Order Correlation Functions Research Articles

Photon blockade in a double transmon system with ultrastrong coupling

Abstract The circuite QED system has brought us into the ultrastrong and deep coupling regime in the light-matter interaction community, in which, the quantum effect has evoked lots of interests. In this paper, we theoretically study the photon blockade phenomenon in a double transmon system, which works in the ultrastrong coupling regime. We take into the effect of the counter rotating wave terms in the interaction Hamiltonian and derive the Master equation in the eigen presentation. We find that, the photon blockade occurs only in one of the eigen modes, and the counter rotating wave terms enhance the blockade by reducing the minimum value of the second order correlation function. Our study will be beneficial in the designing of single-photon device in the circuit QED system, especially in the ultrastrong coupling regime.

Manifestation of strong and ultra-strong coupling in high-order correlation functions

Strong and ultra-strong coupling in a “cavity–single atom” system is of great interest for both fundamental and applied physics. It is considered that the increase in the coupling strength between a cavity mode and an atom leads, first, to transition from weak to strong coupling and, second, to the ultra-strong coupling regime. In this paper, we refute this common opinion and demonstrate that the transitions between the coupling regimes occur in different sequences for the correlation functions of different orders. We show that for n-th order correlation functions, the transition to the strong coupling regime requires a coupling strength approximately n2/3 times greater than the one for first order correlation functions. In contrast, the transition to the ultra-strong coupling regime manifests in the dynamics of n-th order correlation functions at less coupling strength than in the dynamics of first order correlation functions. As a result, the measurement of high-order correlation functions makes it easier to observe the ultra-strong coupling in “cavity mode–single atom.”

Certifying Ground-State Properties of Many-Body Systems

A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalization quickly becomes impossible when increasing the system size, variational approaches are typically employed as a scalable alternative: Energy is minimized over a subset of all possible states and then different physical quantities are computed over the solution state. Despite remarkable success, rigorously speaking, all that variational methods offer are upper bounds on the ground-state energy. On the other hand, so-called relaxations of the ground-state problem based on semidefinite programming represent a complementary approach, providing lower bounds to the ground-state energy. However, in their current implementation, neither variational nor relaxation methods offer provable bound on other observables in the ground state beyond the energy. In this work, we show that the combination of the two classes of approaches can be used to derive certifiable bounds on the value of any observable in the ground state, such as correlation functions of arbitrary order, structure factors, or order parameters. We illustrate the power of this approach in paradigmatic examples of 1D and 2D spin-1/2 Heisenberg models. To improve the scalability of the method, we exploit the symmetries and sparsity of the considered systems to reach sizes of hundreds of particles at much higher precision than previous works. Our analysis therefore shows how to obtain certifiable bounds on many-body ground-state properties beyond energy in a scalable way. Published by the American Physical Society 2024

Nucleon form factors in Nf=2+1 lattice QCD at the physical point: Finite lattice spacing effect on the root-mean-square radii

We present results for the nucleon form factors: electric (GE), magnetic (GM), axial (FA), induced pseudoscalar (FP), and pseudoscalar (GP) form factors, using the second PACS10 ensemble that is one of three sets of 2+1 flavor lattice QCD configurations at physical quark masses in large spatial volumes [exceeding (10 fm)3]. The second PACS10 gauge configurations are generated by the PACS Collaboration with the six stout-smeared O(a) improved Wilson quark action and Iwasaki gauge action at the second gauge coupling β=2.00 corresponding to the lattice spacing of a=0.063 fm. We determine the isovector electric, magnetic and axial radii, and magnetic moment from the corresponding form factors, as well as the axial-vector coupling gA. Combining our previous results for the coarser lattice spacing [E. Shintani , ; ], the finite lattice spacing effects on the isovector radii, magnetic moment, and axial-vector coupling are investigated using the difference between the two results. It was found that the effect on gA is kept smaller than the statistical error of 2% while the effect on the isovector radii was observed as a possible discretization error of about 10%, regardless of the channel. We also report the partially conserved axial-vector current relation using a set of nucleon three-point correlation functions in order to verify the effect by O(a) improvement of the axial-vector current. Published by the American Physical Society 2024

Amplification of the anomalous scaling in the Kazantsev-Kraichnan model with finite-time correlations and spatial parity violation.

By using the field theoretic renormalization group technique together with the operator product expansion, simultaneous influence of the spatial parity violation and finite-time correlations of an electrically conductive turbulent environment on the inertial-range scaling behavior of correlation functions of a passively advected weak magnetic field is investigated within the corresponding generalized Kazantsev-Kraichnan model in the second order of the perturbation theory (in the two-loop approximation). The explicit dependence of the anomalous dimensions of the leading composite operators on the fixed point value of the parameter that controls the presence of finite-time correlations of the turbulent field as well as on the parameter that drives the amount of the spatial parity violation (helicity) in the system is found even in the case with the presence of the large-scale anisotropy. In accordance with the Kolmogorov's local isotropy restoration hypothesis, it is shown that, regardless of the amount of the spatial parity violation, the scaling properties of the model are always driven by the anomalous dimensions of the composite operators near the isotropic shell. The asymptotic (inertial-range) scaling form of all single-time two-point correlation functions of arbitrary order of the passively advected magnetic field is found. The explicit dependence of the corresponding scaling exponents on the helicity parameter as well as on the parameter that controls the finite-time velocity correlations is determined. It is shown that, regardless of the amount of the finite-time correlations of the given Gaussian turbulent environment, the presence of the spatial parity violation always leads to more negative values of the scaling exponents, i.e., to the more pronounced anomalous scaling of the magnetic correlation functions. At the same time, it is shown that the stronger the violation of spatial parity, the larger the anomalous behavior of magnetic correlations.

Finite size effects and optimization of the calculation of the surface tension in surfactant mixtures at liquid/vapour interfaces

The surface tension of monolayers with mixtures of anionic and nonionic surfactant at the liquid/vapour interface is studied. Previous works have observed that calculations of the surface tension of simple fluids show artificial oscillations for small interfacial areas, indicating that the surface tension data fluctuate due to the finite size effects and periodic boundary conditions. In the case of simulations of monolayers composed of surfactant mixtures, the surface tension not only oscillates for small areas but can also give non-physical data, such as negative values. Analysis of the monolayers with different surfactant mixtures, ionic (DTAB, CTAB, SDS) and nonionic (SB3-12), was done for density profiles, parameters of order and pair correlation functions for small and large box areas and all of them present similar behaviour. The fluctuations and the non-physical values of the surface tension are corrected when boxes with large interfacial areas are considered. The results indicate that in order to obtain reliable values of the surface tension, in computer simulations, it is important to choose not only the correct force field but also the appropriate size of the simulation box.

Interaction of a four-level atom with a quantized field in the presence of a nonlinear Kerr medium

Quantum entanglement and atomic coherence are examined for a system consisting of a four-level atom (FLA) interacted with a nonlinear quantum field. We assume that the FLA-field coupling, Kerr medium and quantified field are all f\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f$$\\end{document}-deformed with full nonlinear formalism. We consider N-configuration and cascade (C)-configuration of the FLA. We explore the impact of field deformation and Kerr medium on the dynamics of the quantumness measures when the quantized field is initially prepared in a deformed coherent state without and with Kerr medium effect. Moreover, we examine the statistical properties of the radiation field using the second order correlation function. The results indicate how the considered quantumness measures in the FLA–field system can be manipulated and controlled through the parameters of the quantum model.

Study of Time Correlation and Memory Function for the Derivation of Spectral Density in Plasma

This paper is mainly focused on studying time correlation and memory functions in order to determine the spectral density in plasma. The research aims to understand and quantify the noise produced in the plasma as a result of random processes. Noise can arise from various sources, including fluctuations in particle density, temperature, and other plasma parameters. To ensure a fair comparison, the paper appears to keep the cross-sectional area of the plasma which is same for both the Q-Machine and Fusion Reactor. This means that any observed differences in spectral density can be attributed to the inherent characteristics of the two systems rather than differences in plasma volume. It is observed that Fusion Reactor produced more noise in comparison to the Q-Machine. This research seems to contribute to our understanding of plasma physics, specifically in the context of spectral density and noise production, by comparing two different plasma systems. The observed differences in noise levels between the Q-Machine and Fusion Reactor could have important implications for plasma-based technologies and fusion research.

Statistical features of systems driven by non-Gaussian processes: theory & practice

Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here we consider a class of Markov processes described by Langevin equations driven by a mixture of Gaussian and Poissonian noises, focusing on their non-equilibrium properties. In particular, we prove that detailed balance does not hold even when correlation functions are symmetric under time reversal. In such cases, a breakdown of the time reversal symmetry can be highlighted by considering higher order correlation functions. Furthermore, the entropy production may be different from zero even for vanishing currents. We provide analytical expressions for the average entropy production rate in several cases. We also introduce a scale dependent estimate for entropy production, suitable for inference from experimental signals. The empirical entropy production allows us to discuss the role of spatial and temporal resolutions in characterizing non-equilibrium features. Finally, we revisit the Brownian gyrator introducing an additional Poissonian noise showing that it behaves as a two dimensional linear ratchet. It has also the property that when Onsager relations are satisfied its entropy production is positive although it is minimal. We conclude discussing estimates of entropy production for partially accessible systems, comparing our results with the lower bound provided by the thermodynamic uncertainty relations.

Enhanced spatially focused superbunched emission from a line of few interacting atomic dipoles

An excellent phenomenon in the realm of quantum optics and informatics is the study of radiative characteristics of a set of few identical two-level correlated systems. The system envisaged consists of a line of equidistant atoms probed by a weak resonant laser field. Collective decay and dipole-dipole interactions are incorporated due to a coupling of the atomic system to the common surrounding vacuum field. The correlation functions of the emitted field give important physical information about statistical correlations that exist between the emitting atoms. The dependence of the one-time first, second and third order correlation functions of the emitted field on the detection directions in the far-field domain in steady state has been studied. It has been found that the probability of the coincident detection of two and three photons is very large in particular directions. Interestingly, it is observed that the preferred directions for two-photon emission are the same as the favoured directions for the emission of a triplet of photons. Moreover, these directions are exactly located where the emission of a single uncorrelated photon is extremely unlikely. The variation of these directions where two or three correlated fluorescent photons are detected with high probability has been studied as a function of the magnitude of the dipole-dipole interaction between the emitting atoms. A general trend in this variation can be noted for closely-spaced interacting atoms.

The halo bispectrum as a sensitive probe of massive neutrinos and baryon physics

ABSTRACT The power spectrum has been a workhorse for cosmological studies of large-scale structure. However, the present-day matter distribution is highly non-Gaussian and significant cosmological information is also contained in higher order correlation functions. Meanwhile, baryon physics (particularly active galactic nucleus feedback) has previously been shown to strongly affect the two-point statistics but there has been limited exploration of its effects on higher order functions to date. Here, we use the bahamas suite of cosmological hydrodynamical simulations to explore the effects of baryon physics and massive neutrinos on the halo bispectrum. In contrast to matter clustering which is suppressed by baryon physics, we find that the halo clustering is typically enhanced. The strength of the effect and the scale over which it extends depends on how haloes are selected. On small scales ($k \gtrsim 1$ h Mpc−1, dominated by satellites of groups/clusters), we find that the bispectrum is highly sensitive to the efficiency of star formation and feedback, making it an excellent testing ground for galaxy formation models. We show that the effects of feedback and the effects of massive neutrinos are largely separable (independent of each other) and that massive neutrinos strongly suppress the halo bispectrum on virtually all scales up to the free-streaming length (apart from the smallest scales, where baryon physics dominates). The strong sensitivity of the bispectrum to neutrinos on the largest scales and galaxy formation physics on the smallest scales bodes well for upcoming precision measurements from the next generation of wide-field surveys.

NOON-state generation and superresolved interference in a double-slit experiment

Maximally entangled NOON states are proposed to be generated with $N$ independent photons and a fixed double-slit in the Young's interference experiment. A strict condition is required that these photons have to be arranged in a straight line and separated from each other by certain equal distances. The initial product state turns into a NOON state of the photons at the double-slit, after $N$-photon postselected measurements. With a spatially random laser beam, we experimentally investigate the high-order correlation functions to imitate the behavior of the single-photon and $N$-photon wave packets of the NOON states. Since the $N$-photon wave packet is the product of $N$ single-photon wave packets, two methods are adopted to observe the superresolved fringes. The first method is to use the product of the second-order correlation functions. The second one is to measure the $2N\mathrm{th}$-order correlation functions. In the both cases, the superresolved fringes of up to fourth order are successfully observed.

Shape and interfacial structure of droplets. Exact results and simulations

We consider the fluctuating interface of a droplet pinned on a flat wall. For such a system we compare results obtained within the exact field theory of phase separation in two dimensions and Monte Carlo (MC) simulations for the Ising model. The interface separating coexisting phases splits and hosts drops whose effect is to produce subleading corrections to the order parameter profile and correlation functions. In this paper we establish the first direct measurement of interface structure effects by means of high-performance MC simulations which successfully confirm the field-theoretical results. Simulations are found to corroborate the theoretical predictions for interface structure effects whose analytical expression has recently been obtained. It is thanks to these higher-order corrections that we are able to correctly resettle a longstanding discrepancy between simulations and theory for the order parameter profile. In addition, our results clearly establish the long-ranged decay of interfacial correlations in the direction parallel to the interface and their spatial confinement within the interfacial region also in the presence of a wall from which the interface is entropically repelled.

On weak lensing response functions

We introduce the response function approach to model the weak lensing statistics in the context of separate universe formalism. Numerical results for the RFs are presented for various semi-analytical models that includes perturbative modelling and variants of halo models. These results extend the recent studies of the Integrated Bispectrum and Trispectrum to arbitrary order. We find that due to the line-of-sight projection effects, the expressions for RFs are not identical to the squeezed correlation functions of the same order. We compute the RFs in three-dimensions using the spherical Fourier-Bessel formalism which provides a natural framework for incorporating photometric redshifts, and relate these expressions to tomographic and projected statistics. We generalise the concept of k-cut power spectrum to k-cut response functions. In addition to response functions, we also define their counterparts in real space, since they are easier to estimate from surveys with low sky-coverage and non-trivial survey boundaries.

Operator spreading in quantum hardcore gases

In this article we study a set of integrable quantum cellular automata, the quantum hardcore gases (QHCG), with an arbitrary local Hilbert space dimension, and discuss the matrix product ansatz based approach for solving the dynamics of local operators analytically. Subsequently, we focus on the dynamics of operator spreading, in particular on the out-of-time ordered correlation functions (OTOCs), operator weight spreading and operators space entanglement entropy (OSEE). All of the quantities were conjectured to provide signifying features of integrable systems and quantum chaos. We show that in QHCG OTOCs spread diffusively and that in the limit of the large local Hilbert space dimension they increase linearly with time, despite their integrability. On the other hand, it was recently conjectured that operator weight front, which is associated with the extent of operators, spreads diffusively in both, integrable and generic systems, but its decay seems to differ in these two cases (Lopez-Piqueres et al 2021 Phys. Rev. B 104 104307). We observe that the spreading of the operator weight front in QHCG is markedly different from chaotic, generic integrable and free systems, as the front freezes in the long time limit. Finally, we discuss the OSEE in QHCG and show that it grows at most logarithmically with time in accordance with the conjectured behaviour for interacting integrable systems (Alba et al 2019 Phys. Rev. Lett. 122 250603).

Classical and quantum butterfly effect in nonlinear vector mechanics

We establish the correspondence between the classical and quantum butterfly effects in nonlinear vector mechanics with the broken $O(N)$ symmetry. On one hand, we analytically calculate the out-of-time ordered correlation functions and the quantum Lyapunov exponent using the augmented Schwinger-Keldysh technique in the large-$N$ limit. On the other hand, we numerically estimate the classical Lyapunov exponent in the high-temperature limit, where the classical chaotic behavior emerges. In both cases, Lyapunov exponents approximately coincide and scale as $\kappa \approx 1.3 \sqrt[4]{\lambda T}/N$ with temperature $T$, number of degrees of freedom $N$, and coupling constant $\lambda$.

Cluster mean field plus density matrix renormalization theory for the Bose Hubbard models

The cluster mean-field with density matrix renormalization (CMFT + DMRG) method which combines the simplicity of the mean-field theory and the numerical power of the density-matrix renormalization group method is applied to understand the quantum phases of the one-dimensional Bose–Hubbard models. We show that the CMFT + DMRG method is an effective numerical technique with moderate computational resources to determine relevant order parameters and correlation functions of large one-dimensional systems. We apply the CMFT + DMRG for the Bose Hubbard and extended Bose Hubbard models to account for the superfluid, Mott insulator, and density wave phases in these models. Our results are in good agreement with the known phase diagram of these models, demonstrating the efficacy of this method.

Quantum statistics of light emitted from a pillar microcavity

A quantum behavior of the light emitted by exciton polaritons excited in a pillar semiconductor microcavity with embedded quantum well is investigated. Considering the bare excitons and photon modes as coupled quantum oscillators allows for an accurate accounting of the nonlinear and dissipative effects. In particular, using the method of the quantum states representation in a quantum phase space via quasiprobability functions (namely, a P-function and a Wigner function), we study the impact of the laser and the exciton-photon detuning on the second order correlation function of the emitted photons. We determine the conditions under which the phenomena of bunching, giant bunching, and antibunching of the emitted light emerge. In particular, we predict the effect of a giant bunching for the case of a large exciton to photon population ratio. Within the domain of parameters supporting a bistability regime we demonstrate the effect of bunching of photons.

Unconventional phonon blockade via atom-photon-phonon interaction in hybrid optomechanical systems.

Phonon nonlinearities play an important role in hybrid quantum networks and on-chip quantum devices. We investigate the phonon statistics of a mechanical oscillator in hybrid systems composed of an atom and one or two standard optomechanical cavities. An efficiently enhanced atom-phonon interaction can be derived via a tripartite atom-photon-phonon interaction, where the atom-photon coupling depends on the mechanical displacement without practically changing a cavity frequency. This novel mechanism of optomechanical interactions, as predicted recently by Cotrufo et al. [Phys. Rev. Lett.118, 133603 (2017)10.1103/PhysRevLett.118.133603], is fundamentally different from standard ones. In the enhanced atom-phonon coupling, the strong phonon nonlinearity at a single-excitation level is obtained in the originally weak-coupling regime, which leads to the appearance of phonon blockade. Moreover, the optimal parameter regimes are presented both for the cases of one and two cavities. We compared phonon-number correlation functions of different orders for mechanical steady states generated in the one-cavity hybrid system, revealing the occurrence of phonon-induced tunneling and different types of phonon blockade. Our approach offers an alternative method to generate and control a single phonon in the quantum regime and could have potential applications in single-phonon quantum technologies.

Quantum state engineering using weak measurements

State preparation via postselected weak measurement in three wave mixing process is studied. Assuming the signal input mode prepared in a vacuum state, coherent state or squeezed vacuum state, separately, while the idler input prepared in weak coherent state and passing the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of idler beam's path, the signal output channel is prepared in single-photon Fock state, single-photon-added coherent state or single-photon-added squeezed vacuum state with very high fidelity, depending upon the input signal states and related controllable parameters. The properties including squeezing, signal amplification, second order correlation and Wigner functions of the weak measurement based output states are also investigated. Our scheme promising to provide alternate new effective method for producing useful nonclassical states in quantum information processing.