Nonlinear Jaynes-Cummings Research Articles

Spectral response of a nonlinear Jaynes-Cummings model

Spectral response of a nonlinear Jaynes-Cummings model

The entanglement and second-order coherence function in a two-atom nonlinear Jaynes-Cummings model

The influence of the Kerr nonlinearity on the two two-level atoms entanglement is investigated in Jaynes–Cummings model (JCM), so that one of atoms is inside the cavity field and the other atom is outside it. We show that the entanglement of atoms increases with the decrease of the phase decoherence rate or Kerr coefficient, when considering the effect of external environment. Then due to the statistic properties of the anti-bunching effect of photons are related to entanglement, the nonlinear JCM is examined theoretically to analyze the bunching or anti-bunching effect by using the second-order coherence function. We find that the second-order coherence function decreases with the Kerr coefficient. Our results show that the field reflects the stronger bunching effect with the bigger average photon number.

Adiabatic sensing technique for optimal temperature estimation using trapped ions

We propose an adiabatic method for optimal phonon temperature estimation using trapped ions which can be operated beyond the Lamb-Dicke regime. The quantum sensing technique relies on a time-dependent red-sideband transition of phonon modes, described by the non-linear Jaynes-Cummings model in general. A unique feature of our sensing technique is that the relevant information of the phonon thermal distributions can be transferred to the collective spin-degree of freedom. We show that each of the thermal state probabilities is adiabatically mapped onto the respective collective spin-excitation configuration and thus the temperature estimation is carried out simply by performing a spin-dependent laser fluorescence measurement at the end of the adiabatic transition. We characterize the temperature uncertainty in terms of the Fisher information and show that the state projection measurement saturates the fundamental quantum Cram\'er-Rao bound for quantum oscillator at thermal equilibrium.

Accessing the non-equal-time commutators of a trapped ion

The vibronic dynamics of a trapped ion in the resolved-sideband regime can be described by the explicitly time-dependent nonlinear Jaynes-Cummings model. It is shown that the expectation value of the interaction Hamiltonian and its non-equal-time commutator can be determined by measuring the electronic-state evolution. This yields direct insight into the time-ordering contributions to the unitary time evolution. In order to prove extraction of the quantities of interest works for possibly real data, we demonstrate the procedure by means of generated data.

Time ordering in the classically driven nonlinear Jaynes-Cummings model

Recently, in [Phys. Rev. A 97, 043806 (2018)], the detuned and nonlinear Jaynes-Cummings model describing the quantized motion of a trapped ion was introduced and its corresponding dynamics was solved via considering the driving laser in a quantized manner. In this work we reconsider this model and show that it can likewise be solved with a classical driving laser field. Using the exact solution we investigate the quantum time-ordering effects of the system with respect to nonclassicality of the motional states of the ion. Furthermore, we use the Magnus expansion to analyze the impact of certain orders of the time ordering and derive and exact radius of convergence beyond the established and only sufficient criterion. Finally, the differences of the solution derived here and the previously found one using a quantized pump, are discussed.

A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices: comment

Recently Rodriguez-Lara et al. [Opt. Express 21(10), 12888 (2013)] proposed a classical simulation of the dynamics of the nonlinear Rabi model by propagating classical light fields in a set of two photonic lattices. However, the nonlinear Rabi model has already been rigorously proven to be undefined by Lo [Quantum Semiclass. Opt. 10, L57 (1998)]. Hence, the proposed classical simulation is actually not applicable to the nonlinear Rabi model and the simulation results are completely invalid.

Evolution properties of the field quantum entropy in the nonlinear Jaynes-Cummings model of a trapped ion

The time evolution properties of the field quantum entropy in the system of a trapped ion interacting resonantly with a standing-wave laser field is studied by utilizing the Von Neumann reduced quantum entropy theory, and our attention focuses on the discussion of the influence of the Lamb-Dick parameter, the position of the ion in the standing-wave laser field and the initial state of the trapped ion on the evolution properties of the field quantum entropy. The results obtained from the numerical calculation indicate that: the value of the Lamb-Dick parameter effect the oscillation frequency and amplitude of the quantum entanglement between the trapped ion and the standing-wave laser field, the larger the Lamb-Dick parameter is, the weaker the average entanglement level between the ion and the field will be. When moving the tapped ion from the node of the standing-wave laser to the loop, the vibration frequency of the quantum entanglement between the field and the ion becomes slow gradually, and the entanglement degree gets weaker and weaker. With the decrease of the probability of the trapped ion being in the excited state, the quantum entanglement between the trapped ion and the stanging-wave laser field shows the tendency of increase first and then decrease. These properties have certain reference value for the preparation of entangled states and for the quantum communications with the thapped ion, and so on.

Quantum Entropy of a Nonlinear Two-level Atom with Atomic Motion

The wave function of a system governed by the time-dependent nonlinear Jaynes-Cummings (JC) model is obtained. We compute analytically the eigenvalues of the reduced field density operator by which the dynamics of the entropy of entanglement of the cavity field are analyzed. The influences of the atomic motion, the field-mode structure and the Kerr-like medium on this phenomenon are illustrated. The population dynamics of an excited atom is also discussed for the same set of parameters. The cavity field is assumed to be initially excited in either a Fock or a coherent states. The cavity excitation in a Fock state generates a class of an entanglement without death with fixed amplitude by adjusting the parameters of the atomic motion as well as the Kerr and the field-mode structure. In case of a coherent cavity, the only phenomenon to be noted is the periodical behavior of the dynamics under study when the atomic motion is considered. Although the Kerr medium affects the strength of the entanglement negatively, the entropy of entanglement loses its zeros where the Kerr is taken into consideration.

Pseudo Invariant Eigenoperator Method for Some Generalized Jaynes-Cummings Models

Based on the method of pseudo invariant eigenoperator (PIEO), we investigate three kinds of the generalized Jaynes-Cummings (JC) models such as the super JC model, the Kerr nonlinear JC model, and the two-atomic two-photon JC model. Our main task lies in finding the so-called pseudo invariant eigenoperators and deriving the energy-level gap for the above Hamiltonians, respectively. Compared with the usual Schrodinger equation approach or the directly diagonalizing Hamiltonian, the PIEO method could be quite concise and effective to obtain energy-level gap of the given system.

Solutions of two-mode Jaynes-Cummings models

A simple procedure to solve two fully quantized non-linear Jaynes-Cummings models is presented, one in which an atom interacts with a two-mode radiation field in a Raman-type process and the other involving multiphoton interaction between the two-mode field and the atom. Effect of intensity-dependent coupling between the field and the atom in both the above-mentioned cases has also been investigated. The unitary transformation method presented here not only solves the time-dependent problem but also permits a determination of the eigensolutions of the interacting Hamiltonian at the same time. Graphical features of the time dependence of the population inversion have been analysed when one of the field modes is prepared initially in a coherent state while the other one in a vacuum state.

Two-photon nonlinear jaynes-cummings model with stark shift

Two-photon Jaynes-Cummimgs model is generalized to the case of Kerr medium in this paper. The field and atom are prepared initially in two-photon superposition state and ground state respectively. Nonlinear coefficient affects the dynamic behaviors of the field and atom. Evolutions of the squeezing for the operators of field and atom and the quantum inversion are discussed. In particular, the higher-order squeezing for atomic dipole and the effects of nonlinearity on it, which have not been studied by other authors, are investigated. Increasing the nonlinear coefficient will decrease the squeezing depth of atomic dipole.

K-quantum nonlinear Jaynes-Cummings model in two trapped ions

A k-quantum nonlinear Jaynes-Cummings model for two trapped ions interacting with laser beams resonant to k-th red side-band of center-of-mass mode, far from Lamb-Dicke regime, has been obtained. The exact analytic solution showed the existence of quantum collapses and revivals of the occupation of two atoms.

Thermal and squeezed vacuum Jaynes–Cummings models with a Kerr medium

The dynamics of the Jaynes–Cummings (JCM) model with a nonlinear Kerr medium at initially thermal and squeezed vacuum fields is discussed. At a special choice of the detuning the Rabi frequency can have a minimum at the initial mean photon number [nbar]. Then the situation becomes especially interesting and instead of the first-order ‘usual’ revivals resembling those manifested by the standard coherent JCM, the nonlinear JCM exhibits second-order revivals, also for initially thermal and squeezed vacuum fields, at least for not too large [nbar]. The revival times are highly sensitive to the nature of [nbar]. In the first case the revival period of the oscillations is dependent on whether [nbar] is integer or non-integer (situation similar to an initially coherent field) while in the latter case it depends additionally on the parity of the integer [nbar]. Moreover, for the squeezed vacuum model appearance of the revivals at an integer [nbar] is accelerated when compared to coherent and thermal models.

Evolution of entropy in the nonlinear Jaynes-Cummings model

In this paper we study the correlation between the external and the internal state of the trapped atoms by means of the nonlinear Jaynes-Cummings Hamiltonian, in which we pay special attention to the influence of the nonlinearity. We find that the correlation is reflected by the entropy of the vibration mode, which is strongly affected by the nonlinearity. The nonlinearity, embodied by the nonlinear Rabi frequency, exhibits various effects, of which the most important feature is the appearance of the second local minimum value of the entropy in each collapse-revival cycle of the atomic inversion.

Entanglement Swapping and Preparing Nonclassical Field by Nonlinear Jaynes-Cummings Model with an Entangled State of Atoms

The interaction of a cavity field with an entangled state of atoms is studied according to the nonlinear Jaynes-Cummings model. It is shown that the properties of the cavity field depend on not only the interaction time but also the nonlinear constant. After detecting an atom of the entangled state, the cavity field will be entangled with another atom even it is far away from the cavity. It is proved that the nonclassical properties of the field state are dramatically different from those in the case of no selective measurement.

Nonlinear multiquantum Jaynes-Cummings model with counter-rotating terms

In this paper we have investigated the eigenenergy spectrum of the nonlinear k-quantum Jaynes-Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis has shown that the nonlinear k-quantum JC model without the RWA does not have eigenstates in the Hilbert space spanned by the number states, i.e. the model becomes ill-defined. Hence, the nonlinear k-quantum JC model without the RWA is qualitatively different from the RWA counterpart which is valid for all values of k and the coupling parameter. In other words, the counter-rotating terms do drastically alter the nature of the system.

Nonlinear Jaynes-Cummings Dynamics of a Trapped Ion Under a Dressed-State Description

Introducing a dressed-state description, we show that a trapped ion in a standing wave field can be described by a nonlinear Jaynes-Cummings model different from the counterpart of Vogel and Matos Filho [Phys. Rev. A 52 (1995) 4214] in several aspects, which may carry important implications for the preparation and reconstruction of the nonclassical states of a trapped ion.

Preparation of nonclassical states of a cavity field based on a nonlinear Jaynes-Cummings model

It is proven in this paper that some kinds of nonclassical quantum states of the cavity field, such as Schrödinger cat state (amplitude cat or phase cat), sub-Poissonian photon distribution and Fock state, etc., can be generated by conditional measurements on atoms in the two-photon Jaynes-Cummings model with a Kerr-like medium. The nonlinear constant plays the key modulation role in the preparation of the quantum states, which gives a new controllable parameter for further experimental researches in this field.

Unified and standardized procedure to solve various nonlinear Jaynes-Cummings models

In this article we present a simple and unified procedure to solve various nonlinear two-level Jaynes-Cummings models. By establishing their similarity to the model describing a spin- particle in a magnetic field, we obtain the standardized forms, appropriate uniformly for all Jaynes-Cummings models, of eigenvalues, eigenstates, evolution, and atomic inversion operators. In this way, we show that the analytical solution of any single-mode and two-mode nonlinear Jaynes-Cummings model can easily be obtained. We also apply this procedure to a three-mode Jaynes-Cummings model.

Canonical dressing in nonlinear Jaynes-Cummings models

We present a detailed and exact construction of a unitary operator accomplishing the canonical dressing of a two-level atom by a cavity field for a class of multiphoton and intensity-dependent Jaynes-Cummings models.