Two-photon Jaynes-Cummings Model Research Articles

Unconventional photon blockade in the two-photon Jaynes–Cummings model with two-frequency cavity drivings and atom driving

In a two-frequency cavity driving and atom driving atom-cavity system, we find the photon blockade effect. In a truncated eigenstates space, we calculate the zero-delay second-order correlation function of the cavity mode analytically and obtain an optimal condition for the photon blockade. By including three transition pathways, we find that higher excitations of the cavity mode can be further suppressed and the zero-delay second-order correlation function can be reduced additionally. Based on the master equation, we simulate the system evolution and find that the analytical solutions match well with the numerical results. Our scheme is robust with small fluctuations of parameters and may be used as a new type of single photon source.

Quantum switching between nonclassical correlated single photons and two-photon bundles in a two-photon Jaynes-Cummings model.

We propose a scheme to realize a two-photon Jaynes-Cummings model for a single atom inside an optical cavity. It is shown that the interplay of a laser detuning and atom (cavity) pump (driven) field gives rise to the strong single photon blockade, two-photon bundles, and photon-induced tunneling. With the cavity driven field, strong photon blockade occurs in the weak coupling regime, and switching between single photon blockade and photon-induced tunneling at two-photon resonance are achievable via increasing the driven strength. By turning on the atom pump field, quantum switching between two-photon bundles and photon-induced tunneling at four-photon resonance are realized. More interestingly, the high-quality quantum switching between single photon blockade, two-photon bundles, and photon-induced tunneling at three-photon resonance is achieved with combining the atom pump and cavity driven fields simultaneously. In contrast to the standard two-level Jaynes-Cummings model, our scheme with generating a two-photon (multi-photon) Jaynes-Cummings model reveals a prominent strategy to engineer a series of special nonclassical quantum states, which may pave the way for investigating basic quantum devices to implement in quantum information processing and quantum networks.

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.

Two-photon Jaynes–Cummings model: a two-level atom interacting with the para-Bose field

Two-photon Jaynes–Cummings model: a two-level atom interacting with the para-Bose field

Influence of detuning and Kerr nonlinearity on atom-atom entanglement in the double two-photon Jaynes–Cummings model

In this work, the authors investigated the dynamics of entanglement of two identical two-level atoms (qubits) in the framework of the two-photon double Jaynes–Cummings model, taking into account the detuning between atoms and the double frequency of the field modes of the resonators, as well as the Kerr medium in both resonators. The authors derived the time dependence of the negativity parameter for the Bell initial states of the atoms and the vacuum states of the resonator fields. The results showed that detuning and Kerr nonlinearity leads to stabilization of the entanglement for all initial Bell-type atomic states. For some initial atomic entanglement states, the detuning and Kerr environment in the resonators can prevent the effect of sudden death of the atom-atom entanglement.

Comparison between XY Spin Chains with Spin 1/2 or 1 Interacting with Quantized Electromagnetic Field by One and Two Photon Jaynes-Cummings Model

This paper describes two cases of interaction between a quantized electromagnetic field and two different XY spin molecules; one with spins ½, and the other with spins 1. Both interact with a quantized electromagnetic field, with one of the spins in the chain interacting with the electromagnetic field. The interaction between the field mode and the spin chain with spins 1 is described by the one- and two-photon Jaynes-Cummings model (JC model). On the other hand, the interaction between the spins ½ and the electromagnetic field is described only by the one-photon Jaynes-Cummings model. Analytical and numerical calculations were made for the case of a different number of photons in the field mode, a different number of spins, and a different position of spin, interacting with the electromagnetic field. The invariant and block structures of such a chain are shown with a comparison made between the evolution of the magnetic moment and the number of photons in both cases.

Multiphoton blockade in the two-photon Jaynes-Cummings model

We study multiphoton blockade and photon-induced tunneling effects in the two-photon Jaynes-Cummings model, where a single-mode cavity field and a two-level atom are coupled via a two-photon interaction. We consider both the cavity-field-driving and atom-driving cases, and find that single-photon blockade and photon-induced tunneling effects can be observed when the cavity mode is driven, while the two-photon blockade effect appears when the atom is driven. For the atom-driving case (the two-photon transition process), we present a criterion of the correlation functions for the multiphoton blockade effect. Specifically, we show that quantum interference can enhance the photon blockade effect in the single-photon cavity-field-driving case. Our results are confirmed by analytically and numerically calculating the correlation function of the cavity-field mode. Our work has potential applications in quantum information processing and paves the way for the study of multiphoton quantum coherent devices.

Quantization of Some Generalized Jaynes-Cummings Models in a Kerr-Like Medium

Based on fundamental principles of quantum mechanics, we present a method for a rigorous analytic construction of the spectra of the one- and two-photon Jaynes-Cummings models in a Kerr medium. To obtain an idea of the method, we consider a first generalized Jaynes-Cummings model with a real, linear superpotential using techniques of supersymmetric quantum mechanics. The Hamiltonian of this model is written as a combination of operators generating the underlying superalgebra whose elements are defined as differential matrix operators. Based on the formalism of supersymmetric quantum mechanics and the properties of sets of common observables, we derive solutions of the one- and two-photon models expressed in terms of confluent hypergeometric functions. Finally, using numerical analysis, we study the influence of the Kerr effect on the energy spectra of the physical system.

Entanglement protection in Jaynes–Cummings model

In this work, we study the control of dynamics of entanglement and its protection in different Jaynes–Cummings models. To preserve atom–field entanglement in Jaynes–Cummings model and its extension to two-photon Jaynes–Cummings model, we apply a scheme which is based on the parity kick. In fact, the scheme is based on the anti-symmetry properties of the Hamiltonian of system. We also apply the method to protect atom–atom entanglement for a system of two two-level atoms inside a single-mode cavity. The control process of entanglement dynamics is implemented as a sequence of cyclic evolutions and makes it possible to protect the atom–field and atom–atom entanglements for any given initial state with desired long time.

Effects of Kerr Medium and Stark Shift Parameter on Wehrl Entropy and the Field Purity for Two-Photon Jaynes–Cummings Model Under Dispersive Approximation

We estimate the quantum state of a two-level atom and the coherent field in a Kerr medium subject to the cavity damping. The density matrix of the field is considered within the framework of the dispersive approximation. We study dynamical properties of the linear entropy, Wehrl entropy, and the Wehrl phase density during the time of interaction. The effects of the Kerr medium and cavity damping on the time evolution of different quantities are examined. The results refer to the sensitivity of these aspects to changes either in the decay parameter or in the Kerr-like medium and Stark-shift parameters. Linear entropy and nonclassical properties of the field quantified by the Wehrl entropy are also very sensitive to the Kerr medium and Stark-shift parameter.

Damping in the Interaction of a Two-Photon Field and a Two-Level Atom Through Quantized Caldirola-Kanai Hamiltonian

Following the lines of the recent papers (Daneshmand and Tavassoly, Int. J. Theor. Phys. 56, 1218 (2017)), we study quantum mechanical treatments of an interaction between a two-level atom with a single-mode field in the two-photon Jaynes-Cummings model, where the Hamiltonian of the field is considered to be the quantized Caldirola-Kanai (CK) Hamiltonian. As a result, we would expect that the quantum dynamics of the two-photon JCM in terms of the CK Hamiltonian is qualitatively different from that of the usual one-photon case. We analytically calculate the explicit form of the atom-field entangled state and numerically evaluate the dynamics of its physical properties. The degree of entanglement, atomic population as well as sub-Poissonian statistics and quadrature squeezing of the field are analyzed. We adjust the latter evolved parameters by appropriately tuning the damping parameter within the CK Hamiltonian and detuning factor. Finally, we report a field detuning asymmetry in the collective statistical behavior.

Thermal Entanglement Between Two Two-Level Atoms in a Two-Photon Jaynes-Cummings Model with an Added Kerr Medium

In this paper, we consider a Hamiltonian model that includes interaction of two coupled two-level atoms with a single-mode quantized electromagnetic field in a cavity via the degenerate two-photon transition. The cavity is filled with a Kerr-like medium and is held at a temperature T. The free field Hamiltonian possesses the su(1,1) symmetry which realized by either even or odd photon-number states. The total number of excitation as a constant of motion, provides a decomposition of the Hilbert space of system into direct sums of invariant subspaces. As a results, the representation of the Hamiltonian becomes block-diagonal matrix with three blocks. After diagonalizing each block, we obtain thermal state of system in the whole Hilbert space and within its excitation subspaces. Finally, the effect of temperature, atom-atom and Kerr-type couplings on the degree of thermal entanglement between the atoms are investigated. Our results show that within the single-excitation subspace spanned with odd photon-number states, the entanglement between the atoms is thermally robust.

Two-photon Jaynes–Cummings model interacting with the squeezed vacuum state solved by dressed-state method

We reconsider the problem on a two-photon Jaynes–Cummings model interacting with the squeezed vacuum state, which has been studied by Gerry in 1988 [Phys. Rev. A 37, 2683-2686 (1988)]. By another different way (i.e. dressed state method), we cleverly deal with the dynamic evolution of more properties for the atom and the field in this process. The population inversion of the atom and the photon statistics of the optical field, in terms of photon number distribution, mean photon number, Mandel Q parameter and quadrature squeezing, are discussed in detail. Specially, we derive the analytic expressions and make the numerical simulation for these properties. Some interesting results involving in Gerry's paper are obtained.

Higher-order squeezing oscillations of the single-mode cavity field interacting with a three-level radiator

We study the two-photon interaction between a three-level equidistant radiator (atom, molecule) with different dipole transitions and the single-mode cavity field. It is supposed that the three-level radiator is laser cooled and trapped into the ground vibrational state, in which the vibrational quantum number [Formula: see text]. In the proposed two-photon Jaynes–Cummings model (JCM) of a three-level atom at the initial moment [Formula: see text], the quantized cavity field is prepared in the squeezed vacuum state and the three-level radiator in the first excited state [Formula: see text]. By using the exact analytical solution for the state-vector of the coupled atom-field system, the amplitude-squared squeezing of the quantized cavity field is examined as a function of the [Formula: see text] and [Formula: see text] parameters. In this situation, higher-order squeezing has the tendency towards oscillations, but the exact periodicity of these oscillations is violated by the analogy with the second-order squeezing.

Influence of Stark shift on entanglement of two atoms with degenerate two-photon transitions for entangled and disentangled initial states

Considering two-atom degenerate two-photon Jaynes–Cummings model, we investigate the atom–atom entanglement when (a) atoms and field are prepared initially in the entangled atom-field W- or GHZ state, (b) two atoms are prepared initially in the coherent disentangled state and the cavity field is prepared in a few-photon Fock state, and study the effect of the Stark shift on entanglement. The results show that the atom–atom negativity evolves periodically with time and the periods are affected by the Stark shift and the degree of the initial atomic coherence. Considering different initial states we derived that the atom–atom entanglement can be greatly increased or decreased due to the presence of the Stark shift. In addition, the entanglement sudden death effect vanishes due to the presence of Stark shift for some initial states.

Higher-order squeezing oscillations in Jaynes–Cummings model of a pair of cold atoms

We study interaction between a pair of indistinguishable two-level atoms and the single-mode cavity field. It is supposed that the pair of two-level atoms is laser cooled and trapped into the ground vibrational state, in which vibrational quantum number hnv i¼ 0. Two Jaynes-Cummings models are investigated. One is the Jaynes-Cummings model with intensity-dependent coupling and the another is the two-photon Jaynes-Cummings model of a pair of indistinguishable two-level atoms. It should be noted that in the present model, at initial moment t ¼ 0, in intensity-dependent Jaynes- Cummings model the cavity field is prepared in Holstein-Primakoff SU(1,1) CS, while in two-photon Jaynes-Cummings model it is prepared in the squeezed vacuum state. Moreover, at initial moment t ¼ 0, pair of atoms is supposed to be in the first excited state je1i in both models. By using exact analytical solutions for state-vectors of the coupled atom-field systems amplitude-squared squeezing of the quantized cavity field is examined as a function of the jnj parameter. In this situation, in both models higher-order squeezing has the tendency towards oscillations, but exact periodicity of these oscillations is violated by the analogy with the second-order squeezing.

Nonclassical light in two-photon Jaynes–Cummings model of a three-level atom with different dipole transitions

We investigate two-photon interaction between an equidistant three-level atom and the quantized cavity field. It is supposed that dipole moment matrix transition elements between neighbouring energy levels d 12 and d 23 may be different. This problem generalizes Jaynes–Cummings model of a pair of indistinguishable two-level atoms interacting with the squeezed vacuum. Assuming that at initial moment the field is in the squeezed vacuum state, exact analytical solution for atom-field state-vector is found. With help of this solution quantum-statistical and squeezing properties of nonclassical light are studied as a function of parameter α = d 23/d 12. The numerical results are compared with those for the pair of indistinguishable two-level atoms. It is found that in proposed model, exact periodicity of squeezing revivals is violated by analogy with model of a pair of two-level atoms. The two limiting cases are examined. In first limiting case in which d 12 → d 23, quantum-statistical properties of single-mode cavity field remind those for the pair of indistinguishable two-level atoms. In second one d 12 → 0, quantum-statistical and squeezing features of proposed model are similar to those for single two-level atom model.

Generation of Multi-Atom W States in Microtoroidal Cavity-Atom System

We proposed a scheme for the generation of multi–atom W states with two-photon Jaynes-Cummings Model in ultrahigh-Q toroidal microcavities. We consider that the two modes, clockwise (CW) and counterclockwise (CCW) modes inside the microtoroidal resonator, can be produced by embedding Bragg grating in the microtoroidal.

Level crossing in a two-photon Jaynes—Cummings model

In this paper, the energy spectrum of the two-photon Jaynes—Cummings model (TPJCM) is calculated exactly in the non-rotating wave approximation (non-RWA), and we study the level-crossing problem by means of fidelity. A narrow peak of the fidelity is observed at the level-crossing point, which does not appear at the avoided-crossing point. Therefore fidelity is perfectly suited for detecting the level-crossing point in the energy spectrum.

Effect of the Stark shift on entanglement in a double Jaynes-Cummings model in thermal environment

Considering a double two-photon Jaynes-Cummings (J-C) model, we study the effects of Stark shift and mean photon number on entanglement between two two-level atoms when the atoms are initially in a maximally entangled state and the fields are in the single-mode thermal fields. The results show that the two atoms evolve periodically into a disentangled separable state when Stark shift is not considered. However, in the presence of Stark shift, the two two-level atoms are no longer disentangled and long-lived entanglement can be obtained. For a larger value of the Stark shift parameter and a smaller mean photon number, the two atoms can remain in a stationary entangled state. These properties show that the Stark shift can be used to control entanglement in the double two-photon J-C model under the influence of thermal environment.