Two-mode Field Research Articles

Thermodynamic sensing of quantum nonlinear noise correlations

Abstract We put forth the concept of quantum noise sensing in nonlinear two-mode interferometers coupled to mechanical oscillators. These autonomous machines are capable of sensing quantum nonlinear correlations of two-mode noisy fields via their thermodynamic variable of extractable work, alias work capacity (WC) or ergotropy. The fields are formed by thermal noise input via its interaction with multi-level systems inside the interferometer. Such interactions amount to the generation of two-mode quantum nonlinear gauge fields that may be partly unknown. We show that by monitoring a mechanical oscillator coupled to the interferometer, one can sense the WC of one of the output field modes and thereby reveal the quantum nonlinear correlations of the field. The proposed quantum sensing method can provide an alternative to quantum multiport interferometry where the output field is unraveled by tomography. This method may advance the simulation and control of multimode quantum nonlinear gauge fields.

Witness of non-Markovian dynamics based on Bhattacharyya quantum distance

Non-Markovian effects due to quantum memory in the dynamics of open systems typically correspond to information backflows from the surrounding environment to the system. We propose a witness to quantify the non-Markovianity of quantum evolutions using the Bhattacharyya distance (BD), a specific quantum statistical distance. This witness has the advantage of not requiring the calculation of the evolved density matrix and only computes through the initial and final states of the system, therefore leading to the improvement of quantum metrology. It means that we calculate the quantum angle between two states to detect non-Markovian effects. This proposal is investigated by considering several instances of open quantum systems, such as two and three-level atoms interacting in single and two-mode fields, respectively, and two effective two-level atoms interacting locally with two independent environments. We demonstrate that the suggested BD-based non-Markovianity witness identifies memory effects, consistent with well-established witnesses based on Bures distance, quantum Fisher information, and Hilbert-Schmidt speed, showing sensitivity to information backflows.

The Physical Transient Spectrum and Squeezing of a Three-Level Atom Interacting with Two-Mode Field in Finite Pair Coherent State in the Presence of a Classical External Field

The Physical Transient Spectrum and Squeezing of a Three-Level Atom Interacting with Two-Mode Field in Finite Pair Coherent State in the Presence of a Classical External Field

Exploring entanglement dynamics in an optomechanical cavity with a type-[formula omitted] qutrit and quantized two-mode field

In this work, the main objective is to measure the degree of interaction of a type-V qutrit with a two-mode quantized field in an optomechanical cavity. To achieve this objective, we first deduce the Hamiltonian in the interaction picture to identify the oscillatory terms. Using the Coarse-Grained Method (CGM), we obtain the effective Hamiltonian analytically. By selecting initial conditions for the atom, the two-mode field, and the moving mirror, we can determine the state vector of the entire system through a first-order approximation of the effective Hamiltonian. With this information, we proceed to solve the Schrödinger equation, generating a coupled set of differential equations that is solved numerically based on the initial conditions. In this context, the atomic von Neumann entropy allows us to obtain the temporal evolution of the degree of entanglement of the qutrit in the cavity and the atomic population inversion. The results indicate that entanglement in this tripartite system, composed of the qutrit and the mirror-field subsystems, as well as the population inversion, can be manipulated by the initial state conditions of the system, the qutrit-field and mirror-field coupling coefficients, the pump field, and the dissipation rates of the two-mode field and the movable mirror, respectively.

Ground-state phase diagram, symmetries, excitation spectra and finite-frequency scaling of the two-mode quantum Rabi model

We investigate the two-mode quantum Rabi model (QRM) describing the interaction between a two-level atom and a two-mode cavity field. The quantum phase transitions are found when the ratio η of transition frequency of atom to frequency of cavity field approaches infinity. We apply the Schrieffer–Wolff (SW) transformation to derive the low-energy effective Hamiltonian of the two-mode QRM, thus yielding the critical point and rich phase diagram of quantum phase transitions. The phase diagram consists of four regions: a normal phase, an electric superradiant phase, a magnetic superradiant phase and an electromagnetic superradiant phase. The quantum phase transition between the normal phase and the electric (magnetic) superradiant phase is of second order and associates with the breaking of the discrete Z 2 symmetry. On the other hand, the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1) symmetry. Several important physical quantities, for example the excitation energy and average photon number in the four phases, are derived. We find that the excitation spectra exhibit the Nambu–Goldstone mode. We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities. To confirm the validity of the low-energy effective Hamiltonians analytically derived by us, the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.

Probing correlations in two-mode bosonic fields via Gaussian noise channels

Gaussian noise channels arise naturally in many physical situations and play an important role in information transmission involving continuous-variable quantum systems. In this work we employ Gaussian noise channels to probe and characterize correlations in two-mode bosonic fields. Based on the fact that local channels often cause more decoherence for global states than for local states due to correlations, we introduce a notion of conditional coherence relative to a local channel, which is defined as the difference between the global and local decoherence caused by the channel. We discuss its connections with quantum discord and relative quantum Fisher information and propose a class of correlation quantifiers for two-mode bosonic states in terms of conditional coherence relative to local Gaussian noise channels. We prove that any nonproduct state exhibits such correlations and show that these correlation quantifiers are measures of total correlations, which may include both classical and quantum parts. We further illustrate these correlation quantifiers through several typical two-mode bosonic states and make a comparative study between these correlation quantifiers and other known ones such as entanglement and discord.

Quantum entanglement of photons on free electrons

The quantum entanglement of photons is one of the interesting and important manifestations of the quantum world, which is already being used in quantum technologies. The study of new methods of quantum entanglement of photons is one of the promising areas of quantum optics. In this work, it is shown that photons, in a two-mode electromagnetic field, can be quantum entangled when they interact with free electrons. It is shown that the quantum entanglement of such photons can be very large and such photons can be a good source of high quantum entanglement. In addition, it is shown that free electrons can be a beam splitter for a two-mode electromagnetic field.

The Thermo-field Dynamics Method for Electron with Two-mode Electromagnetic Field

The quick progress in quantum entanglement research allows us not one to study quantum systems down to N-bodies but also to take a new look at these systems in different branches of physics; particularly the statistical thermodynamics where the application of the thermo-field dynamics (<I>TFD</I>) method to the investigation of entanglement is fruitful. Because the traditional methods based on the identification of a specific parameter show their limit. The process using (<I>TFD</I>) facilitates the understanding of entanglement because it focuses directly on the eigenstate of the system and it is useful in the equilibrium and the non-equilibrium states also. In this context, the (<I>TFD</I>) method is used in this paper to analyze entanglement of an electron interacting with a two-mode electromagnetic field assimilated to an electron with two harmonic oscillators. Entanglement entropies are derived between concerned, not concerned harmonic oscillator and electron compute when the system is in a thermodynamic equilibrium and non-equilibrium state. For the equilibrium case, an increase in the number of particles per unit volume increases the quantum entanglement consequently entanglement appears more important for the couple oscillator-electron than the one electron, this trend is reversed for the non-equilibrium case. By respecting the entanglement parameters, such results allow us to know the relative equilibrium state of the overall system.

QUANTUM TELEPORTATION OF ENTANGLED STATES VIA GENERALIZED PHOTON-ADDED PAIR COHERENT STATE

In this paper, we study the quantum teleportation of an unknown atomic state based on the two-photon Jaynes-Cummings model, consisting of an effective two-level atom with a two-mode field in the generalized photon-added pair coherent state (GPAPCS). By applying the detecting method, we use a scheme that includes two two-level atoms and a cavity field to teleport the unknown atomic state from a sender to a receiver. The results show that the number of photons added to the field and the intensity of the initial field influence the average fidelity and success probability of the teleportation process. The time-evolution dependence of the average fidelity is also considered and compared for the field in the pair coherent state and in the GPAPCS.

Inside Front Cover: Observation of Robust Polarization Squeezing via the Kerr Nonlinearity in an Optical Fiber (Adv. Quantum Technol. 3/2023)

The cover shows the evolution of the state of the light field represented on the Poincaré sphere (green) due to the nonlinear Kerr interaction described in article number 2200143 by Nikolay Kalinin, Gerd Leuchs, and co-workers. The quantum uncertainty of the initial coherent two-mode laser field is the small grey sphere on the larger Poincaré sphere which develops into the orange squeezed ellipsoid.

Efficient and energy stable numerical schemes for the two-mode phase field crystal equation

In this paper, we propose four time marching schemes for the two-mode phase field crystal equation with the periodic boundary condition. The first- and second-order schemes are based on the stabilized semi-implicit approach with a combination of the backward Euler method, Crank–Nicolson method, and second-order backward differentiation formula, respectively. Based on the convex splitting method and third-order backward differentiation formula, a third-order scheme is developed. Different stabilized terms are added so that the energy stability of the proposed schemes can be guaranteed. Theoretically, the unique solvability and energy stability of the proposed schemes are rigorously proved. The error estimate of the first-order scheme is also given. Various numerical examples and simulations in the 2D and 3D cases are presented to demonstrate the accuracy, stability, and efficiency of the proposed schemes.

Geometry, quantum correlations, and phase transitions in the Λ-atomic configuration

The quantum phase diagram for a finite three-level system in the Λ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility and entanglement, applied to the reduced density matrix of the matter sector of the system. The quantum phases are explained by emphasizing the spontaneous symmetry breaking along the separatrix. Additionally, a description of the reduced density matrix of one atom in terms of a simplex allows a geometric representation of the entanglement and purity properties of the system. These concepts are calculated for both, the symmetry-adapted variational coherent states and the numerical diagonalisation of the Hamiltonian, and compared. The differences in purity and entanglement obtained in both calculations can be explained and visualised by means of this simplex representation.

Effect of Mth coherent state on the interaction between two two-level atoms and two-mode quantized field

The objective of this work is to measure the influence of the Mth coherent state on the optics model of two atoms interacting with two-mode quantized field. Also, two atoms interacting together is included in this optics model. The time-dependent wave function is computed analytically. The two-mode quantized field is in the Mth coherent state while the two atoms have two levels. The influence of the Mth coherent state on the quantum model is measured via studying the atomic inversion, von Neumann entropy, variance squeezing, correlation function and Husimi function. The influence of each mode of the quantized field separately and both modes together are discussed. The statistical measures indicate that the nonclassical quantized features increase in the presence of the Mth coherent state, and it features a controlling mechanism. This study opens up a wide range of a large number of serious applications for the quantum optics models.

A structure-preserving and variable-step BDF2 Fourier pseudo-spectral method for the two-mode phase field crystal model

For the two-mode phase field crystal models, the evolutions of the solutions and energy vary fast at certain time. To resolve varying time scales efficiently and reduce the computational cost, a variable-step BDF2 Fourier pseudo-spectral method is proposed. It is shown that the fully-discrete scheme is volume-conserving and unconditional energy-stable. Moreover, a robust error estimate is established by using the discrete orthogonal convolution kernels and the corresponding convolution inequalities. Numerical experiments by using the random and adaptive time-stepping strategies are presented to confirm the effectiveness of the scheme.

Entanglement and Fisher information for a two-atom system interacting with deformed fields in correlated two-mode states

Based on the deformed Heisenberg algebra, we propose a nonlinear Tavis–Cummings model (TCM) which is obtained from the usual TCM by using deformed operators of a two-mode field. Such a generalization of the TCM considers the interaction of a two-atom system with a correlated two-mode field in the presence of time-dependent coupling. We show the effect of the deformation and interaction process between the two modes and atoms on the time variation of current interest quantum phenomena, such as entanglement and parameter estimation. The obtained results provide a new approach to manipulate the interaction between the atoms and fields that can be useful for considerable applications in quantum optics and information.

Dynamics of quantum effects in a three-level system interacting with two-mode time-dependent fields including parametric down conversion and damping

In this article, the interaction between a time-dependent damping field and Λ-type of three-level atom is investigated. The effect of the atom and the fields' parameters on the behaviour of the atomic inversion, the generated entanglement between the atom and the cavity modes, the Pancharatnam geometric phase are discussed. It is shown that the phenomena of the collapses and revivals for the three physical quantities depend on the time-dependent coupling and the damping parameter. The long-lived behaviour of the non-classical correlation is observed either on the presence of only time-dependent coupling or at large values of the damping parameter. The damping effect has different features on the three phenomena, where the atomic inversion decays, the upper bounds of entanglement increases and increases periodic time of the Pancharatnam geometric phase.

Nonlinear interaction of a three-level atom with a two-mode field in an optomechanical cavity: Field and mechanical mode dissipations

In this paper we investigate the dynamics of f-deformed interaction (nonlinear atom-field coupling) of a three-level atom in V-configuration with a two-mode quantized field in the presence and absence of Kerr medium as well as the phonon and photon dissipations in an optomechanical cavity. We solve the associated time-dependent Schrödinger equation and arrive at the corresponding state vector at arbitrary time. In the continuation, we evaluate several nonclassical properties including atomic von Neumann entropy, atomic information entropy squeezing, sub-Poissonian statistics and atomic squeezing, numerically. Our numerical results show that, with the parameters at our disposal, we can adjust the above-mentioned properties according to our purposes. For instance, significant amount of von Neumann entropy may be achieved, in the linear and nonlinear atom-field coupling, without or even with considered dissipations. However, atomic information entropy squeezing can be observed only in the presence of nonlinear atom-field coupling by tuning the proper values of Lamb-Dicke parameter. Atomic squeezing can be seen in the presence or absence of linear and nonlinear atom-field coupling. Negative values of Mandel parameter, showing the sub-Poissonian statistics as the nonclassicality of the field can be observed with and without nonlinear atom-field coupling, however, the presence of Lamb-Dicke nonlinearity can make this effect more visible. Unless the atomic information entropy squeezing, in all above-mentioned physical phenomena stability of the evaluated parameters can be accessible via choosing appropriate parameters containing Lamb-Dicke parameter, Kerr effects, dissipation parameters, laser pumps and photon-phonon coupling.

A double Λ-five-level moving atom interacting with a two-mode field in the presence of damping and nonlinear Kerr medium

In this paper, we present the interaction between a five-level [Formula: see text]-configuration atom and a two-mode quantized field in the presence of the damping with the nonlinearity. According to the generalized nonlinear Jaynes–Cummings model (JCM) and the analytical solution of the Schrödinger equation, the general formula of the wave function for this system under special conditions, where the atom (the field) is initially prepared in the excited state (coherent state), has been found. Under some particular conditions, the five-level [Formula: see text]-type atom can be reduced to the three-level [Formula: see text]-type atom. Some physical aspects of the atom-field entangled state showing the entanglement degree, such as the field entropy. Moreover, we evaluate some of their non-classical statistical aspects such as atomic inversion. The effects of the physical parameters such as a Kerr medium, detuning parameter and the intensity-dependent coupling on the temporal behavior of the latter mentioned non-classical statistical aspects have been explored. We show that by choosing the evolved parameters in the interaction process, each of the above non-classical statistical features can be treated. We found that the parameters have an important influence on the properties of these phenomena.

A study of a nonlinear interaction between a two-mode cavity field and ♢-type four-level with field damping

In this paper, the effects of the field damping and Kerr-like medium on a system of a four-level atom in the [Formula: see text]-type interacting nonlinearly with a two-mode field are studied. Analytical solution of the system of differential equations resulting from the Schrödinger equation is obtained. The effects of detuning parameters, Kerr-like parameter, coupling function and damping rate are discussed for atomic population inversion, the second-order correlation function, Shannon information entropy, and linear entropy. Under justifiable all conditions, extreme entanglement states may appear periodically with the evolution of time. The arrival of the quantum system to a pure state can be controlled by variations of the Kerr medium and the damping parameters. The results also exhibit that the periods of strong and weak entanglement between the parts of the system are achieved during the periods of collapses and revivals of the atomic population inversion. Moreover, the photon distribution changes from non-classical to classical by increasing the damping rate.

Evaluation of grain boundary energy, structure and stiffness from phase field crystal simulations

A two-mode phase field crystal (PFC) model is employed to investigate the equilibrium configurations of a range of grain boundaries in fcc-structured materials. A total of 80 different symmetrical tilt grain boundaries are evaluated by PFC simulations in 3D and the results are shown to agree well with data taken from the literature, both regarding the variation of grain boundary energy and also in terms of the resulting grain boundary structures. This verification complements existing PFC studies which are almost exclusively focused either on grain boundaries found in 2D systems or in bcc lattices in 3D. The present work facilitates application of PFC in the analysis of grain boundary mechanics in an extended range of materials, in particular such mechanics that take place at extended time scales not tractable for molecular dynamics (MD) simulations. In addition to the verification of predicted grain boundary energies and structures, wavelet transforms of the density field are used in the present work to obtain phase fields from which it is possible to identify grain boundary fluctuations that provide the means to evaluate grain boundary stiffness based on the capillarity fluctuation method. It is discussed how PFC provides benefits compared to alternative methods, such as MD simulations, for this type of investigations.