We show, by explicit examples, that the Jaynes inference scheme based on maximization of entropy can produce inseparable states even if there exists a separable state compatible with the measured data. It can lead to problems with processing of entanglement. The difficulty vanishes when one uses inference scheme based on minimization of entanglement.
We investigate entanglement dynamics and properties of double Jaynes-Cummings model. In particular we study the dynamics of double Jaynes-Cummings model based on geometric invariants for four qubits. We show that these geometric invariants provide us with useful information about different types of entanglement during the quantum evolution of the system.
We investigate entanglement dynamics of two isolated atoms, each in its own Jaynes-Cummings cavity. We show analytically that initial entanglement has an interesting subsequent time evolution, including the so-called sudden death effect.
This paper provides a scheme for generating maximally entangled qubit states in the anti-Jaynes-Cummings interaction mechanism, so called entangled anti-polariton qubit states. We demonstrate that in an initial vacuum-field, Rabi oscillations in a cavity mode in the anti-Jaynes-Cummings interaction process, occur in the reverse sense relative to the Jaynes-Cummings interaction process and that time evolution of entanglement in the anti-Jaynes-Cummings interaction process takes the same form as in the Jaynes-Cummings interaction process. With the generated anti-polariton qubit state as one of t…
Recently, it has been known that a quantum entangled state plays an important role in the field ofquantum information theory such as quantum teleportation and quantum computation. The research on quantifying entangled states has been done by several measures. In this letter, we will adopt the method using quantum mutual entropy to measure the degree of entanglement of Jaynes-Cummings model.
We study in detail entanglement properties of the Jaynes-Cummings model assuming a two-level atom (qubit) interacting with the first $N$ levels of an electromagnetic field mode (qudit) in a cavity. In the Jaynes-Cummings model, the number operator is the conserved quantity that allows for the exact diagonalization of the Hamiltonian and thus we study states that commute with this conserved quantity and whose structure is preserved under the Jaynes-Cummings dynamics. Contrary to the common belief, we show that there are bound entangled states that satisfy the symmetries imposed by the conservat…
We provide the first solution of a time-dependent metric operator for the non-Hermitian Jaynes-Cummings Hamiltonian. We use this solution to calculate the entanglement between two identical isolated such Hamiltonians. The presence of a non-Hermitian interaction term leads to a spontaneously broken $\mathcal{PT}$-symmetric regime which manifests itself in the exotic time-evolution of entanglement. When the symmetry is broken, oscillatory modes transition into decay. As such that there is a drastic difference in behaviour between the broken and unbroken regimes.
We study a particular example considered in {[Phys. Rev. A {\bf 59,} 1799 (1999)]}, concerning the statistical inference of quantum entanglement using the Jaynes principle. Assume a Clauser-Horne-Simony-Holt (CHSH) Bell operator, a sum of two operators $\sqrt{2}(X+Z)$. Given only an average of the Bell-CHSH operator, we may overestimate entanglement. However, the estimated entanglement is decreased (never increases) when we use the expectation value of the operator $X$ as additional information. A minimum entanglement state is obtained by minimizing the variance of the observable $X$.
We study entanglement dynamics between four qubits interacting through two isolated Jaynes-Cummings hamiltonians, via the entanglement measure based on the wedge product. We compare the results with similar results obtained using bipartite concurrence resulting in what is referred to as "entanglement sudden death". We find a natural entanglement invariant under evolution demonstrating that entanglement sudden death is caused by ignoring (tracing over) some of the system's degrees of freedom that become entangled through the interaction.
The entanglement between two atoms in a damping Jaynes-Cummings model is investigated with different decay coefficients of the atoms from the upper level to other levels under detuning between the atomic frequency and the quantized light field frequency. The results indicate that the larger the decay coefficient is, the more quickly the entanglement decays. The detuning enhances the entanglement's average value at long times. More importantly, the results show that the so-called sudden death effect can be avoided by enhancing the detuning or the decay coefficient.
In this paper we study the evolution of the two two-level atoms interacting with a single-mode quantized radiation field, namely, two-atom multiphoton Jaynes-Cummings model when the radiation field and atoms are initially prepared in the superpostion of displaced number states and excited atomic states, respectively. For this system we investigate the atomic inversion, Wigner function, phase distribution and entanglement.
In this paper, by using the notion of negativity, we study the degree of entanglement of a two-level atom interacting with a quantized radiation field, described by the Jaynes-Cummings model (JCM). We suppose that initially the field is in a pure state and the atom is in a general mixed state. In this case the negativity fully captures the entanglement of the JCM. We investigate the case for that the initial state of the field is a coherent state. The influences of the detuning on the degree of entanglement is also examined.
An exact solution of the problem of two-atom one- and two-mode Jaynes-Cummings model with intensity-dependent coupling is presented. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom-field entanglement is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process for both models is shown. Conditions and times of disentanglement are derived.
We show how to probe multipartite entanglement in $N$ coupled Jaynes-Cummings cells where the degrees of freedom are the electronic energies of each of the $N$ atoms in separate single-mode cavities plus the $N$ single-mode fields themselves. Specifically we propose probing the combined system as though it is a dielectric medium. The spectral properties and transition rates directly reveal multipartite entanglement signatures. It is found that the Hilbert space of the $N$ cell system can be confined to the totally symmetric subspace of two states only that are maximally-entangled W states with…
We find that a suppression of the collapse and revival of population inversion occurs in response to insertion of Gaussian quenched disorder in atom-cavity interaction strength in the Jaynes-Cummings model. The character of suppression can be significantly different in the presence of non-Gaussian disorder, which we uncover by studying the cases when the disorder is uniform, discrete, and Cauchy-Lorentz. Interestingly, the quenched averaged atom-photon entanglement keeps displaying nontrivial oscillations even after the population inversion has been suppressed. Subsequently, we show that disor…
We study the entanglement dynamics of two atoms coupled to their own Jaynes-Cummings cavities in single-excitation space. Here we use the concurrence to measure the atomic entanglement. And the partial Bell states as initial states are considered. Our analysis suggests that there exist collapses and recovers in the entanglement dynamics. The physical mechanism behind the entanglement dynamics is the periodical information and energy exchange between atoms and light fields. For the initial Partial Bell states, only if the ratio of two atom-cavity coupling strengths is a rational number, the evo…
Adopting the framework of the Jaynes-Cummings model with an external quantum field, we obtain exact analytical expressions of the normally ordered moments for any kind of cavity and driving fields. Such analytical results are expressed in the integral form, with their integrands having a commom term that describes the product of the Glauber-Sudarshan quasiprobability distribution functions for each field, and a kernel responsible for the entanglement. Considering a specific initial state of the tripartite system, the normally ordered moments are then applied to investigate not only the squeezi…
Using the algebraic dynamical method, the dynamics of entanglement in an atom-field bipartite system in a mixed state is investigated. The atomic center-ofmass motion and the field-mode structure are also included in this system. We find that the larger values of the detuning and the average photon number, the smaller fluctuation of the entanglement, but the period for the evolution of the entanglement doesn't increase accordingly; It is also found that the fluctuation of the entanglement varies slightly with the atomic motion and oscillates fast with the value of the fieldmode structure and t…
The effect of retardation in the atom-field interaction on the dynamics of entanglement in a double Jaynes-Cummings system is investigated. We consider large cavities in which a finite time necessary for light to travel between the atoms and the cavity mirrors may result in retardation effects. Our results demonstrate the qualitatively new behaviour observable in the time evolution of entanglement when the retardation effects are included. Solutions for single and double excitation in the system are presented. We follow the temporal evolution of an initial entanglement and find that the evolut…
We present a mathematical procedure which leads us to obtain analytical solutions for the atomic inversion and Wigner function in the framework of the Jaynes-Cummings model with an external quantum field, for any kinds of cavity and driving fields. Such solutions are expressed in the integral form, with their integrands having a commom term that describes the product of the Glauber-Sudarshan quasiprobability distribution functions for each field, and a kernel responsible for the entanglement. Considering two specific initial states of the tripartite system, the formalism is then applied to cal…
A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes-Cummings (JC) model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom-cavity couplings and off-resonant ineractions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin correlated and anti-correlated Bell states Φand Ψ, a ful…
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level…
We study the entanglement properties of a pair of two-level atoms going through a cavity one after another. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the cavity photon field result in the final two-atom state being of a mixed entangled type. We consider the field statistics of the Fock state field, and the thermal field, respectively, inside the cavity. The entanglement of formation of the joint two-atom state is calculated for both these cases as a function of the Rabi-angle $gt$. We present a comparitive study of two-atom e…
The linear entropy, the von Neumann entropy and the atomic Wehrl entropy are frequently used to quantify entanglement in the quantum systems. These relations provide typical information on the entanglement in the Jaynes-Cummings model (JCM). In this Letter, we explain the origin of this analytically and derive a closed form for the atomic Wehrl entropy. Moreover, we show that it is more convenient to use the Bloch sphere radius for quantifying entanglement in the JCM instead of these entropic relations.
Analytical solution and entanglement swapping of a double Jaynes-Cummings model in non-Markovian environments are investigated by the timeconvolutionless master equation method. We obtain the analytical solution of this model and discuss in detail the influence of atom-cavity coupling, non-Markovian effect and initial state purity on entanglement dynamics. The results show that, in the non-Markovian environments, the entanglement between two cavities can be swapped to other bipartite subsystems by interaction between an atom and its own cavity. Due to the dissipation of environment, the entang…
We report on the geometric character of the entanglement dynamics of to pairs of qubits evolving according to the double Jaynes-Cummings model. We show that the entanglement dynamics for the initial states |ψ_0> = Cosα |1 0> + Sinα |0 1> and |ϕ_0> = Cosα |1 1> + Sinα |0 0> cover 3-dimensional surfaces in the diagram C_ij\timesC_ik\timesC_il, where C_mn stands for the concurrence between the qubits m and n, varying 0\leqα\leqπ/2. In the first case projections of the surfaces on a diagram C_ij\timesC_kl are conics. In the second case the curves can be more complex. We relate those conics with a …
The quantum thermalization of the Jaynes-Cummings (JC) model in both equilibrium and non-equilibrium open-system cases is sdudied, in which the two subsystems, a two-level system and a single-mode bosonic field, are in contact with either two individual heat baths or a common heat bath. It is found that in the individual heat-bath case, the JC model can only be thermalized when either the two heat baths have the same temperature or the coupling of the JC system to one of the two baths is turned off. In the common heat-bath case, the JC system can be thermalized irrespective of the bath tempera…
Entanglement evolution of two independent Jaynes-Cummings atoms without rotating-wave approximation (RWA) is studied by an numerically exact approach. The previous results in the RWA are essentially modified in the strong coupling regime ($g\ge 0.1$), which has been reached in the recent experiments on the flux qubit coupled to the LC resonator. For the initial Bell state with anti-correlated spins, the entanglement sudden death (ESD) is absent in the RWA, but does appear in the present numerical calculation without RWA. Aperiodic entanglement evolution in the strong coupling regime is observe…
In this paper we investigate the quantum phase properties for the coherent superposition states (Schrödinger-cat states) for two-mode multiphoton Jaynes-Cummings model in the framework of the Pegg-Barnett formalism. We also demonstrate the behavior of the Wigner ($W$) function at the phase space origin. We obtain many interesting results such as there is a clear relationship between the revival-collapse phenomenon occurring in the atomic inversion (as well as in the evolution of the $W$ function) and the behavior of the phase distribution of both the single-mode and two-mode cases. Furthermore…
In this paper, we study the interaction between the two-level atom and a bimodal cavity field, namely, two-mode Jaynes-Cummings model when the atom and the modes are initially in the atomic superposition state and two-mode squeezed vacuum state, respectively. For this system we investigate the atomic inversion, linear entropy and atomic Wehrl entropy. We show that there is a connection between all these quantities. Also we prove that the atomic Wehrl entropy exhibits behaviors similar to those of the linear entropy and the von Neumann entropy. Moreover, we show that the bipartite exhibits peri…
The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace (instead of Hilbert space), we describe time evolution of density matrices in terms of path integrals which are formally identical for quantum and classical mechanics. They only differ by the interaction contributing to the action. This allows to import tools developed for Feynman path integrals, in order to deal with superoperators instead of quantum mechanical …
We show that the Jaynes principle is indeed a proper inference scheme when applied to compound systems and will correctly produce the entangled maximum entropy states compatible with appropriate data. This is accomplished by including the dispersion of the entanglement along with its mean value as constraints and an application of the uncertainty principle. We also construct a "thermodynamic-like" description of the entanglement arising out of the maximum entropy principle.
The Jaynes-Cummings model is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight (S. J. D. Phoenix, P. L. Knight, Annals of Physics 186, 381). of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e. where the rate of change of the two are anti-correlated. This behavior contrasts with the case of pure light-matter states in which the rate…
In the previous paper, we adopted the method using quantum mutual entropy to measure the degree of entanglement in the time development of the Jaynes-Cummings model. In this paper, we formulate the entanglement in the time development of the Jaynes-Cummings model with squeezed states, and then show that the entanglement can be controlled by means of squeezing.
The method of perturbative expansion of master equation is employed to study the dissipative properties of system and of atom in the two-photon Jaynes-Cummings model (JCM) with degenerate atomic levels. The numerical results show that the degeneracy of atomic levels prolongs the period of entanglement between the atom and the field. The asymptotic value of atomic linear entropy is apparently increased by the degeneration. The amplitude of local entanglement and disentanglement is suppressed. The better the initial coherence property of the degenerate atom, the larger the coherence loss.
In this paper we have considered the interaction of a Jaynes and Cummings system with the electromagnetic field in its vacuum state and, solving the dynamical problem, we have analyzed the amount of entanglement induced in the bipartite system (atom + cavity mode) by the common electromagnetic reservoir. This has allowed us to quantitatively characterize the regime under which field-induced cooperative effects are not vanished by dissipation. Once the Decoherence Free Regime is reached, transient entanglement tends to become stationary and, therefore, usable for quantum gate implementation.
We study the dynamics of the photon entanglement, $E_{\mathrm{N}}(t)$, for the two-mode Jaynes-Cummings model in the few-photon case. The atomic transitions associated with the photons with different polarizations are assumed to be independent and, hence, the evolution of the "+"- and "-"-polarized photons is formally separable. However, due to the photons indistinguishability such interaction still leads to entanglement of initially disentangled states owing to the non-linear dependence of the characteristic frequencies on the photon population numbers. The time dependence of entanglement is …
An exact density matrix of a phase-damped Jaynes - Cummings model (JCM) with entangled Bell-like initial states formed from a model two-state atom and sets of adjacent photon number states of a single mode radiation field is presented. The entanglement of the initial states and the subsequent time evolution is assured by finding a positive lower bound on the concurrence of local 2x2 projections of the full 2xinfinity JCM density matrix. It is found that the time evolution of the lower bound of the concurrence systematically captures the corresponding collapse and revival features in atomic inv…
We study the entanglement in a system consisting of two non-interacting atoms located in separate cavities, both in their ground states. A single incoming photon has a non-zero probability of entering either of the two cavities. The Jaynes-Cummings interaction in the rotating wave approximation describes the coupling of each atom with the radiation field. We compute and analyze the atom-atom entanglement, the entanglement between the two photon modes, and also the entanglement between each atom and each photon mode. The measure of entanglement is the von Neumann entropy. For the case in which …
We develop a thermodynamical theory to describe the behavior of the entanglement between a single two-level atom with a single mode of the electromagnetic field. The resonant Jaynes-Cummings model is used to study both the entanglement thermodynamics, in particular the entanglement temperature, and its connection with the average number of photons in the optical cavity. We find that this entanglement temperature has a strong dependence with the initial conditions of the atom. We show that the entanglement temperature between the photons and the atom defined in this work is the same temperature…
With the Jaynes-Cummings model, we have studied the atom and light field quantum entanglement of multiphoton transition, and researched the effect of initial state superposition coefficient $C_{1}$, the transition photon number $N$, the quantum discord $δ$ and the nonlinear coefficient $χ$ on the quantum entanglement degrees. We have given the quantum entanglement degrees curves with time evolution, and obtained some results, which should have been used in quantum computing and quantum information.
In this paper, the 2+1 Dirac-Moshinsky oscillator (2+1 DMO) coupled to an external isospin field is mapped onto the Jaynes-Cummings model (JCM), which describes the interaction between two two-level systems and a quantum single-mode field. The time-dependent wave function and the density matrix are obtained in the two cases. In the first case, the quantum number state is considered, while in the second case, the coherent state is considered as an initial state. The effect of both the detuning parameter and the coherence angle are studied on the entanglement and on the population inversion. It …
We investigate the conditions of entanglement for a system of two atoms and two photon modes in vacuum, using the Jaynes-Cummings model in the rotating-wave approximation. It is found, by generalizing the existing results, that the strength of entanglement is a periodic function of time. We explicitly show that our results are in agreement with the existing results of entanglement conditions under appropriate limits. Results for the two-atom and two-photon system are generalized to the case of arbitrary values for the atomic energies, corresponding to photon modes frequencies. Though it is app…
A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 59}, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from $N$ copies of a bipartite quantum system about which only partial information is known, for instance in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. …
We describe a mathematical solution for the generation of entangled N-photon states in two field modes. A simple and compact solution is presented for a two-mode Jaynes-Cummings model by combining the two field modes in a way that only one of the two resulting quasi-modes enters in the interaction term. The formalism developed is then applied to calculate various generation probabilities analytically. We show that entanglement, starting from an initial field and an atom in one defined state may be obtained in a single step. We also show that entanglement may be built up in the case of an empty…
Dynamics of atom-field correlations and single-mode nonclassicalities present in the resonant Jaynes-Cummings model are investigated using negativity and entanglement potential for a set of initial states. The study has revealed the interplay between three different types of nonclassicality present in the model and established that the nonclassicality is continuously exchanged between the field and atom through the atom-field correlations. Further, it is observed that the entanglement potential does not capture all the single-mode nonclassicality and there exists some residual nonclassicality …
We study the evolution of a photonic state in a coupled pair of anharmonic cavities and compare it with the corresponding system of two coupled harmonic cavities. The photons in the anharmonic cavities interact with a two-level atom and are described within the Jaynes-Cummings model. Starting from an eigenstate of the Jaynes-Cummings model with N photons, the evolution of this state in the presence of photon tunneling between the cavities is studied. We evaluate the spectral density, the dynamics of the return as well as the transition amplitudes and the probability for the dynamical creation …
The rise in linear entropy of a subsystem in the N-atom Jaynes-Cummings model is shown to be strongly influenced by the shape of the classical orbits of the underlying classical phase space: we find a one-to-one correspondence between maxima (minima) of the linear entropy and maxima (minima) of the expectation value of atomic excitation J_z. Since the expectation value of this operator can be viewed as related to the orbit radius in the classical phase space projection associated to the atomic degree of freedom, the proximity of the quantum wave packet to this atomic phase space borderline pro…
We propose a method of generating multipartite entanglement by considering the interaction of a system of N two-level atoms in a cavity of high quality factor with a strong classical driving field. It is shown that, with a judicious choice of the cavity detuning and the applied coherent field detuning, vacuum Rabi coupling produces a large number of important multipartite entangled states. It is even possible to produce entangled states involving different cavity modes. Tuning of parameters also permits us to switch from Jaynes-Cummings to anti-Jaynes-Cummings like interaction.
We show the existence of dynamical purity swapping phenomena in the Jaynes-Cummings model. Moreover we show that purity swapping between a qubit and a generic quantum system is possible, provided they are coupled via non-unitary matrix elements interaction. We particularize to the case of a quantum optical Ramsey interferometer. We show that using purity swapping, a perfect interference pattern can be obtained at the output port of the interferometer even if we start from totally unpolarized sources. This feature is shown to be associated with the phenomena of recreation of the state vector at…
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of the radiation field is investigated, as the state of the field is gradually changed from a coherent state to a squeezed coherent state. The effect of mild squeezing on the coherent light is shown to be striking: the photon number distribution gets localized and it peaks maximally for a particular value of squeezing. The atomic inversion retains its structure for a longer time. The mean linear entropy shows that the atom has a tendency to get disentangled from field within the collapse region a…
We consider a generalized double Jaynes-Cummings model consisting of two isolated two-level atoms, each contained in a lossless cavity, with the cavities interacting with each other through a controlled photon hopping mechanism. The temporal dynamics of entanglement between the two atoms, as the atom-cavity system evolves with time, is investigated for different values of the mediated cavity-cavity interaction. We analytically show that at low values of such an interaction, entanglement between the atoms evolves under the effects of cavity perturbation and exhibits the well-known phenomenon of…