Third-order Correlation Research Articles

Remotely preparing optical Schrödinger cat states via homodyne detection in nondegenerate triple-photon spontaneous downconversion

Optical downconversion is a key resource for generating nonclassical states. Very recently, direct nondegenerate triple-photon spontaneous downconversion (NTPSD) with bright photon triplets and strong third-order correlations has been demonstrated in a superconducting device (2020 Phys. Rev. X 10 011011). Besides, linear and nonlinear tripartite entanglement in this process have also been predicted (2018 Phys. Rev. Lett. 120 043601; 2020 Phys. Rev. Lett. 125 020502). In this paper, we consider the generation of nonclassical optical quantum superpositions and investigate nonlinear quantum steering effects in NTPSD. We find that large-size Schrödinger cat states of one downconverted mode can be achieved when the other two modes are subjected to homodyne detection. Also, a two-photon Bell entangled state can be generated when only one mode is homodyned. We further reveal that such ability of remote state steering originates from nonlinear quantum steerable correlations among the triplets. This is specifically embodied by the seeming violation of the Heisenberg uncertainty relation for the inferred variances of two noncommutating higher-order quadratures of downconverted modes, based on the outcomes of homodyne detection on the other mode, i.e., nonlinear quantum steering, compared to original Einstein–Podolsky–Rosen steering. Our results demonstrate non-Gaussian nonclassical features in NTPSD and would be useful for the fundamental tests of quantum physics and implementations of optical quantum technologies.

Two-Phonon Blockade in Quadratically Coupled Optomechanical Systems

We propose a scheme to realize the two-phonon blockade effect in a quadratically coupled optomechanical system. We consider the case that the optical cavity is simultaneously driven by a strong pumping field and a weak driving field. By strongly driving the optical cavity, the nonlinear interaction between the optical mode and the mechanical resonator can be significantly enhanced and an effective second-order nonlinearity between photons and phonons is induced. Based on this effectively strong nonlinearity, the two-phonon blockade effect can be achieved when a weak driving field is applied into the optical cavity. By contrast, we study the case of weakly driving the mechanical resonator. In this case, the single-phonon blockade is generated, while the two-phonon blockade cannot be observed. By numerically calculating the second-order and third-order correlation function, we investigate the statistical characteristics of phonons. In addition, we also study the influence of the thermal noise on the achieved two-phonon blockade effect. Our work provides an alternative approach for implementing multiphonon blockade and has potential applications in quantum information processing.

An Analysis of Transient Response Moments of a Linear System Subjected to Non-Gaussian Random Excitation Using Higher-Order Autocorrelation Functions of Excitation

Abstract We present the analytical solutions of the second-, third-, and fourth-order response moments of a single-degree-of-freedom linear system subjected to a class of non-Gaussian random excitation. The non-Gaussian excitation is a zero-mean stationary stochastic process prescribed by an arbitrary probability density and a power spectrum whose peak is located at zero frequency. The excitation is described by an Itô stochastic differential equation in which the drift and diffusion coefficients are determined from the probability density and spectral density of the excitation. In order to obtain the analytical solutions of the response moments, first, we derive the third- and fourth-order autocorrelation functions of the non-Gaussian excitation using its Markov and detailed balance properties. The third-order correlation function is given by the same expression regardless of the difference in the probability density function of the excitation. On the other hand, the fourth-order correlation function is derived under the assumption that the excitation probability density belongs to the Pearson distribution family, which is one of the widest classes of probability distributions. Then, combining the autocorrelation functions of the excitation and the convolution representation of the response, we obtain the exact solutions of the response moments, and it is shown what kind of components the response moments are composed of. Finally, we investigate the dominant time-varying components of the response moments for several different excitation bandwidths.

Self-Preservation of Turbulence Statistics in the Wall-Wake Flow of a Bed-Mounted Horizontal Pipe

This research article analyzed the self-preserving behaviour of wall-wake region of a circular pipe mounted horizontally over a flat rigid sand bed in a shallow flow in terms of mean velocity, RSS, and turbulence intensities. The study aims to investigate self-preservation using appropriate length and velocity scales.in addition to that wall-normal distributions of the third-order correlations along the streamwise direction in the wake region are analyzed. An ADV probe was used to record the three-dimensional instantaneous velocities for four different hydraulic and physical conditions corresponding to four cylinder Reynolds numbers. The results revealed that the streamwise velocity deficits, RSS deficits, and turbulence intensities deficits distributions displayed good collapse on a narrow band when they were non-dimensionalized by their respective maximum deficits. The wall-normal distance was non-dimensionalized by the half velocity profile width for velocity distributions, while the half RSS profile width was used in the case of the RSS deficits and turbulence intensities deficits distributions. The results indicate the self-preserving nature of streamwise velocity, RSS, and turbulence intensities in the wall-wake region of the pipe. The third-order correlations distributions indicate that sweep is the dominant bursting event in the near-bed zone. At the same time, ejection is the dominant bursting event in the region above the cylinder height.

Improving few-photon optomechanical effects with coherent feedback.

Few-photon effects such as photon blockade and tunneling have potential applications in modern quantum technology. To enhance the few-photon effects in an optomechanical system, we introduce a coherent feedback loop to cavity mode theoretically. By studying the second-order correlation function, we show that the photon blockade effect can be improved with feedback. Under appropriate parameters, the photon blockade effect exists even when cavity decay rate is larger than the single-photon optomechanical coupling coefficient, which may reduce the difficulty of realizing single-photon source in experiments. Through further study of the third-order correlation function, we show that the tunneling effect can also be enhanced by feedback. In addition, we discuss the application of feedback on Schrödinger-cat state generation in an optomechanical system. The result shows that the fidelity of cat state generation can be improved in the presence of feedback loop.

Turbulent flow characteristics over an abrupt step change in bed roughness

Turbulent flow characteristics over an abrupt step change in bed roughness from smooth to rough are studied measuring the flow field by a Particle Image Velocimetry (PIV) system. The smooth and rough beds are referred to as the upstream and downstream beds, respectively. The velocity color maps and profiles show that an abrupt step change in bed roughness causes flow retardation in the downstream bed owing to the combined effects of roughness-induced and separated flows. The results of the Reynolds stresses reveal that the profiles in the downstream bed exhibit discriminable bulges, whose size increases with an increase in the streamwise distance. The stress color maps illustrate the creation of a roughness-induced layer that grows over the downstream bed as the streamwise distance increases. The bed shear stress evidences an overshooting behavior immediate downstream of the abrupt step change in bed roughness to reach its peak magnitude. The third-order correlations indicate that the effects of the abrupt step change in bed roughness produce an inrush of rapidly moving fluid streaks in the near-bed flow and arrival of slowly moving fluid streaks in the away-bed flow. Regarding the turbulent kinetic energy (TKE) budget, the enhanced magnitudes of the TKE budget terms within the roughness-induced layer are prevalent. The TKE dissipation rate lags the production rate, and the negative TKE diffusion rate implies an addition in the TKE production. Bursting analysis endorses that the sweeps govern the near-bed flow on the downstream bed and the ejections prevail far from the bed.

A sparse regression approach to modelling the relation between galaxy stellar masses and their host haloes

ABSTRACT Sparse regression algorithms have been proposed as the appropriate framework to model the governing equations of a system from data, without needing prior knowledge of the underlying physics. In this work, we use sparse regression to build an accurate and explainable model of the stellar mass of central galaxies given properties of their host dark matter (DM) halo. Our data set comprises 9521 central galaxies from the EAGLE hydrodynamic simulation. By matching the host haloes to a DM-only simulation, we collect the halo mass and specific angular momentum at present time and for their main progenitors in 10 redshift bins from z = 0 to z = 4. The principal component of our governing equation is a third-order polynomial of the host halo mass, which models the stellar-mass–halo-mass relation. The scatter about this relation is driven by the halo mass evolution and is captured by second- and third-order correlations of the halo mass evolution with the present halo mass. An advantage of sparse regression approaches is that unnecessary terms are removed. Although we include information on halo specific angular momentum, these parameters are discarded by our methodology. This suggests that halo angular momentum has little connection to galaxy formation efficiency. Our model has a root mean square error (RMSE) of 0.167log10(M*/M⊙), and accurately reproduces both the stellar mass function and central galaxy correlation function of EAGLE. The methodology appears to be an encouraging approach for populating the haloes of DM-only simulations with galaxies, and we discuss the next steps that are required.

A new lithostratigraphic framework and unified nomenclature for the Nsuze Group of the Nkandla sub-basin, southern Kaapvaal Craton, South Africa

AbstractDuring the early 20th century the term Insuzi Series, later reclassified as the Nsuze Group of the Pongola Supergroup, was proposed for a volcano-sedimentary succession exposed in the upper Nsuze River valley in central KwaZulu-Natal, South Africa. Subsequently, however, there has been little consensus on lithostratigraphic frameworks within the type area, and limited correlation with the exceptionally well-defined stratigraphy within the main Pongola basin. Recent mapping, combined with newly acquired high-resolution aeromagnetic data, satellite imagery, and available published geochronological data suggest that previously published schemes within the Nkandla sub-basin require revision. Utilising important regional marker units, as well as the stratigraphic positions of distinct sedimentary facies within the otherwise volcanic Nsuze Group, a working model is proposed. Lithostratigraphic units are well represented in the Mhlatuze and Nkandla inliers with examples from these areas given prominence. Where exposed, potential correlates within the Nsuze nappe complex are discussed. Within the proposed scheme the siliciclastic Mantonga Formation forms the base of the Nsuze Group, nonconformably overlying basement granitoids of the Kaapvaal Craton within the Mhaltuze Inlier. Mafic volcanics of the Nhlebela Formation overlie the Mantonga Formation in the inlier. These two lower units are, however, not exposed elsewhere in the sub-basin. The sedimentary White Mfolozi Formation forms the base of the succession in the Nkandla Inlier. Diamictites and stromatolite-bearing carbonate lithologies unique to this unit are utilised for regional third-order correlations with the type-area in the White Mfolozi Inlier. Mafic volcanics of the Agatha Formation overlie the White Mfolozi Formation in all exposures, but are most extensively developed within the Mdlelanga syncline of the Nkandla Inlier. Sedimentary and volcaniclastic lithologies of the Mkuzane Formation cap the Nsuze Group in the Mhlatuze and Nkandla inliers. Thickness of this formation is, however, highly variable having been subjected to pre-Vutshini Formation erosion. Through detailed reinterpretation of the stratigraphy of the Nkandla sub-basin we present a third order, (formation) scale, lithostratigraphic scheme encompassing all the formational units of the currently accepted stratigraphy within the main Pongola basin. This working model has the potential for lower-ranking units to be identified and be placed at their appropriate stratigraphic levels in future.

Modelling of weak quantum measurements consistent with conservation laws

We discuss quantum mechanical detection models in the weak limit in the context of conservation laws of physical quantities. In particular, we analyze what kind of system–detector interaction can preserve the global conservation or the related symmetry, and how the final measurement on the detector affects the measured observable of the systems and its presumed conservation. It turns out that the order of noncommuting measurements results in observable differences on the level of third-order correlations functions.

Analysis of Recent BLYP- and PBE-Based Range-Separated Double-Hybrid Density Functional Approximations for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions.

We investigate the effects of range separation of the exchange energy on electronic ground-state properties for recently published double-hybrid density functionals (DHDFs) with the extensive GMTKN55 database for general main-group thermochemistry, kinetics, and noncovalent interactions. We include the semiempirical range-separated DHDFs ωB2PLYP and ωB2GP-PLYP developed by our group for excitation energies, together with their ground-state-parametrized variants, which we denote herein as ωB2PLYP18 and ωB2GP-PLYP18. We also include the nonempirical range-separated DHDFs RSX-0DH and RSX-QIDH. For all six DHDFs, damping parameters for the DFT-D3 dispersion correction (and for its DFT-D4 variant) are presented. We comment on when the range-separated functionals can be more beneficial than their global counterparts and conclude that range separation alone is no guarantee for overall improved results. We observe that the BLYP-based functionals generally outperform the PBE-based functionals. We finally note that the best-performing DHDFs for GMTKN55 are still the semiempirical range-separated double hybrids ωDSD3-PBEP86-D4 and ωDSD72-PBEP86-D4, the former of which includes a third-order perturbative correlation term in addition to the more conventional second-order perturbation that DHDFs are based upon.

EXPERIMENT OF UNIQUE COMBINATION NUMBER DUE TO THE THIRD-ORDER NEUTRON-CORRELATION

From zero-power reactor noise measurement, the second- and third-order neutron correlation factors Y and y3 can be evaluated by analyzing mean, variance, the third-order central moment of neutron count data. Theoretically, it is expected that the neutron-correlation ratio y3/Y2 converges to the unique combination number “3” at a near-critical state in an arbitrary system without depending on the fissile material and the neutron-energy spectrum of core, as the neutron counting gate width T increases sufficiently. Thus, the information about the difference between y3/Y2 and “3” has the potential to judge whether a target unknown system is critical or not and to roughly guess the absolute value of subcriticality. In this study, the detector dead-time effect on y3/Y2 is theoretically investigated based on the heuristic method using the single-, pair-, and trio-detection probabilities with the fundamental mode approximation. As a result, it is clarified that the saturation value of y3/Y2 converges to “3” independent of the dead time, when a target system is a critical state. For validation, actual experimental results are presented for a non-multiplication system driven by 252Cf spontaneous source, and shallow and deep subcritical systems at Japanese experimental facilities (UTR-KINKI and KUCA) under the shutdown state. Consequently, it is demonstrated that y3/Y2 shows a significant difference from “3” in the non-multiplication system. In the case of subcritical systems driven by inherent neutron sources, it is confirmed that the ratios y3/Y2 are close to the unique combination number “3,” and the slight difference from “3” is measurable by the long-time reactor noise measurement for the deep subcritical system.

Exotic supersolid phase of one-dimensional Bose-Hubbard model inside an optical cavity

Using a state-of-the-art numerical method density-matrix renormalization-group, we study the ground states of one-dimensional spinless Bose-Hubbard model inside a red-detuned cavity. By calculating the superfluid order, density distribution, second and third-order correlation functions, we find that there exist two novel supersolid phases with diagonal, off-diagonal orders beyond mean-field theory. One has package type density modulation along the lattice axis, another exhibits uniform density distribution. Moreover, by calculating the superradiant order parameter and the number of photon inside the cavity, we find that the novel supersolid phases are highly related to cavity-field fluctuation. Our work gives the physics beyond the mean-field theory of the Bose-Hubbard model inside an optical cavity, and provides the complete approach to fully explore the collective state of light and matter inside an optical cavity.

Isotropic turbulence correlation functions modelling on the basis of Karman-Howarth equation

A closure model for the von Karman-Howarth equation is considered. The offered algebraic closure model is based on a single spatial-point third-order correlation function, unlike the widely used models based on a distance between two separated points. The model holds for homogeneous isotropic turbulence theory. Numerical solution of the von Karman-Howarth equation for the flow behind a bi-plane grid of circular cylinders in comparison to experimental data is presented.

Spiking Correlation Analysis of Synchronous Spikes Evoked by Acupuncture Mechanical Stimulus.

Acupuncturing the ST36 acupoint can evoke the response of the sensory nervous system, which is translated into output electrical signals in the spinal dorsal root. Neural response activities, especially synchronous spike events, evoked by different acupuncture manipulations have remarkable differences. In order to identify these network collaborative activities, we analyze the underlying spike correlation in the synchronous spike event. In this paper, we adopt a log-linear model to describe network response activities evoked by different acupuncture manipulations. Then the state-space model and Bayesian theory are used to estimate network spike correlations. Two sets of simulation data are used to test the effectiveness of the estimation algorithm and the model goodness-of-fit. In addition, simulation data are also used to analyze the relationship between spike correlations and synchronous spike events. Finally, we use this method to identify network spike correlations evoked by four different acupuncture manipulations. Results show that reinforcing manipulations (twirling reinforcing and lifting-thrusting reinforcing) can evoke the third-order spike correlation but reducing manipulations (twirling reducing and lifting-thrusting reducing) does not. This is the main reason why synchronous spikes evoked by reinforcing manipulations are more abundant than reducing manipulations.

Third-order photon cross-correlations in resonance fluorescence

We investigated third-order correlations between photons from a single quantum dot's resonance fluorescence in the strong excitation regime originating from opposite sidebands of the power spectrum. The three-time correlation measurements for photons filtered using three independent Fabry-Perot etalons resulted in correlation maps with ``antibunching'' features as a consequence of correlations originating from the same sideband, and ``bunching ridges'' due to opposite sideband correlated photons.

Extended Second-Order Multireference Algebraic Diagrammatic Construction Theory for Charged Excitations.

We report a new implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulations of electron attachment and ionization in strongly correlated molecular systems (EA/IP-MR-ADC). Following our recent work on IP-MR-ADC [J. Chem. Theory Comput. 2019, 15, 5908], we present the first implementation of the second-order MR-ADC method for electron attachment (EA-MR-ADC(2)) and two extended second-order approximations (EA- and IP-MR-ADC(2)-X) that incorporate a partial treatment of third-order electron correlation effects. Introducing a small approximation for the second-order amplitudes of the effective Hamiltonian, our implementation of EA- and IP-MR-ADC(2)-X has a low computational scaling with the basis set size M. Additionally, we describe an efficient algorithm for solving the first-order amplitude equations in MR-ADC and partially contracted second-order N-electron valence perturbation theory (NEVPT2) which completely avoids computation of the four-particle reduced density matrices without introducing any approximations or imaginary-time propagation. For a benchmark set of eight small molecules, a carbon dimer, and a twisted ethylene, we demonstrate that EA- and IP-MR-ADC(2)-X achieve an accuracy similar to that of strongly contracted NEVPT2 while having a lower computational scaling with the active space size and providing efficient access to transition properties.

Representation of foreseeable choice outcomes in orbitofrontal cortex triplet-wise interactions.

Shared neuronal variability has been shown to modulate cognitive processing. However, the relationship between shared variability and behavioral performance is heterogeneous and complex in frontal areas such as the orbitofrontal cortex (OFC). Mounting evidence shows that single-units in OFC encode a detailed cognitive map of task-space events, but the existence of a robust neuronal ensemble coding for the predictability of choice outcome is less established. Here, we hypothesize that the coding of foreseeable outcomes is potentially unclear from the analysis of units activity and their pairwise correlations. However, this code might be established more conclusively when higher-order neuronal interactions are mapped to the choice outcome. As a case study, we investigated the trial-to-trial shared variability of neuronal ensemble activity during a two-choice interval-discrimination task in rodent OFC, specifically designed such that a lose-switch strategy is optimal by repeating the rewarded stimulus in the upcoming trial. Results show that correlations among triplets are higher during correct choices with respect to incorrect ones, and that this is sustained during the entire trial. This effect is not observed for pairwise nor for higher than third-order correlations. This scenario is compatible with constellations of up to three interacting units assembled during trials in which the task is performed correctly. More interestingly, a state-space spanned by such constellations shows that only correct outcome states that can be successfully predicted are robust over 100 trials of the task, and thus they can be accurately decoded. However, both incorrect and unpredictable outcome representations were unstable and thus non-decodeable, due to spurious negative correlations. Our results suggest that predictability of successful outcomes, and hence the optimal behavioral strategy, can be mapped out in OFC ensemble states reliable over trials of the task, and revealed by sufficiency complex neuronal interactions.

Hydrodynamics of flow over two-dimensional dunes

The turbulence characteristics in flow over and within the interface of two-dimensional dunes are investigated experimentally. Besides the spatial flow and turbulence quantities, their double-averaged profiles are also analyzed. The flow over dunes is recognized to be a wake-interference flow, where the decelerated flow at the immediate downstream of the crest causes the kolk-boil effect. The flow reattachment can be explained from the perspective of the Coandă effect. The inner boundary layer edge follows the locus of the inflection points of velocity profiles having a velocity defect. The Reynolds shear stress profiles attain their respective peaks along this locus. In addition, the dispersive shear stress initiates from the edge of the form-induced sublayer being negative, indicating a spatially decelerated flow. The third-order correlations reveal that an inrush of rapidly moving fluid streaks coupled with a downward-downstream Reynolds stress diffusion prevails within the interfacial sublayer, while an arrival of slowly moving fluid streaks coupled with an upward-upstream stress diffusion governs the flow zone above the crest. The turbulent kinetic energy (TKE) flux results corroborate the similar findings. Concerning the TKE budget, the dispersive kinetic energy diffusion is found to be substantial within the roughness sublayer. The budget terms exhibit their respective peaks near the crest. The production rate is greater than the dissipation rate. However, the TKE diffusion and pressure energy diffusion rates are negative in the interfacial sublayer. The bursting analysis endorses that the sweeps and ejections govern within the interfacial sublayer and the flow zone above the crest, respectively.

A Triple Correlator of Radiation Intensities of a Multimode Semiconductor Laser

In this work, temporal correlations of radiation intensities of a multimode Fabry-Perot (FP) semiconductor laser are studied. Second- and third-order intensity correlation functions are measured both for the multimode FP laser and a pulsed Ti: Sapphire (TiSp) laser. Triple correlators of the latter demonstrate an ordinary product of double correlators (the classic case). The behavior of the multimode laser is more complex and can indicate the quantum nature of optical field correlations. We follow a specific phenomenological formula for calculation of the triple temporal correlator.

Multi-order quantum beating effect of three-photon temporal interference with nondegenerate fluorescence sources

The multi-order quantum beating effect of three-photon temporal interference generated by three nondegenerate fluorescence sources is studied. The third-order temporal correlation function of three nondegenerate photons results from the superposition of two-photon and three-photon bunching, multi-order quantum beating and temporal interference of three-photon. The simulate results show strong quantum beating and photon bunching behavior. The visibility of interference pattern, and the switching between photon bunching and beating effect can be modulated by the frequency difference, bandwidth of photons and the relative time delay of detectors. Such controllable coherent signal has potential applications as router and logic gate in quantum communication and information processing.