Standard Jaynes-Cummings Model Research Articles

Effects of classical drivings on the power broadening of atomic lineshapes

In the framework of the Jaynes–Cummings model, we investigate how atomic lineshapes are affected by coherently driving the atom–field interaction. We pay particular attention to the two-level atom interaction with a thermal cavity field when both are influenced by external classical fields. Adopting a density matrix formalism, we calculate the average atomic inversion and demonstrate how the corresponding lineshapes vary as a function of the average number of thermal photons and the atom–field classical coupling. Furthermore, we compare these results with those obtained from the standard Jaynes–Cummings model and validate our findings through numerical calculations.

Invariant approach to the driven Jaynes-Cummings model

We investigate the dynamics of the driven Jaynes-Cummings model, where a two-level atom interacts with a quantized field and both, atom and field, are driven by an external classical field. Via an invariant approach, we are able to transform the corresponding Hamiltonian into the one of the standard Jaynes-Cummings model. Subsequently, the exact analytical solution of the Schrödinger equation for the driven system is obtained and employed to analyze some of its dynamical variables.

Universal Zeno competition in the dissipative Jaynes-Cummings model

In this paper we demonstrate competitive Zeno physics in the dissipative Jaynes-Cummings model. The mechanism relies on Zeno coexistence between the single-mode field and the environment. We show that the Zeno suppression of coherent evolution predicted by the standard Jaynes-Cummings model can dramatically fail in the presence of the dissipative environment. For hydrogen atom, such a Zeno effect is not usually observable because the environment ignored previously would, in fact, work in a dominant manner. Moreover, beyond the extremely short-time measurement limit in atomic decay, the Zeno time for hydrogen reaches ${10}^{\ensuremath{-}10}$ s in the dressed-state picture, which presents an immediately realizable Zeno scheme for the decay of a real atom in the current technology.

Interaction of a para-Bose state with two two-level atoms: control of dissipation by a local classical field

We consider a parity-deformed Jaynes–Cummings model (JCM) consisting of two identical two-level atoms interacting with a single-mode para-Bose field in a cavity. Compared to the standard JCM, this model introduces the action of a specific local classical field as an external control which can be simulated through an intensity-dependent two-atom JCM with a particular intensity-dependent function. The conservation of the total excitation number and overall parity provides a complete number parity basis for the Hilbert space of the system. In this basis, the matrix representation of the system’s Hamiltonian becomes block diagonal. The corresponding eigenvalues and eigenstates of the system are then analytically calculated by diagonalizing the block matrices. In continuum, we investigate the dynamical evolution of some physical properties such as entanglement, atomic inversion, photon statistics and atomic squeezing in the parity representation, with emphasis on the control role of the local external classical fields. In addition, in the presence of the cavity decay, we study the effect of cavity dissipation on the quantum dynamics of the system. In the ideal case (without the cavity dissipation), we show that the initial states of the system with even–odd parity manifest qualitatively distinct control role of the local external classical fields on the dynamical behavior of the physical properties. In the dissipation regime, we show that the control of local classical fields has the general effect to improve the stabilization of the quantum properties of the system generated during the time evolution.

Photon blockade and the quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator

We investigate the driven quantum phase transition between the oscillating motion and the classical nearly free rotations of the Josephson pendulum coupled to a harmonic oscillator in the presence of dissipation. We refer to this as the Josephson-Rabi model. This model describes the standard setup of circuit quantum electrodynamics, where typically a transmon device is embedded in a superconducting cavity. We find that by treating the system quantum mechanically this transition occurs at higher drive powers than expected from an all-classical treatment, which is a consequence of the quasiperiodicity originating in the discrete energy spectrum of the bound states. We calculate the photon number in the resonator and show that its dependence on the drive power is nonlinear. In addition, the resulting multiphoton blockade phenomenon is sensitive to the truncation of the number of states in the transmon, which limits the applicability of the standard Jaynes-Cummings model as an approximation for the pendulum-oscillator system. We calculate the $n\mathrm{th}$-order correlation functions of the blockaded microwave photons and observe the differences between the rotating-wave approximation and the full multilevel Josephson-Rabi Hamiltonian with the counter-rotating terms included. Finally, we compare two different approaches to dissipation, namely the Floquet-Born-Markov and the Lindblad formalisms.

Dynamics of a deformed atom cavity field system in presence of a Kerr-like medium

In this paper, we investigate the interaction between a vee-type three-level atom and a single mode of the electromagnetic field in the presence of a nonlinear Kerr-like medium and an intensity-dependent coupling. We have elucidated the system by a nonlinear Hamiltonian constructed from the standard Jaynes–Cummings model by deforming the field operators and adding some nonlinear terms. Using the initial conditions that the atom is prepared in an excited state and the field is in a coherent state, the state vector of the entire system is determined analytically. The time evolution of nonclassical properties such as Mandel Q, quantum entanglement and position-momentum uncertainty relation (squeezing) of the field are investigated. The quasiprobability distributions are also computed for the resultant state. The effects of the detuning parameters, generalized Kerr medium and intensity-dependent coupling on the previous nonclassicality signs are analysed, in detail.

Optical nonreciprocity via the standard Jaynes–Cummings model in a gain microcavity

Optical nonreciprocal devices are essential to quantum information processing and communication. We proposed a scheme for optical nonreciprocity via the nonlinear Jaynes–Cummings model in a gain cavity. In addition, the gain cavity is coupled to two fibers with different coupling strengths. In the scheme, the nonlinearity, which is induced by the interaction between a two-level quantum emitter and the cavity field, is enhanced by the cavity gain. Our calculations show that the nonlossy optical nonreciprocity is achievable with high isolation ratio in proper parameter range. Especially, the analytic method further shows the reciprocity broken by the combination of the asymmetric coupling and enhanced nonlinearity.

Entanglement between atomic thermal states and coherent or squeezed photons in a damping cavity

In the present study, the standard Jaynes–Cummings model, in a lossy cavity, is employed to characterize the entanglement between atoms and photons when the former is initially in a thermal state (mixed ensemble) while the latter is described by either coherent or squeezed distributions. The whole system is thus assumed to be in equilibrium with a heat reservoir at a finite temperature T, and the measure of negativity is used to determine the time evolution of atom–photon entanglement. To this end, the master equation for the density matrix, in the secular approximation, is solved and a partial transposition of the result is made. The degree of atom–photon entanglement is then numerically computed, through the negativity, as a function of time and temperature. To justify the behavior of atom–photon entanglement, moreover, we employ the so obtained total density matrix to compute and analyze the time evolution of the initial photonic coherent or squeezed probability distributions and the squeezing parameters. On more practical points, our results demonstrate that as the initial photon mean number increases, the atom–photon entanglement decays at a faster pace for the coherent distribution compared to the squeezed one. Moreover, it is shown that the degree of atom–photon entanglement is much higher and more stable for the squeezed distribution than that for the coherent one. Consequently, we conclude that the time intervals during which the atom–photon entanglement is distillable is longer for the squeezed distribution. It is also illustrated that as the temperature increases the rate of approaching separability is faster for the coherent initial distribution. The novel point of the present report is the calculation of dynamical density matrix (containing all physical information) for the combined system of atom–photon in a lossy cavity, as well as the corresponding negativity, at a finite temperature.

Quantum dynamics of two quantum dots coupled through localized plasmons: An intuitive and accurate quantum optics approach using quasinormal modes

We study the quantum dynamics of two quantum dots (QDs) or artificial atoms coupled through the fundamental localized plasmon of a gold nanorod resonator. We derive an intuitive and efficient time-local master equation, in which the effect of the metal nanorod is taken into consideration self-consistently using a quasinormal mode (QNM) expansion technique of the photon Green function. Our efficient QNM technique offers an alternative and more powerful approach over the standard Jaynes-Cummings model, where the radiative decay, nonradiative decay, and spectral reshaping effect of the electromagnetic environment is rigorously included in a clear and transparent way. We also show how one can use our approach to compliment the approximate Jaynes-Cummings model in certain spatial regimes where it is deemed to be valid. We then present a study of the quantum dynamics and photoluminescence spectra of the two plasmon-coupled QDs. We first explore the non-Markovian regime, which is found to be important only on the ultrashort time scale of the plasmon mode which is about 40$\,$fs. For the field free evolution case of excited QDs near the nanorod, we demonstrate how spatially separated QDs can be effectively coupled through the plasmon resonance and we show how frequencies away from the plasmon resonance can be more effective for coherently coupling the QDs. Despite the strong inherent dissipation of gold nanoresonators, we show that qubit entanglements as large as 0.7 can be achieved from an initially separate state, which has been limited to less than 0.5 in previous work for weakly coupled reservoirs. We also study the superradiance and subradiance decay dynamics of the QD pair. Finally, we investigate the rich quantum dynamics of QDs that are incoherently pumped, ...

A transparent mechanism of Q function splitting in a Jaynes–Cummings model with intensity-dependent level shift

We investigate the tripartite relationship between the collapse and revival, the Q function splitting and the energy level structure in the Jaynes–Cummings (JC) model with an intensity-dependent level shift whose magnitude is tuned to give rise to periodic collapse and revivals. We show that this constitutes a clearer demonstration of the mechanism of Q function splitting and its relation with the collapse and revival than the standard JC model itself. The eigenstates form two groups, both of which form equidistant ladders with differing energy intervals. This structure gives rise to the periodic splitting and reunion of the Q function. Only when the reunion happens, a non-vanishing mutual interference between the two groups is possible and gives rise to observable Rabi oscillations. The possibility of observing the phenomena using a Rubidium atom in a cavity is also discussed. We believe the present work could contribute to the understanding of the collapse and revival and the Q function-splitting phenomena.

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.

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

AbstractIn this paper we study the interaction between a two‐level atom and a quantized single‐mode field, namely, the 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 field has a smooth envelope.

Single-atom entropy squeezing for two two-level atoms interacting with a single-mode radiation field

In this paper we consider a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via l-photon-transition mechanism. The field and the atoms are initially prepared in the coherent state and the excited atomic states, respectively. For this system we investigate the entropy squeezing, the atomic variances, the von Neumann entropy and the atomic inversions for the single-atom case. Also we comment on the relationship between spin squeezing and linear entropy. We show that the amounts of the nonclassical effects exhibited in the entropy squeezing for the present system are less than those produced by the standard Jaynes–Cummings model. The entropy squeezing can give information on the corresponding von Neumann entropy. Also the nonclassical effects obtained from the asymmetric atoms are greater than those obtained from the symmetric ones. Finally, the entropy squeezing gives better information than the atomic variances only for the asymmetric atoms.

Microscopic theory of quantum dot interactions with quantum light: Local field effect

A theory of both linear and nonlinear electromagnetic responses of a single quantum dot (QD) exposed to quantum light, accounting for depolarization induced local field has been developed. Based on the microscopic Hamiltonian accounting for the electron-hole exchange interaction, an effective two-body Hamiltonian has been derived and expressed in terms of the incident electric field, with a separate term describing the QD depolarization. The quantum equations of motion have been formulated and solved using the Hamiltonian for various types of the QD optical excitation, such as Fock qubit, coherent fields, vacuum state of electromagnetic field, and light with arbitrary photonic state distribution. For a QD exposed to coherent light, we predict the appearance of two oscillatory regimes in the Rabi effect separated by the bifurcation. In the first regime, the standard collapse-revival phenomenon does not reveal itself and the QD population inversion is found to be negative, while in the second one, the collapse-revival picture is found to be strongly distorted as compared to that predicted by the standard Jaynes-Cummings model. For the case of QD interaction with an arbitrary quantum light state in the linear regime, it has been shown that the local field induces a fine structure of the absorbtion spectrum. Instead of a single line with frequency corresponding to the exciton transition frequency, a duplet appears, with one component shifted by the amount of the local field coupling parameter. It has been demonstrated that the strong light--matter coupling regime arises in the weak-field limit. A physical interpretation of the predicted effects has been proposed.

Rabi oscillations a quantum dot exposed to quantum light

The influence of the local field on the excitonic Rabi oscillations in an isolated quantum dot driven by the coherent state of light has been theoretically investigated. Local field is predicted to entail the appearance of two oscillatory regimes in the Rabi effect separated by the bifurcation. In the first regime Rabi oscillations are periodic and do not reveal collapse–revivals phenomenon, while in the second one collapse and revivals appear, showing significant difference as compared to those predicted by the standard Jaynes-Cummings model.

Revival-collapse phenomenon in the quadrature squeezing of the multiphoton intensity-dependent Jaynes–Cummings model

For the multiphoton intensity-dependent Jaynes–Cummings model (JCM) described by a two-level atom interacting with a radiation field, we prove that there is a relationship between the atomic inversion and the quadrature squeezing. We give the required condition to obtain best information from this relation. Also we show that this relation is only sensitive to large values of the detuning parameter. Furthermore, we discuss briefly such relation for the off-resonance standard JCM.

Pseudo-invariant Eigen-operator for Deriving Energy-Level Gap forJaynes–Cummings Model

We extend the concept of invariant eigen-operator to pseudo-invarianteigen-operator case through analyzing the standard Jaynes–Cummings model. Wefind the pseudo-invariant eigen-operator in terms of supersymmetricgenerators of this model, which diretly leads to the energy-level gap forJaynes–Cummings Hamiltonian.

Exactly solvable non-Hermitian Jaynes–Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry

It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for certain shape-invariant potentials, including a non-hermitian version of the standard Jaynes-Cummings model for which the parent supersymmetric Hamiltonian is the superoscillator. The positive-definite metric operator in the Hilbert space is constructed explicitly along with the introduction of a new inner product structure, so that the eigenstates form a complete set of orthonormal vectors and the time-evolution is unitary.

Jaynes-Cummings model with atomic position distribution.

The position as well as the width of the atomic wave packet passing through an optical cavity may affect the matter-field interaction. As a result, the internal dynamics of a two-level atom, such as the Rabi oscillations or the collapse and revival phenomenon, may be strongly modified with respect to the standard Jaynes-Cummings model. In particular, for a sufficiently large spread of the atomic position, the atomic population inversion displays the characteristic ringing behavior of the Bessel function ${\mathit{J}}_{0}$ differently from the usual full Rabi oscillation.

Inverse of Radiation Field Operators and the Generalized Jaynes–Cummings Model11The project supported by National Natural Science Foundation of China.

We generalize the standard Jaynes–Cummings model (JCM) to a model Hamiltonian with the radiation field operators being the inverse of a harmonic oscillator's creation and annihilation operators. Some new commutative relations about the inverse operators are derived and the generalized JCM Hamiltonian's eigenstates are derived.