Search Results (30)

We built a discrete model that simulates the ubiquitous competition between the free internal evolution of a two-level system and the decoherence induced by the interaction with its surrounding environment. It is aimed at being as universal as possible, so that no specific Hamiltonian is assumed. This leads to an analytic criterion, depending on the level of short time decoherence, allowing one to determine whether the system will freeze due to the Zeno effect. We checked this criterion on several classes of functions which correspond to different physical situations. In the most generic case, the free evolution wins over decoherence, thereby explaining why the universe is indeed not frozen. We finally make a quantitative comparison with the continuous model of Presilla, Onofrio and Tambini, based on a Lindblad’s master equation, a find good agreement at least in the low coupling regime. Full article

In the present manuscript, we demonstrate the potential to control and enhance the accuracy of parameter estimation (P-E) in a two-level atom (TLA) immersed in a cavity field that interacts with another cavity. We investigate the dynamics of quantum Fisher information (FI), considering the influence of coupling strength between the two cavities and the detuning parameter. Our findings reveal that, in the case of a perfect cavity, a high quantum FI value can be maintained during the dynamics concerning the detuning and coupling strength parameters. The results indicate that with a proper choice of quantum model parameters, long-term protection of the FI can be achieved without being affected by decoherence. Full article

The Autler–Townes (AT) doublet, a fundamental manifestation of quantum interference effects, serves as a critical tool for studying the dynamic behavior of Rydberg atoms. Here, we investigate the asymmetry of the Autler–Townes (AT) doublet in the trap-loss fluorescence spectroscopy (TLFS) of cesium (Cs) atoms confined in a magneto-optical trap (MOT) with single-step Rydberg excitation using a 319-nm ultraviolet (UV) laser. A V-type three-level system involving the ground state $6{\mathrm{S}}_{1/2}$ (F = 4), excited state $6{\mathrm{P}}_{3/2}$ (${\mathrm{F}}^{\prime }$ = 5), and Rydberg state ($n{\mathrm{P}}_{3/2}$ (${\mathrm{m}}_{\mathrm{J}}$ = +3/2)) is theoretically modeled to analyze the nonlinear dependence of the AT doublet’s asymmetry and interval on the cooling laser’s detuning. Experiments reveal that as the cooling laser detuning ${\mathsf{\Delta }}_1$ decreases from −15 MHz to −10 MHz, the AT doublet exhibits increasing symmetry, while its interval shows a nonlinear decrease. Theoretical simulations based on the density matrix equation and Lindblad master equation align closely with experimental data, confirming the model’s validity. This study provides insights into quantum interference dynamics in multi-level systems and offers a systematic approach for optimizing precision measurements in cold atom spectroscopy. Full article

We use superoperator techniques to solve the master equation for the interaction between a single-mode quantized field and a single mechanical mode of a moving mirror, which is coupled to a zero-temperature reservoir that damps its amplitude. The solution we provide allows for its application in any initial state of the combined system. Furthermore, we obtain solutions to the stationary master equation for an initial number state for the field that is consistent with the result obtained for the average number of phonons. Full article

In this study, we present an exact solution to the Lindblad master equation describing the interaction of two quantized electromagnetic fields in a decaying cavity coupled to a thermal reservoir at a finite temperature. The solution is obtained using the superoperator technique, leveraging commutation relations to factorize the exponential of the Lindblad superoperators into a product of exponentials. To demonstrate the applicability of this approach, we analyze the dynamics of the system both analytically and numerically for two initial conditions: nonentangled and entangled coherent states, exploring their temporal evolution. Additionally, we employ entropy and quantum discord analysis to characterize quantum correlations and analyze the behavior of entanglement (or lack thereof) during the evolution. This comprehensive analysis provides valuable insights into the behavior of open quantum systems and their interaction with the environment. Full article

In a dissipative regime, we study the properties of several qubits coupled to a driven resonator in the framework of a Jaynes–Cummings model. The time evolution and the steady state of the system are numerically analyzed within the Lindblad master equation, with up to several million components. Two semi-analytical approaches, at weak and strong (semiclassical) dissipations, are developed to describe the steady state of this system and determine its validity by comparing it with the Lindblad equation results. We show that the synchronization of several qubits with the driving phase can be obtained due to their coupling to the resonator. We establish the existence of two different qubit synchronization regimes: In the first one, the semiclassical approach describes well the dynamics of qubits and, thus, their quantum features and entanglement are suppressed by dissipation and the synchronization is essentially classical. In the second one, the entangled steady state of a pair of qubits remains synchronized in the presence of dissipation and decoherence, corresponding to the regime non-existent in classical synchronization. Full article

Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase space description. We perform a numerical inspection of the Wehrl entropy for the benchmark problem of a harmonic potential, since the existence of a steady state and its analytical formula have been proven theoretically in this case. When there is friction in the noise terms, no theoretical results on the monotonicity of absolute entropy are available. We provide numerical results of the time evolution of the entropy in the case with friction using a stochastic (Euler–Maruyama-based Monte Carlo) numerical solver. For all the chosen initial conditions studied (all of them Gaussian states), up to the inherent numerical error of the method, one cannot disregard the possibility of monotonic behavior even in the case under study, where the noise includes friction terms. Full article

Within the framework of the quantum-statistical approach, utilizing both non-Hermitian Hamiltonian and Lindblad’s jump operators, one can derive various generalizations of the von Neumann equation for reduced density operators, also known as hybrid master equations. If one considers the evolution of pure states only, i.e., disregarding the coherence between states and spontaneous transitions from pure to mixed states, then one can resort to quantum-mechanical equations of the Schrödinger type. We derive them from the hybrid master equations and study their main properties, which indicate that our equations have a larger range of applicability compared to other generalized Schrödinger equations proposed hitherto. Among other features, they can describe not only systems which remain in the stationary eigenstates of the Hamiltonian as time passes, but also those which evolve from those eigenstates. As an example, we consider a simple but important model, a quantum harmonic oscillator driven by both Hamiltonian and non-Hamiltonian terms, and derive its classical limit, which turns out to be the damped harmonic oscillator. Using this model, we demonstrate that the effects of dissipative environments of different types can cancel each other, thus resulting in an effectively dissipation-free classical system. Another discussed phenomenon is whether a non-trivial quantum system can reduce to a classical system in free motion, i.e., without experiencing any classical Newtonian forces. This uncovers a large class of quantum-mechanical non-Hamiltonian systems whose dynamics are not determined by conventional mechanics’ potentials and forces, but rather come about through quantum statistical effects caused by the system’s environment. Full article

This article is devoted to developing an approach for manipulating the von Neumann entropy $S\left(\rho \right(t\left)\right)$ of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy $S\left(\rho \right(T\left)\right)$; (b) steering $S\left(\rho \right(T\left)\right)$ to a given target value; (c) steering $S\left(\rho \right(T\left)\right)$ to a target value and satisfying the pointwise state constraint $S\left(\rho \left(t\right)\right)\le \overline{S}$ for a given $\overline{S}$; (d) keeping $S\left(\rho \right(t\left)\right)$ constant at a given time interval. Under the Markovian dynamics determined by a Gorini–Kossakowski–Sudarshan–Lindblad type master equation, which contains coherent and incoherent controls, one- and two-step gradient projection methods and genetic algorithm have been adapted, taking into account the specifics of the objective functionals. The corresponding numerical results are provided and discussed. Full article

In this paper, we present a theoretical scheme for the generation and manipulation of bipartite atom–atom entanglement in a dissipative optomechanical system containing two atoms in the presence of linear and nonlinear (quadratic) couplings. To achieve the goal of paper, we first obtain the interaction Hamiltonian in the interaction picture, and then, by considering some resonance conditions and applying the rotating wave approximation, the effective Hamiltonian, which is independent of time, is derived. In the continuation, the system solution was obtained via solving the Lindblad master equation, which includes atomic, optical and mechanical dissipation effects. Finally, bipartite atom–atom entanglement is quantitatively discussed, by evaluating the negativity, which is a well-known measure of entanglement. Our numerical simulations show that a significant degree of entanglement can be reached via adjusting the system parameters. It is noticeable that the optical and mechanical decay rates play an important role in the quasi-stability and even stability of the obtained atom–atom entanglement. Full article

We consider a micromaser model of a quantum battery, where the battery is a single mode of the electromagnetic field in a cavity, charged via repeated interactions with a stream of qubits, all prepared in the same non-equilibrium state, either incoherent or coherent, with the matter–field interaction modeled by the Jaynes–Cummings model. We show that the coherent protocol is superior to the incoherent one, in that an effective pure steady state is achieved for generic values of the model parameters. Finally, we supplement the above collision model with cavity losses, described by a Lindblad master equation. We show that battery performances, in terms of stored energy, charging power, and steady-state purity, are slightly degraded up to moderated dissipation rate. Our results show that micromasers are robust and reliable quantum batteries, thus making them a promising model for experimental implementations. Full article

In this work, we consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates ${\gamma }_k\left(t\right)$ (via time-dependent spectral density of incoherent photons) for generation of single-qubit gates for a two-level open quantum system which evolves according to the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation with time-dependent coefficients determined by these coherent and incoherent controls. The control problem is formulated as minimization of the objective functional, which is the sum of Hilbert-Schmidt norms between four fixed basis states evolved under the GKSL master equation with controls and the same four states evolved under the ideal gate transformation. The exact expression for the gradient of the objective functional with respect to piecewise constant controls is obtained. Subsequent optimization is performed using a gradient type algorithm with an adaptive step size that leads to oscillating behaviour of the gradient norm vs. iterations. Optimal trajectories in the Bloch ball for various initial states are computed. A relation of quantum gate generation with optimization on complex Stiefel manifolds is discussed. We develop methodology and apply it here for unitary gates as a testing example. The next step is to apply the method for generation of non-unitary processes and to multi-level quantum systems. Full article

We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert–Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information. Full article

We study the quantum dynamics of the opened three-level su(1, 1) bosonic model. The effective non-Hermitian Hamiltonians describing the system of the Lindblad equation in the short time limit are constructed. The obtained non-Hermitian Hamiltonians are exactly solvable by the Algebraic Bethe Ansatz. This approach allows representing biorthogonal and nonorthogonal bases of the system. We analyze the biorthogonal expectation values of a number of particles in the zero mode and represent it in the determinantal form. The time-dependent density matrix satisfying the Lindblad master equation is found in terms of the nonorthogonal basis. Full article

The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action. A novel symplectic thermodynamics and information geometry known as “Lie group thermodynamics” then explains foliation structures of thermodynamics. We then infer a geometric structure for heat equation from this archetypal model, and we have discovered a pure geometric structure of entropy, which characterizes entropy in coadjoint representation as an invariant Casimir function. The coadjoint orbits form the level sets on the entropy. By using the KKS 2-form in the affine case via Souriau’s cocycle, the method also enables the Fisher metric from information geometry for Lie groups. The fact that transverse dynamics to these symplectic leaves is dissipative, whilst dynamics along these symplectic leaves characterize non-dissipative phenomenon, can be used to interpret this Lie group thermodynamics within the context of an open system out of thermodynamics equilibrium. In the following section, we will discuss the dissipative symplectic model of heat and information through the Poisson transverse structure to the symplectic leaf of coadjoint orbits, which is based on the metriplectic bracket, which guarantees conservation of energy and non-decrease of entropy. Baptiste Coquinot recently developed a new foundation theory for dissipative brackets by taking a broad perspective from non-equilibrium thermodynamics. He did this by first considering more natural variables for building the bracket used in metriplectic flow and then by presenting a methodical approach to the development of the theory. By deriving a generic dissipative bracket from fundamental thermodynamic first principles, Baptiste Coquinot demonstrates that brackets for the dissipative part are entirely natural, just as Poisson brackets for the non-dissipative part are canonical for Hamiltonian dynamics. We shall investigate how the theory of dissipative brackets introduced by Paul Dirac for limited Hamiltonian systems relates to transverse structure. We shall investigate an alternative method to the metriplectic method based on Michel Saint Germain’s PhD research on the transverse Poisson structure. We will examine an alternative method to the metriplectic method based on the transverse Poisson structure, which Michel Saint-Germain studied for his PhD and was motivated by the key works of Fokko du Cloux. In continuation of Saint-Germain’s works, Hervé Sabourin highlights the, for transverse Poisson structures, polynomial nature to nilpotent adjoint orbits and demonstrated that the Casimir functions of the transverse Poisson structure that result from restriction to the Lie–Poisson structure transverse slice are Casimir functions independent of the transverse Poisson structure. He also demonstrated that, on the transverse slice, two polynomial Poisson structures to the symplectic leaf appear that have Casimir functions. The dissipative equation introduced by Lindblad, from the Hamiltonian Liouville equation operating on the quantum density matrix, will be applied to illustrate these previous models. For the Lindblad operator, the dissipative component has been described as the relative entropy gradient and the maximum entropy principle by Öttinger. It has been observed then that the Lindblad equation is a linear approximation of the metriplectic equation. Full article