonlinear nanophotonics in particular emerging as a frontier for combining both spatial and temporal engineering. At present, cutting-edge experiments in nonlinear nanophotonics place us just above the mesoscopic regime, where a few hundred photons suffice to trigger highly nonlinear dynamics. In contrast to classical or deep-quantum optics, the mesoscale is characterized by dynamical interactions between mean-field, Gaussian, and non-Gaussian quantum features, all within a close hierarchy of scales. When combined with the inherent multimode complexity of optical fields, such hybrid quantum-classical dynamics present theoretical, experimental, and engineering challenges to the contemporary framework of quantum optics. In this review, we highlight the unique physics that emerges in multimode nonlinear optics at the mesoscale and outline key principles for exploiting both classical and quantum features to engineer novel functionalities. We briefly survey the experimental landscape and draw attention to outstanding technical challenges in materials, dispersion engineering, and device design for accessing mesoscopic operation. Finally, we speculate on how these capabilities might usher in some new paradigms in quantum photonics, from quantum-augmented information processing to nonclassical-light-driven dynamics and phenomena to all-optical non-Gaussian measurement and sensing. The physics unlocked at the mesoscale present significant challenges and opportunities in theory and experiment alike, and this review is intended to serve as a guide to navigating this new frontier in ultrafast quantum nonlinear optics.

Orbital magnetization of a metal is not a bulk property in the mesoscopic regime

Orbital magnetization of a metal is not a bulk property in the mesoscopic regime

Temperature fluctuations in mesoscopic systems.

Temperature is a fundamental concept in thermodynamics. In macroscopic thermodynamics, systems possess their own intrinsic temperature which equals the reservoir temperature when they equilibrate. In stochastic thermodynamics for simple systems at the microscopic level, thermodynamic quantities other than temperature (a deterministic parameter of the reservoir) are stochastic. To bridge the disparity in the perspectives about temperature between the micro- and macroregimes, we assign a generic mesoscopic N-body system an intrinsic fluctuating temperature T in this work. We simplify the complicated dynamics of numerous particles to one stochastic differential equationwith respect to T, where the noise term accounts for finite-size effects arising from random energy transfer between the system and the reservoir. Our analysis reveals that these fluctuations make the extensive quantities (in the thermodynamic limit) deviate from being extensive. Moreover, we derive finite-size corrections, characterized by heat capacity of the system, to the Jarzynski equality. A possible violation of the principle of maximum work that scales with N^{-1} is also discussed. Additionally, we examine the impact of temperature fluctuations in a finite-size Carnot engine. We show that irreversible entropy production resulting from the temperature fluctuations of the working substance diminishes the average efficiency of the cycle as η_{C}-〈η〉∼N^{-1}, highlighting the unattainability of the Carnot efficiency η_{C} for mesoscopic heat engines even under the quasistatic limit. Our general framework paves the way for further exploration of nonequilibrium thermodynamics and the corresponding finite-size effects in a mesoscopic regime.

Monte Carlo modeling of temporal point spread functions and sensitivity functions for mesoscopic time-resolved fluorescence molecular tomography

The paper describes a TurbidMC code that implements a perturbative Monte Carlo method to model temporal point spread functions and sensitivity functions for time-resolved fluorescence molecular tomography (FMT). The code is aimed at working with a particular FMT method published earlier (Ref. [22]) which defines the specificity of sensitivity function calculation. The method solves the inverse problem first for a generalized fluorescence parameter distribution function and then calculates separate distributions for the fluorophore absorption coefficient and the fluorescence lifetime. The proper operation of the code was verified through a comparison between fluorescence temporal point spread functions from test calculations and data from experiments where a phantom with a fluorophore was scanned with a three-channel probe in the mesoscopic reflectance regime. An example is given on the reconstruction of fluorescence parameter distributions. It shows that the sensitivity functions are calculated correctly.

Cooling the optical-spin driven limit cycle oscillations of a levitated gyroscope

Birefringent microspheres, trapped in vacuum and set into rotation by circularly polarised light, demonstrate remarkably stable translational motion. This is in marked contrast to isotropic particles in similar conditions. Here we demonstrate that this stability is obtained because the fast rotation of these birefringent spheres reduces the effect of azimuthal spin forces created by the inhomogeneous optical spin of circularly polarised light. At reduced pressures, the unique profile of these rotationally averaged, effective azimuthal forces results in the formation of nano-scale limit cycles. We demonstrate feedback cooling of these non-equilibrium oscillators, resulting in effective temperatures on the order of a milliKelvin. The principles we elaborate here can inform the design of high-stability rotors carrying enhanced centripetal loads or result in more efficient cooling schemes for autonomous limit cycle oscillations. Ultimately, this latter development could provide experimental access to non-equilibrium quantum effects within the mesoscopic regime.

Exact one-particle density matrix for SU(N) fermionic matter-waves in the strong repulsive limit

We consider a gas of repulsive NN-component fermions confined in a ring-shaped potential, subjected to an effective magnetic field. For large repulsion strengths, we work out a Bethe ansatz scheme to compute the two-point correlation matrix and then the one-particle density matrix. Our results hold in the mesoscopic regime of finite but sufficiently large number of particles and system size that are not accessible by numerics. We access the momentum distribution of the system and analyse its specific dependence of interaction, magnetic field and number of components NN. In the context of cold atoms, the exact computation of the correlation matrix to determine the interference patterns that are produced by releasing cold atoms from ring traps is carried out.

Nonsteady dynamics at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model.

With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the transition fields as well as static and dynamic exponents are accurately determined based on the short-time dynamic scaling form. Different from the usual assumption, two distinguished growth processes of spatial correlation lengths for the velocity and height of the domain wall are found. Thus, the universality class of the depinning transition is established, which significantly differs from that of the quenched disorder equationbut agrees with that of the recent experiment as well as other simulations works. Under the influence of the mesoscopic time regime, the crossover from the second-order phase transition to the first-order one is confirmed in the weak-disorder regime, yielding an abnormal disorder-dependent nature of the criticality.

Experimental Validation of the Statistical Properties of Speckled-Speckle Fields in the Mesoscopic Intensity Regime

Several imaging techniques, such as ghost imaging, are based on the use of classical and quantum correlated light states. This fact has encouraged the search for new strategies to produce light states more correlated than the thermal states that are typically used. In this work, we produce and characterize classical states of light with “more than thermal” statistics. Such states are obtained by means of a sequence of two rotating ground-glass disks and by appropriately selecting the speckle field produced at the output of each disk. The experimental results are in excellent agreement with the developed theoretical model, suggesting the potential of this kind of light for imaging applications.

Functional central limit theorems for Wigner matrices

We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f(W). Going beyond the well-studied tracial mode, Trf(W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf(W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f(W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine the fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent multiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048).

Feasibility of a Novel Quantum Communication Protocol in Jerlov Type I Water.

Underwater communication based on the use of optical quantum resources has attracted a lot of attention in the last five years due to the potential advantages offered by quantum states of light. In this context, we propose to operate in the mesoscopic intensity regime, where the optical states are well populated and the employed detectors have photon-number resolution. By exploiting these features, we demonstrate that a novel communication protocol based on the experimental quantification of nonclassicality of mesoscopic twin-beam states can be used to transmit binary signals encoded in two single-mode pseudothermal states with different mean values through a Jerlov type I water channel. The experimental results are in perfect agreement with the developed theoretical model, and the feasibility of the protocol is also investigated as a function of the data samples corresponding to each one of the two signals. The good quality of the results encourages a more realistic implementation of the protocol, also exploring the maximum distance at which the quantum states remain nonclassical and thus can be still properly discriminated.

Resolution of 100 photons and quantum generation of unbiased random numbers

Macroscopic quantum phenomena, such as observed in superfluids and superconductors, have led to promising technological advancements and some of the most important tests of fundamental physics. At present, quantum detection of light is mostly relegated to the microscale, where avalanche photodiodes are very sensitive to distinguishing single-photon events from vacuum but cannot differentiate between larger photon-number events. Beyond this, the ability to perform measurements to resolve photon numbers is highly desirable for a variety of quantum information applications, including computation, sensing and cryptography. True photon-number resolving detectors do exist, but they are currently limited to the ability to resolve on the order of 10 photons, which is too small for several quantum-state generation methods based on heralded detection. Here we extend photon measurement into the mesoscopic regime by implementing a detection scheme based on multiplexing highly quantum-efficient transition-edge sensors to accurately resolve photon numbers between 0 and 100. We then demonstrate the use of our system by implementing a quantum random-number generator with no inherent bias. This method is based on sampling a coherent state in the photon-number basis and is robust against environmental noise, phase and amplitude fluctuations in the laser, loss and detector inefficiency as well as eavesdropping. Beyond true random-number generation, our detection scheme serves as a means to implement quantum measurement and engineering techniques valuable for photonic quantum information processing. A spatially multiplexed detection system of three transition-edge sensors is developed to resolve photon numbers up to 100 in a single laser pulse. Using the detector to measure parity of a coherent state allows for the extraction of quantum random numbers.

Reconstruction of fluorophore absorption and fluorescence lifetime using early photon mesoscopic fluorescence molecular tomography: a phantom study.

Fluorescence molecular lifetime tomography (FMLT) plays an increasingly important role in experimental oncology. The article presents and experimentally verifies an original method of mesoscopic time domain FMLT, based on an asymptotic approximation to the fluorescence source function, which is valid for early arriving photons. The aim was to justify the efficiency of the method by experimental scanning and reconstruction of a phantom with a fluorophore. The experimental facility included the TCSPC system, the pulsed supercontinuum Fianium laser, and a three-channel fiber probe. Phantom scanning was done in mesoscopic regime for three-dimensional (3D) reflectance geometry. The sensitivity functions were simulated with a Monte Carlo method. A compressed-sensing-like reconstruction algorithm was used to solve the inverse problem for the fluorescence parameter distribution function, which included the fluorophore absorption coefficient and fluorescence lifetime distributions. The distributions were separated directly in the time domain with the QR-factorization least square method. 3D tomograms of fluorescence parameters were obtained and analyzed using two strategies for the formation of measurement data arrays and sensitivity matrices. An algorithm is developed for the flexible choice of optimal strategy in view of attaining better reconstruction quality. Variants on how to improve the method are proposed, specifically, through stepped extraction and further use of a posteriori information about the object. Even if measurement data are limited, the proposed method is capable of giving adequate reconstructions but their quality depends on available a priori (or a posteriori) information. Further research aims to improve the method by implementing the variants proposed.

Testing de Broglie’s Double Solution in the Mesoscopic Regime

We present here solutions of a non-linear Schrödinger equation in presence of an arbitrary linear external potential. The non-linearity expresses a self-focusing interaction. These solutions are the product of the pilot wave with peaked solitons the velocity of which obeys the guidance equation derived by Louis de Broglie in 1926. The degree of validity of our approximations increases when the size of the soliton decreases and becomes negligible compared to the typical size over which the pilot wave varies. We discuss the possibility to reveal their existence by implementing a humpty-dumpty Stern-Gerlach interferometer in the mesoscopic regime.

Towards underwater quantum communication in the mesoscopic intensity regime.

The problem of secure underwater communication can take advantage of the exploitation of quantum resources and novel quantum technologies. At variance with the current experiments performed at the single photon level, here we propose a different scenario involving mesoscopic twin-beam states of light and two classes of commercial photon-number-resolving detectors. We prove that twin-beam states remain nonclassical even if the signal propagates in tubes filled with water, while the idler is transmitted in free space. We also demonstrate that from the study of the nonclassicality information about the loss and noise sources affecting the transmission channels can be successfully extracted.

Probing Majorana modes via local spin dynamics

We investigate Majorana modes in a quantum spin chain with bond-dependent exchange interactions by studying its dynamics. Specifically, we consider two-time correlations for the Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. Here, the model coincides with a phase boundary of two uncoupled instances of Kitaev's model for p-wave superconductors, together supporting a degenerate ground state characterized by multiple Majorana modes. In this regime, the real-time dynamics of local spins reveal a set of strong zero modes, corresponding to a set of protruding frequencies in the two-time correlation function. We derive perturbative interactions that map the KH spin chain onto the topological regime of Kitaev's fermionic model, thus opening up a bulk gap whilst retaining almost degenerate modes in the mesoscopic regime, i.e., for finite system sizes. This showcases the emergence of Majorana modes in a chain of effective dimers. Here, the binding energy within each unit cell competes with the inter-dimer coupling to generate a finite size energy gap, in analogy with local energy terms in the transverse-field Ising model. These modes give rise to long coherence times of local spins located at the system edges. By breaking the local symmetry in each dimer, one can also observe a second class of Majorana modes in terms of a beating frequency in the two-time correlations function of the edge spin. Furthermore, we develop a scenario for realizing these model predictions in ion-trap quantum simulators with collective addressing of the ions.

Scanning near-field optical spectroscopy and carrier transport based analysis in mesoscopic regions for two-dimensional semiconductors

The measurements of photoexcited transport in mesoscopic regimes reveal the states and properties of mesoscopic systems. In this study, we focused on direct measurements of electromagnetic energy transports in the mesoscopic regions and constructed a scanning tunnelling microscope-assisted multi-probe scanning near-field optical microscope spectroscopy system. After producing an emission energy map through a single-probe measurement, two-probe measurement enables us to observe and analyse carrier transport characteristics. It suggests that exciton generation and transport in the mesoscopic region of semiconductors with quantum structure changes, such as the bias of dopant, affect the excited carrier emission recombination process. The measured probability density of the carrier transported with quantum effects can be used for applications in natural intelligence research by combining it with the analysis using tournament structures. Our developed measurement and analysis methods are expected to clarify the details of carrier's behaviour in the mesoscopic region in various materials and lead to applications for novel optoelectronic devices.

Meniscus osculation and adsorption on geometrically structured walls.

We study the adsorption of simple fluids at smoothly structured, completely wet walls and show that a meniscus osculation transition occurs when the Laplace and geometrical radii of curvature of locally parabolic regions coincide. Macroscopically, the osculation transition is of fractional, 7/2, order and separates regimes in which the adsorption is microscopic, containing only a thin wetting layer, and mesoscopic, in which a meniscus exists. We develop a scaling theory for the rounding of the transition due to thin wetting layers and derive critical exponent relations that determine how the interfacial height scales with the geometrical radius of curvature. Connection with the general geometric construction proposed by Rascón and Parry is made. Our predictions are supported by a microscopic model density functional theory for drying at a sinusoidally shaped hard wall where we confirm the order of the transition and also an exact sum rule for the generalized contact theorem due to Upton. We show that as bulk coexistence is approached the adsorption isotherm separates into three regimes: A preosculation regime where it is microscopic, containing only a thin wetting layer; a mesoscopic regime, in which a meniscus sits within the troughs; and finally another microscopic regime where the liquid-gas interface unbinds from the crests of the substrate.

Onset of non-Gaussian quantum physics in pulsed squeezing with mesoscopic fields

We study the emergence of non-Gaussian quantum features in pulsed squeezed light generation with a mesoscopic number (i.e., dozens to hundreds) of pump photons. Due to the strong optical nonlinearities necessarily involved in this regime, squeezing occurs alongside significant pump depletion, compromising the predictions made by conventional semiclassical models for squeezing. Furthermore, nonlinear interactions among multiple frequency modes render the system dynamics exponentially intractable in naïve quantum models, requiring a more sophisticated modeling framework. To this end, we construct a nonlinear Gaussian approximation to the squeezing dynamics, defining a “Gaussian interaction frame” in which non-Gaussian quantum dynamics can be isolated and concisely described using a few dominant (i.e., principal) supermodes. Numerical simulations of our model reveal non-Gaussian distortions of squeezing in the mesoscopic regime, largely associated with signal-pump entanglement. We argue that state of the art in nonlinear nanophotonics is quickly approaching this regime, providing an all-optical platform for experimental studies of the semiclassical-to-quantum transition in a rich paradigm of coherent, multimode nonlinear dynamics. Mesoscopic pulsed squeezing, thus, provides an intriguing case study of the rapid rise in dynamic complexity associated with semiclassical-to-quantum crossover, which we view as a correlate of the emergence of new information processing capacities in the quantum regime.

Exploring black hole mechanics in cotangent bundle geometries

The classical and continuum limit of a quantum gravitational setting could lead, at mesoscopic regimes, to a very different notion of geometry with respect to the pseudo-Riemannian one of special and general relativity. A possible way to characterize this modified spacetime notion is by a momentum-dependent metric, in such a way that particles with different energies could probe different spacetimes. Indeed, doubly special relativity theories, deforming the special relativistic kinematics while maintaining a relativity principle, have been understood within a geometrical context, by considering a curved momentum space. The extension of these momentum spaces to curved spacetimes and its possible phenomenological implications have been recently investigated. Following this line of research, we address here the first two laws of black holes thermodynamics in the context of a cotangent bundle metric, depending on both momentum and spacetime coordinates, compatible with the relativistic deformed kinematics of doubly special relativity.

3D k-space reflectance fluorescence tomography via deep learning.

We report on the potential to perform image reconstruction in 3D k-space reflectance fluorescence tomography (FT) using deep learning (DL). Herein, we adopt a modified AUTOMAP architecture and develop a training methodology that leverages an open-source Monte-Carlo-based simulator to generate a large dataset. Using an enhanced EMNIST (EEMNIST) dataset as an embedded contrast function allows us to train the network efficiently. The optical strategy utilizes k-space illumination in a reflectance configuration to probe tissue in the mesoscopic regime with high sensitivity and resolution. The proposed DL model training and validation is performed with both in silico data and a phantom experiment. Overall, our results indicate that the approach can correctly reconstruct both single and multiple fluorescent embedding(s) in a 3D volume. Furthermore, the presented technique is shown to outperform the traditional approaches [least-squares (LSQ) and total-variation minimization (TVAL)], especially at higher depths. We, therefore, expect the proposed computational technique to have future implications in preclinical studies.