Two-photon Jaynes-Cummings Model Research Articles

The DKP equation for a spin-1 boson in a magnetic field and the two-photon Jaynes–Cummings model

We consider the Duffin–Kemmer–Petiau (DKP) equation for a spin-1 particle moving in the plane under the action of a perpendicular Homogeneous Magnetic Field (HMF) using a fully algebraic method. Interestingly, we show that this quantum relativistic model can be exactly mapped onto the Two-Photon Jaynes-Cummings Model (TPJCM) so widely used in quantum optics to describe two-photon processes during the interaction of a two-level atom with a single-mode radiation field. The Hamiltonian of the equivalent TPJCM we obtain is pseudo-Hermitian, reinforcing the idea that pseudo-Hermitian models are physically relevant. Moreover, using the spectral method, we were able to work out exact closed forms for the associated metric operator and Hermitian Hamiltonian. It turns out that the latter is diagonal and therefore we identified the transformation we applied to calculate it from the TPJCM Hamiltonian as a Foldy-Wouthuysen transformation.

Exploring photon blockade in a two-photon Jaynes-Cummings model with atom and cavity drivings

Exploring photon blockade in a two-photon Jaynes-Cummings model with atom and cavity drivings

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.

Strong single-photon to two-photon bundles emission in spin-1 Jaynes–Cummings model

High-quality special nonclassical states beyond the strong single atom-cavity coupling regime are fundamental elements in quantum information science. Here, we study strong single-photon blockade to two-photon bundles emission in a single spin-1 atom coupled to an optical cavity by constructing a spin-1 Jaynes–Cummings model (JCM). By tuning the quadratic Zeeman shift, the energy-spectrum anharmonicity can be significantly enhanced, leading to a remarkable increase in the dressed-state splitting of the well-resolved n-photon resonance. The mechanism, which benefits from the internal degrees of freedom in high-spin systems, compensates for the strong coupling condition required by the multi-photon blockade, thereby facilitating the experimental feasibility of engineering special nonclassical states beyond the strong-coupling limit. It is shown that the photon emission from the spin-1 JCM demonstrates high-quality single photon and two-photon bundles with large steady-state photon numbers in the cavity-driven and atom-pump cases, respectively. In particular, compared to the two-level two-photon JCM, the antibunching amplitude of the three-order correlation function for two-photon bundles in the spin-1 JCM is enhanced by 3 orders of magnitude. More interestingly, a multimode transducer, enabling a transition from strong single-photon blockade to two-photon bundles and super-Poissonian photon emission, is achieved and highly controllable by the light-cavity detuning in the presence of both atom and cavity driven fields. This study based on the high-spin JCM broadens the scope of engineering special nonclassical quantum states beyond the standard two-level JCM. Our proposal not only opens up a new avenue for generating high-quality n-photon sources but also provides versatile applications in quantum networks and metrology.

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.