Initial Coherent State Research Articles

Entropy variances of pure coherent states in the diffusion channel

Abstract Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, we solve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation of its analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in the diffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions in the diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes of the initial coherent states.

Approximate analytic solution of the dissipative semiclassical Rabi model near the three-photon resonance and comparison with the quantum behavior

We consider the semiclassical Rabi model in the presence of Markovian dissipation and study the system dynamics in the vicinity of the three-photon resonance, when the laser frequency is nearly one third of the atomic transition frequency. Closed analytic expressions are derived for the system density operator, in excellent agreement with exact numeric results. We also study semi-analytically the dynamics of the quantum Rabi model for the initial coherent state, and show how the semiclassical behavior emerges from the quantum three-photon Rabi oscillations as the amplitude of the coherent state increases.

Exploring optical tomography dynamics for a dissipative coherent cavity in interaction with two-level atomic system

In this paper, we explore the optical tomography and quantum coherence dynamics for a coherent cavity field interacting with a two-level atom via intensity dependent coupling. We derive a specific solution to the master equation for the Jaynes–Cummings model, considering cavity damping. This solution reveals how the atom coherent-cavity interactions can produce new coherent states when the initial dissipative cavity-field state is coherent state or even coherent state. The effects of the atom-coherent-cavity interactions and the cavity damping, on the dynamics of the initial coherent state optical tomography and coherence is examined. In addition to the nonclassical properties, the atom-cavity interactions have a remarkable capacity to form distinct cavity field states linked to certain optical tomography distributions. Additionally, we investigate the maximal optical tomography dynamics for coherent state and even coherent state considering a range of cavity damping and detuning values.

Boosting energy transfer between quantum devices through spectrum engineering in the dissipative ultrastrong coupling regime

The coherent energy transfer between two quantum devices (a quantum charger and a quantum battery) mediated by a photonic cavity is investigated, in presence of dissipative environments, with particular focus on the ultrastrong coupling regime. Here, very short transfer times and high charging power can be achieved in comparison with the usually addressed weak coupling case. Such phenomenology is further magnified by the presence of level crossings appearing in the energy spectrum and which reveal very robust against dissipative environmental effects. Moreover, by carefully controlling the physical parameters of the model, e.g., the matter-radiation coupling and the frequencies of the system, it is possible to tune these crossings making this device more flexible and experimentally feasible. Finally to broaden our analysis, we assume the possibility of choosing between a Fock and a coherent initial state of the cavity, with the latter showing better energetic performances. Published by the American Physical Society 2024

Temporal evolution of a driven optomechanical system in the strong coupling regime

We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, G/ω m , is not negligible compared to one, i.e., the system operates in the strong-coupling regime. Due to the forcing term, the interaction picture Hamiltonian contains the number operator in the exponents, and in order to deal with it, we approximate these exponentials by their average values taken between initial coherent states. Our approximation is justified when we compare our results with the numerical solution of the number of photons, phonons, Mandel parameter, and the Wigner function, showing an excellent agreement. In contrast to other works, our approach does not use the standard linearized description in the optomechanical interaction. Therefore, highly non-classical (non-Gaussian) states of light emerge during the time evolution.

Distribution dynamics of fisher and Wigner–Yanase information correlations of two qubits coupled to an open superconducting cavity

In this paper, we explore distribution dynamics of two-qubit Fisher and skew information correlations of a dissipative microwave cavity field interacting with two charged superconducting qubits. Besides the negativity function, non-classical correlations beyond entanglement are studied using local quantum Fisher information (LQFI) and local quantum uncertainty (LQU). We find that the two-qubit non-classical correlations are sensitive to qubit–qubit distribution angle, two-qubit dissipation parameter, and initial coherent state intensity. The phenomena of frozen quantum correlations, sudden death or birth, as well as revival dynamical maps are feasible in the current two-qubit state when exposed to a microwave cavity. The non-classical correlations and entanglement have been found damped under the two-qubit dissipation appearance in the field. For the increasing strength of coherence intensity of the field, the two-qubit non-classical correlations functions remain to emerge quickly and oscillate with higher frequency, although with the least amplitudes. Interestingly, unlike the non-classical correlations, negativity does not emerge against higher coherence strengths of the cavity and remains completely zero. Finally, for the least dissipation and higher coherence strength, one can readily generate non-classical two-qubit states employing a microwave cavity.

Quantum Zeno effect in a classical viscous medium

Based on the formalism of quasi-classical canonical quantization, the translational motion of a particle in a viscous medium is studied. The case is considered when, in addition to the resistance forces, an external conservative force acts on the particle. It is shown that due to the forces of viscous resistance of the medium, the initial coherent state of the particle does not decay. This behavior of the wave function is accompanied by a partial suppression of the quantum properties of the particle. In this case, a viscous medium should be considered as a classical device that continuously measures the state of a particle. Therefore, the stability of the coherent state of a particle can be interpreted as a manifestation of the quantum Zeno effect.

Quantum correlations beyond entanglement between two moving atoms interacting with a coherent cavity

Studying the ability of atom-photon interactions, especially in two two-level atomic systems, to generate quantum information resources has recently become an important research topic in quantum information science. Therefore, this paper explores the ability of two moving atoms coupling with a coherent field through a two-photon transition to generate atomic quantum correlations by using local quantum uncertainty (LQU), local quantum Fisher information (LQFI) as well as logarithmic negativity (LN). Schrödinger equation is used to obtain the time evolution of the atom-cavity-atom interactions with an initial coherent cavity state and an initial atomic uncorrelated pure state. The generation of atomic LQU, LQFI, and LN correlations are exactly examined under the unitary interaction parameter effects, including the atom-cavity coupling strengths, the cavity field half-wave number, and the initial coherent state intensity. The atom-cavity-atom interaction parameters lead to notable changes in the amplitudes, speed, and regularity of the LQU, LQFI, and LN dynamics, which can be enhanced by increasing the initial coherent intensity. The cavity field half-wave number leads to generating atomic quantum correlations with regular oscillatory behavior. The sudden death-birth phenomenon of the logarithmic negativity depends on the atom-cavity-atom interaction and the atomic location parameter.

Quantum coherence controls the nature of equilibration and thermalization in coupled chaotic systems.

A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax toward an equilibrium. It is found that quantum coherence of the initial product states in the energy eigenbasis of the subsystems-quantified by the off-diagonal elements of the subsystem density matrices-can be viewed as a resource for equilibration and thermalization as manifested by the entanglement generated. Results are given for four distinct perturbation strength regimes, the ultraweak, weak, intermediate, and strong regimes. For each, three types of tensor product states are considered for the initial state: uniform superpositions, random superpositions, and individual subsystem eigenstates. A universal timescale is identified involving the interaction strength parameter. In particular, maximally coherent initial product states (a form of uniform superpositions) thermalize under time evolution for any perturbation strength in spite of the fact that in the ultraweak perturbative regime the underlying eigenstates of the system have a tensor product structure and are not at all thermal-like; though the time taken to thermalize tends to infinity as the interaction vanishes. Moreover, it is shown that in the ultraweak regime the initial entanglement growth of the system whose initial states are maximally coherent is quadratic-in-time, in contrast to the widely observed linear behavior.

Quantum Oscillator at Temperature T and the Evolution of a Charged-Particle State in the Electric Field in the Probability Representation of Quantum Mechanics

A short review constructing the probability representation of quantum mechanics is given, and examples of the probability distributions describing the states of quantum oscillator at temperature T and the evolution of quantum states of a charged particle moving in the electric field of an electrical capacitor are considered. Explicit forms of time-dependent integrals of motion, linear in the position and momentum, are used to obtain varying probability distributions describing the evolving states of the charged particle. Entropies corresponding to the probability distributions of initial coherent states of the charged particle are discussed. The relation of the Feynman path integral to the probability representation of quantum mechanics is established.

Coherent radiation of photons by particle wave packets

The radiation of photons by electrons is investigated in the framework of quantum electrodynamics up to the second order in the coupling constant e. The N-particle, coherent, and thermal initial states are considered and the forms of the electron wave packets are taken into account. The explicit expressions for the intensity of radiation and the inclusive probability to record a photon are obtained. It is found that there are three processes in this order of perturbation theory where the electron wave packet radiates coherently and can be regarded as a charged fluid even on integrating over the final states of the electron, i.e., in considering the inclusive probabilities and intensity of radiation. These processes are stimulated radiation by an electron, coherent radiation from a beam of particles, and reradiation of a photon in the Compton process. We obtain the explicit expressions for the intensity of radiation and the inclusive probability to record a photon for these processes. As particular cases, we consider: stimulated transition radiation produced by an electron wave packet traversing a mirror and backlighted by a laser wave, reradiation of photons in a coherent state by an electron wave packet. In the latter case, we deduce that the wave packet of a single electron can be endowed with the susceptibility tensor and this tensor has the same form as for an electron plasma in the small recoil limit.

Geometric imaginary and quasi-probability functions of multi-component Schrödinger cat state

Superposition is one of unusual features in quantum mechanics. This paper investigates the properties of multi-component Schrödinger cat state, generated by amplitude dispersion. The geometrical imaginary of the multi-component Schrödinger cat state is studied, and the entropy of the geometrical imaginary is proposed. This entropy is inverse proportional to the amplitude of the initial coherent state in the large amplitude regime. Additionally, the superposition of the multi-component cat state can be vividly displayed by the Wigner function and the Pegg–Barnett phase operator.

Quantum metrology with a non-linear kicked Mach–Zehnder interferometer

We study the sensitivity of a Mach–Zehnder interferometer that contains in addition to the phase shifter a non-linear element. By including both elements in a cavity or a loop that the light transverses many times, a non-linear kicked version of the interferometer arises. We study its sensitivity as function of the phase shift, the kicking strength, the maximally reached average number of photons, and damping due to photon loss for an initial coherent state. We find that for vanishing damping Heisenberg-limited scaling of the sensitivity arises if squeezing dominates the total photon number. For small to moderate damping rates the non-linear kicks can considerably increase the sensitivity as measured by the quantum Fisher information per unit time.

Dependent random variables in quantum dynamics

We consider the many-body time evolution of weakly interacting bosons in the mean field regime for initial coherent states. We show that bounded k-particle operators, corresponding to dependent random variables, satisfy both a law of large numbers and a central limit theorem.

Vibrational response functions for multidimensional electronic spectroscopy in the adiabatic regime: A coherent-state approach.

Multi-dimensional spectroscopy represents a particularly insightful tool for investigating the interplay of nuclear and electronic dynamics, which plays an important role in a number of photophysical processes and photochemical reactions. Here, we present a coherent state representation of the vibronic dynamics and of the resulting response functions for the widely used linearly displaced harmonic oscillator model. Analytical expressions are initially derived for the case of third-order response functions in an N-level system, with ground state initialization of the oscillator (zero-temperature limit). The results are then generalized to the case of Mth order response functions, with arbitrary M. The formal derivation is translated into a simple recipe, whereby the explicit analytical expressions of the response functions can be derived directly from the Feynman diagrams. We further generalize to the whole set of initial coherent states, which form an overcomplete basis. This allows one, in principle, to derive the dependence of the response functions on arbitrary initial states of the vibrational modes and is here applied to the case of thermal states. Finally, a non-Hermitian Hamiltonian approach is used to include in the above expressions the effect of vibrational relaxation.

Semiclassical gravitational collapse of a radially symmetric massless scalar quantum field

We present a method to study the semiclassical gravitational collapse of a radially symmetric scalar quantum field in a coherent initial state. The formalism utilizes a Fock space basis in the initial metric, is unitary and time reversal invariant up to numerical precision. It maintains exact compatibility of the metric with the expectation values of the energy momentum tensor in the scalar field coherent state throughout the entire time evolution. We find a simple criterion for the smallness of discretization effects, which is violated when a horizon forms. As a first example, we study the collapse of a specific state in the angular momentum $l=0$ approximation. Outside the simulated volume it produces a Schwarzschild metric with $r_s \sim 3.5 \ell_p$. We see behaviour that is compatible with the onset of horizon formation both in the semiclassical and corresponding classical cases in a regime where we see no evidence for large discretization artefacts. In our example setting, we see that quantum effects accelerate the possible horizon formation and move it radially outward. We find that this effect is robust against variations of the radial resolution, the time step, the volume, the initial position and shape of the inmoving state, the vacuum subtraction, the discretization of the time evolution operator and the integration scheme of the metric. We briefly discuss potential improvements of the method and the possibility of applying it to black hole evaporation. We also briefly touch on the extension of our formalism to higher angular momenta, but leave the details and numerics for a forthcoming publication.

Entanglement of two superconducting qubits induced by a thermal noise of a cavity with Kerr medium taking into account the atomic coherence

The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence of Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.

Photon scattering from a quantum acoustically modulated two-level system

We calculate the resonance fluorescence signal of a two-level system coupled to a quantized phonon mode. By treating the phonons in the independent boson model and not performing any approximations in their description, we also have access to the state evolution of the phonons. We confirm the validity of our model by simulating the limit of an initial quasi-classical coherent phonon state, which can be compared to experimentally confirmed results in the semiclassical limit. In addition, we predict the photon scattering spectra in the limit of purely quantum mechanical phonon states by approaching the phononic vacuum. Our method further allows us to simulate the impact of the light scattering process on the phonon state by calculating Wigner functions. We show that the phonon mode is brought into characteristic quantum states by the optical excitation process.

Nonclassicality dynamics of a dissipative cavity field containing two qubits with Kerr medium: Linear and Wehrl phase entropies

An analytical solution for a dissipative cavity field interacting with two qubits (TQs) in presence of Kerr-like medium is obtained. The super-operator method is used to obtaining the field density matrix elements under the dispersive approximation. Linear entropy is calculated to determine the entanglement between the cavity field and the TQs. Moreover, the Wehrl entropy and Wehrl phase distribution are discussed to discover the nonclassicality dynamics of a dissipative cavity field. It is found that the Kerr medium and the dissipation reduce the generated quantum coherence due to the qubit–cavity interactions. It is possible to control the ability of cavity–qubit interactions to generate quantum coherence by the mean photon number of the initial coherent cavity state. Moreover, the nonclassicality of the initial coherent state reduces the dissipative and the Kerr medium effects.

Partial stability of induced entanglement in an off-resonance qutrit-cavity system with nonlinear coupling and intrinsic decoherence

In this article, we introduce an analytical description for the nonlinear off-resonance qutrit-cavity system through intensity-dependent nonlinear coupling under intrinsic decoherence. When the cavity is initially in coherent and even coherent states. The dynamics of the negativity entanglement, in the off-resonance qutrit-cavity system, is investigated under the physical parameters of the qutrit-cavity detuning, the intrinsic decoherence as well as the initial cavity coherent states. It is found that the ability of the off-resonance qutrit-cavity interaction to generate the entanglement, depends on the physical parameters. The high nonclassicality of the even coherent state can enhance the generated entanglement and its stability. For the intrinsic decoherence, the amount and the stability of the generated qutrit-cavity entanglement can be controlled by the coherent field intensity of the initial cavity states.