Multiphoton Jaynes-Cummings Model Research Articles

Two‐Mode Correlated Multiphoton Bundle Emission

AbstractThe preparation of correlated multiphoton sources is an important research topic in quantum optics and quantum information science. Here, two‐mode correlated multiphoton bundle emission in a nondegenerate multiphoton Jaynes–Cummings model, which is comprised of a two‐level system coupled with two cavity modes is studied. The two‐level system is driven by a near‐resonant strong laser such that the Mollow regime dominates the physical processes in this system. Under certain resonance conditions, a perfect super‐Rabi oscillation between the zero‐photon state and the ()‐photon state of the two cavity modes can take place. Induced by the photon decay, the two‐mode correlated multiphoton bundle emission occurs in this system. More importantly, the results show that there is an antibunching effect between the strongly‐correlated photon bundles, so that the system behaves as an antibunched ()‐photon source. The work opens up a route toward achieving two‐mode correlated multiphoton source device, which has potential applications in modern quantum technology.

Spin-Boson Model as A Simulator of Non-Markovian Multiphoton Jaynes-Cummings Models

The paradigmatic spin-boson model considers a spin degree of freedom interacting with an environment typically constituted by a continuum of bosonic modes. This ubiquitous model is of relevance in a number of physical systems where, in general, one has neither control over the bosonic modes, nor the ability to tune distinct interaction mechanisms. Despite this apparent lack of control, we present a suitable transformation that approximately maps the spin-boson dynamics into that of a tunable multiphoton Jaynes-Cummings model undergoing dissipation. Interestingly, the latter model describes the coherent interaction between a spin and a single bosonic mode via the simultaneous exchange of n bosons per spin excitation. Resorting to the so-called reaction coordinate method, we identify a relevant collective bosonic mode in the environment, which is then used to generate multiphoton interactions following the proposed theoretical framework. Moreover, we show that spin-boson models featuring structured environments can lead to non-Markovian multiphoton Jaynes-Cummings dynamics. We discuss the validity of the proposed method depending on the parameters and analyse its performance, which is supported by numerical simulations. In this manner, the spin-boson model serves as a good analogue quantum simulator for the inspection and realization of multiphoton Jaynes-Cummings models, as well as the interplay of non-Markovian effects and, thus, as a simulator of light-matter systems with tunable interaction mechanisms.

Multiphoton Jaynes-Cummings Model: Arbitrary Rotations in Fock Space and Quantum Filters.

The multiphoton Jaynes-Cummings model is investigated and applications in quantum information science are explored. Considering the strong atom-field coupling regime and an N-photon interaction, a nonlinear driving field can perform an arbitrary rotation in the Fock space of a bosonic mode involving the vacuum and an M-Fock state, with M<N. In addition, driving a bosonic mode with a linear coherent field (superposition of many Fock states), only the cavity states within the Fock subspace {|0⟩,|1⟩,…,|N-1⟩} can be populated; i.e., we show how to implement a Fock state filter, or quantum scissor, that restricts the dynamics of a given bosonic mode to a limited Hilbert space. Such a device can be employed as a generator of finite-dimensional quantum-optical states and also as a quantum-optical intensity limiter, allowing as a special case the generation of single-photon pulses. On the other hand, our system also provides a very rich physics in the weak atom-field coupling regime, in particular, multiphoton electromagnetically induced transparencylike phenomena, inducing a narrow (controllable) reflectivity window for nonlinear probe fields. These results are useful for applications in quantum information processing and also motivate further investigations, e.g., the use of an N-photon Jaynes-Cummings system as a qudit with harmonic spectrum and the exploration of multiphoton quantum interference.

Biorthogonal quantum mechanics for non-Hermitian multimode and multiphoton Jaynes–Cummings models

We develop a biorthogonal formalism for non-Hermitian multimode and multiphoton Jaynes–Cummings models. For these models, we define supersymmetric generators, which are especially convenient for diagonalizing the Hamiltonians. The Hamiltonian and its adjoint are expressed in terms of supersymmetric generators having the Lie superalgebra properties. The method consists in using a similarity dressing operator that maps onto spaces suitable for diagonalizing Hamiltonians even in an infinite-dimensional Hilbert space. We then successfully solve the eigenproblems related to the Hamiltonian and its adjoint. For each model, the eigenvalues are real, while the eigenstates do not form a set of orthogonal vectors. We then introduce the biorthogonality formalism to construct a consistent theory.

Massless Dirac fermions in an electromagnetic field

We study the relations between massless Dirac fermions in an electromagneticfield and atoms in quantum optics. After getting the solutions for the energyspectrum, we show that it is possible to reproduce the 2D Dirac Hamiltonian,with all its quantum relativistic effects, in a controllable system such as asingle trapped ion, through the Jaynes–Cummings and anti-Jaynes–Cummingsmodels. Also we show that under certain conditions, the evolution of the DiracHamiltonian provides us with Rashba spin–orbit and linear Dresselhaus couplings.Considering the multimode multiphoton Jaynes–Cummings model interacting withN modes of an electromagnetic field prepared in general pure quantum states, we analyze theRabi oscillation. Evaluating the time evolution of the Dirac position operator, we determinethe Zitterbewegung frequency and the corresponding oscillating term as a function of theelectromagnetic field.

Entanglement dynamics of a moving multi-photon Jaynes—Cummings model in mixed states

Using the algebraic dynamical method, the entanglement dynamics of an atom-field bipartite system in a mixed state is investigated. The atomic center-of-mass motion and the field-mode structure are also included in this system. We find that the values of the detuning and the average photon number are larger, the amplitude of the entanglement is smaller, but its period does not increase accordingly. Moreover, with the increase of the field-mode structure parameter and the transition photon number, the amplitude of the entanglement varies slightly while the oscillation becomes more and more fast. Interestingly, a damping evolution of the entanglement appears when both the detuning and the atomic motion are considered simultaneously.

Entanglement and preparation for an atom interacting with two-mode coherent strong field via intensity-dependent coupling multiphoton processes

In this paper, effective Hamiltonian of the two-mode multiphoton Jaynes-Cummings model is given via the intensity-dependent coupling in the rotating wave approximation. Under strong field, the atom-field entanglement and the entanglement between two modes of coherent field, according to the above model, are investigated by using the quantum reduced entropy and the quantum relative entropy, respectively. It is showed that properties of these two types of entanglements are considerably relevant to the absorption or emission photon number k, per atomic transition. Different properties of entanglements in the processes of two-photon (k=1) and mutiphoton (k&gt;2) are revealed respectively. The preparation of entangled states is discussed. The Einstein-Podolsky-Rosen states of atom-field irrelevant to time, as well as entangled states between two models of the coherent field are prepared, respectively.

Exactly solving the general non-degenerate multimode multiphoton Jaynes–Cummings model with field nonlinearity

For the general non-degenerate multimode multiphoton Jaynes–Cummings (JC) model, including any forms of intensity-dependent coupling, field-dependent detuning and field nonlinearity, we obtain its energy eigenvalues and eigenstates via the supersymmetric unitary transformation (SUT) method. In addition, its pseudo-invariant eigen-operator (PIEO) is also found, which directly leads to the energy-level gap.

Revival-collapse phenomenon in the quadrature squeezing of the multiphoton Jaynes-Cummings model with the binomial states

In this paper we study the interaction between two-level atom and quantized single-mode field, namely, Jaynes-Cummings model (JCM). The field and the atom are initially prepared in the binomial state and the excited atomic state, respectively. For this system we prove that the revival-collapse phenomenon exhibited in the atomic inversion of the standard JCM can be numerically (naturally) manifested in the evolution of the squeezing factor of the three-photon (standard) JCM provided that the initial photon-number distribution of the radiation has a smooth envelope.

Evolution of the superposition of displaced number states with the two-atom multiphoton Jaynes–Cummings model: interference and entanglement

In this paper, we study the evolution of two two-level atoms interacting with a single-mode quantized radiation field, namely, the two-atom multiphoton Jaynes–Cummings model (JCM). We assume that the field and the atoms are initially prepared in the superposition of displaced number states and excited atomic states, respectively. For this system, we investigate the atomic inversion, Wigner function, phase distribution and entanglement. We show that for symmetric (asymmetric) atoms, the system can generate asymmetric (symmetric) cat states at a quarter of the revival time. Furthermore, the degrees of entanglement for the field–atoms and the one-atom–remainder tangles depend on the rate of energy flow between the parties. The interference in phase space decreases the degree of entanglement in the bipartite.

Influence of Kerr-like medium on a nonlinear two-level atom

Abstract In this paper some aspects through the two-level atom interacting with a radiation field modeled as a multiphoton Jaynes–Cummings model are presented. The exact results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy, phase distribution and Q -function. The influence of Kerr-like medium on the Q -function and phase distribution in both presence and absence of the nonlinear medium is examined. The results show that the effect of Kerr-like medium changes the quasi-period of the field entropy and hence the entanglement between the particle and the field. General conclusions reached are illustrated by numerical results.

The revival–collapse phenomenon in the quadrature field components of the two-mode multiphoton Jaynes–Cummings model

In this paper we consider a system consisting of a two-level atom in an excited state interacting with two modes of a radiation field prepared initially in $l$-photon coherent states. This system is described by two-mode multiphoton (, i.e., $k_1, k_2$) Jaynes-Cummings model (JCM). For this system we investigate the occurrence of the revival-collapse phenomenon (RCP) in the evolution of the single-mode, two-mode, sum and difference quadrature squeezing. We show that there is a class of states for which all these types of squeezing exhibit RCP similar to that involved in the corresponding atomic inversion. Also we show numerically that the single-mode squeezing of the first mode for $(k_1,k_2)=(3,1)$ provides RCP similar to that of the atomic inversion of the case $(k_1,k_2)=(1,1)$, however, sum and difference squeezing give partial information on that case. Moreover, we show that single-mode, two-mode and sum squeezing for the case $(k_1,k_2)=(2,2)$ provide information on the atomic inversion of the single-mode two-photon JCM. We derive the rescaled squeezing factors giving accurate information on the atomic inversion for all cases. The consequences of these results are that the homodyne and heterodyne detectors can be used to detect the RCP for the two-mode JCM.

The revival–collapse phenomenon in the higher-order fluctuations of quadrature field components of the multiphoton Jaynes–Cummings model

In this paper we consider a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a radiation field prepared in generalized quantum states in the framework of multiphoton Jaynes–Cummings model. For this system, we show that there is a class of states for which the fluctuation factors can exhibit the revival-collapse phenomenon (RCP) similar to that exhibited in the corresponding atomic inversion. This is shown not only for normal fluctuations but also for amplitude-squared fluctuations. Furthermore, apart from this class of states we generally demonstrate that the fluctuation factors associated with three-photon transition can provide the RCP similar to that occurring in the atomic inversion of the one-photon transition. These are novel results and their consequence is that the RCP occurring in the atomic inversion can be measured via a homodyne detector. Furthermore, we discuss the influence of the atomic relative phases on such phenomenon.

The revival-collapse phenomenon in the fluctuations of quadrature field components of the multiphoton Jaynes–Cummings model

In this paper we consider a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a radiation field prepared in generalized quantum states in the framework of multiphoton Jaynes-Cummings model. For this system we show that there is a class of states for which the fluctuation factors can exhibit revival-collapse phenomenon (RCP) similar to that exhibited in the corresponding atomic inversion. This is shown not only for normal fluctuations but also for amplitude-squared fluctuations. Furthermore, apart from this class of states we generally demonstrate that the fluctuation factors associated with three-photon transition can provide RCP similar to that occurring in the atomic inversion of the one-photon transition. These are novel results and their consequence is that RCP occurred in the atomic inversion can be measured via a homodyne detector. Furthermore, we discuss the influence of the atomic relative phases on such phenomenon.

Quantum phase properties of two-mode Jaynes–Cummings model for Schrödinger-cat states: interference and entanglement

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 the existence of 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, we find that the phase variances of the single-mode case can exhibit revival-collapse phenomenon about the long-time behavior. We show that such behavior occurs for interaction time several times smaller than that of the single-mode Jaynes–Cummings model.

Relationship between the atomic inversion and Wigner function for multimode multiphoton Jaynes–Cummings model

In this paper we consider the multimode multiphoton Jaynes–Cummings model, which consists of a two-level atom, initially prepared in an excited atomic state, interacting with N modes of electromagnetic field prepared in general pure quantum states. For this system we show that under certain conditions the evolution of the Wigner function at the phase-space origin provides direct information on the corresponding atomic inversion. This relation is also valid even if the system includes Kerr-like nonlinearity, Stark shift effect, different types of initial atomic states as well as moving atoms. Furthermore, based on this fact we discuss for the single-mode case the possibility of detecting the atomic inversion by means of techniques similar to those used for the Wigner function.

Exact solutions to the time-dependent supersymmetric Jaynes-Cummings model and the Chiao-Wu model

By using both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside the optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses the supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schr\"{o}dinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories.

On the evolution of superposition of squeezed displaced number states with the multiphoton Jaynes Cummings model

In this paper we discuss the quantum properties for superposition of squeezed displaced number states against the multiphoton Jaynes–Cummings model (JCM). In particular, we investigate atomic inversion, photon number distribution, purity, quadrature squeezing, the Mandel Q parameter and the Wigner function. We show that quadrature squeezing for the three-photon absorption case can exhibit revivals and collapses typical of those occurring in atomic inversion in the one-photon absorption case. Also, we prove that for odd number absorption parameter there is a connection between the evolution of the atomic inversion and the evolution of the Wigner function at the origin in phase space. Furthermore, we show that the nonclassical states whose Wigner function values at the origin are negative will always be nonclassical when they evolve through the JCM with even absorption parameter. We demonstrate that various types of cat states can be generated via this system.

Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model

On the basis of the fact that the two-level multiphoton Jaynes-Cummings (TLMJC) model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (the time-independent invariant). In this paper, we investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.

An Approach to Exact Solutions of the Time-dependent Supersymmetric Two-Level Three-Photon Jaynes–Cummings Model

By utilizing the property of the supersymmetric structure in the two-level multiphoton Jaynes-Cummings model, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators. We obtain the exact solutions of the time-dependent Schr\"{o}dinger equation which describes the time-dependent supersymmetric two-level three-photon Jaynes-Cummings model (TLTJCM) by using the invariant-related unitary transformation formulation. The case under the adiabatic approximation is also discussed. Keywords: Supersymmetric Jaynes-Cummings model; exact solutions; invariant theory; geometric phase factor; adiabatic approximation