D. S. Freitas, A. Vidiella-Barranco, J. A. Roversi
We have found that, in the intensity-dependent Jaynes-Cummings model, a field initially prepared in a statistical mixture of two coherent states, $|α>$ and $|-α>$, evolves toward a pure state. We have also shown that an even-coherent state turns periodically a into rotated odd-coherent state during the evolution.
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Diagonalizing the Jaynes-Cummings Hamiltonian and Jaynes-Cummings coherent states
该研究确定了对角化Jaynes-Cummings哈密顿量的幺正变换形式，借助修饰态解释相关算符作用，并提出基于修饰态的相干态与自旋相干态。
We consider ultracold atoms inside a ring optical cavity that supports a single plane-wave mode. The cavity field, together with an external coherent laser field, drives a two-photon Raman transition between two internal pseudo-spin states of the atom. This gives rise to an effective coupling between atom's pseudo-spin and external center-of-mass (COM) motion. For the case of a single atom inside the cavity, We show how the spin-orbit coupling modifies the static and dynamic properties of the Jaynes-Cummings (JC) model. In the case of many atoms in thermodynamic limit, we show that the spin-or…
The semiclassical approximation of coherent state path integrals is employed to study the dynamics of the Jaynes-Cummings model. Decomposing the Hilbert space into subspaces of given excitation quanta above the ground state, the semiclassical propagator is shown to describe the exact quantum dynamics of the model. We also present a semiclassical approximation that does not exploit the special properties of the Jaynes-Cummings Hamiltonian and can be extended to more general situations. In this approach the contribution of the dominant semiclassical paths and the relevant fluctuations about them…
Temporal evolution of atomic properties including the population inversion and quantum fluctuations of atomic dipole variables are discussed in three various variants of two-photon q-deformed Jaynes-Cummings model.With the the field initially being in three different types of q-deformed coherent states,the quantum collapse and revival effects as well as atomic diploe squeezing are studied for both on-and off-resonant atom-field interaction. Particularly, it is shown that for nonzero detuning the atomic inversion exhibits superstructures which are absent in the non-deformed Jaynes-Cummings mode…
Invariant approach to the Driven Jaynes-Cummings model
本文研究了外部经典场同时驱动原子和量子化场的 Jaynes-Cummings 模型，通过不变方法将其 Hamiltonian 转换为标准形式，从而求得了系统 Schrödinger 方程的精确解析解以分析其动力学变量。
Quantum Optics of harmonic generation in the strongly driven Jaynes-Cummings-type system
本研究改编Jaynes-Cummings模型，在无近似条件下揭示强低频经典驱动下多光子共振产生非经典量子关联谐波的机制，献给Eberly教授。
The m-photon Jaynes-Cummings Hamiltonian is a natural generalization of the much studied Jaynes-Cummings Hamiltonian. In this short note we give the relevant operators for the time-dependent generalized m-photon Jaynes-Cummings Hamiltonian. The dynamical equations for these operators are also given. These operators are needed and indeed are the basic building blocks for performing calculations in the context of the Maximum Entropy Formalism.
This paper provides a scheme for generating maximally entangled qubit states in the anti-Jaynes-Cummings interaction mechanism, so called entangled anti-polariton qubit states. We demonstrate that in an initial vacuum-field, Rabi oscillations in a cavity mode in the anti-Jaynes-Cummings interaction process, occur in the reverse sense relative to the Jaynes-Cummings interaction process and that time evolution of entanglement in the anti-Jaynes-Cummings interaction process takes the same form as in the Jaynes-Cummings interaction process. With the generated anti-polariton qubit state as one of t…
We study analytically and numerically the properties of Jaynes-Cummings model under monochromatic driving. The analytical results allow to understand the regime of two branches of multi-photon excitation in the case of close resonance between resonator and driven frequencies. The rotating wave approximation allows to reduce the description of original driven model to an effective Jaynes-Cummings model with strong coupling between photons and qubit. The analytical results are in a good agreement with the numerical ones even if there are certain deviations between the theory and numerics in the …
A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schrödinger matrix Hamiltonians is characterized. The applications are oriented towards the Jaynes-Cummings eigenvalue problem, so that exactly solvable $2\times 2$ matrix Hamiltonians of the Jaynes-Cummings type are obtained. It is also established that the Jaynes-Cummings Hamiltonian is a quadratic function of a Dirac-type Hamiltonian.
We investigate entanglement dynamics and properties of double Jaynes-Cummings model. In particular we study the dynamics of double Jaynes-Cummings model based on geometric invariants for four qubits. We show that these geometric invariants provide us with useful information about different types of entanglement during the quantum evolution of the system.
With the Jaynes-Cummings model, we have studied the atom and light field quantum entanglement of multiphoton transition, and researched the effect of initial state superposition coefficient $C_{1}$, the transition photon number $N$, the quantum discord $δ$ and the nonlinear coefficient $χ$ on the quantum entanglement degrees. We have given the quantum entanglement degrees curves with time evolution, and obtained some results, which should have been used in quantum computing and quantum information.
In this paper the possibility of generating nonlinear coherent states of the radiation field in a micromaser is explored. It is shown that these states can be provided in a lossless micromaser cavity under the weak Jaynes-Cummings interaction with intensity-dependent coupling of large number of individually injected two-level atoms in a coherent superposition of the upper and lower states. In particular, we show that the so-called nonlinear squeezed vacuum and nonlinear squeezed first excited states, as well as the even and odd nonlinear coherent states can be generated in the presence of two-…
A class of shape-invariant bound-state problems which represent two-level systems are introduced. It is shown that the coupled-channel Hamiltonians obtained correspond to the generalization of the Jaynes-Cummings Hamiltonian.
Quantum Phase Transition in a Modified Jaynes-Cummings Model
该研究提出一个修正的Jaynes-Cummings模型，通过压缩光子交换参数r连接Rabi模型与Jaynes-Cummings模型，并证明其存在量子相变，导致超辐射现象。
The Jaynes-Cummings model is solved with the raising and lowering (shift) operators by using the matrix-diagonalizing technique. Bell nonlocality is also found present ubiquitously in the excitations states of the model.
We investigate entanglement dynamics of two isolated atoms, each in its own Jaynes-Cummings cavity. We show analytically that initial entanglement has an interesting subsequent time evolution, including the so-called sudden death effect.
The dynamics of an atom on the Jaynes-Cummings model has been studied by an atomic inversion, von Neumann entropy and so on. In this letter, we will treat the Jaynes-Cummings model as a problem in non-equilibrium statistical mechanics and apply quantum mutual entropy to study the irreversible dynamics of a state for the atom on this model.
We develop a systematic method of solving two non-interacting Jaynes-Cummings models by using the dressed state formalism in Hilbert space $\mathcal{H}_{AB}^{(2\otimes2)}$. It is shown that such model, called Double Jaynes-Cummings model (D-JCM), can be exactly solved if we take the initial bare state as the linear superposition of two Bell states. The collapse and revival oscillation, which is the standard trait of typical Jaynes-Cummings model, can be recovered if we make measurement at each local sites. Some consequence of the entanglement-induced dressing is discussed.
We considered the anti-Jaynes-Cummings (AJC) interaction of a two-level atom in an initial ground state interacting with a field mode in an initial squeezed coherent state at arbitrary values of squeeze parameter r and provided the Jaynes-Cummings (JC) interaction as a comparison. We analysed the degree of entanglement (DEM) measured by the von Neumann entropy and the nature of the field quantified by the Mandel Q parameter in relation to the atomic population inversion during the AJC interaction and separately the corresponding JC interaction. We noted in our examples that at r>1.4, photon st…
We have numerically obtained theoretical results for the collapse and the revival of the quantum Rabi oscillations for low average number of coherent photons injected on a two-level system in a lossy resonant cavity. We have adopted the multimode Jaynes-Cummings model for the same and especially treated the ``Ohmic" loss to the walls of the cavity, the leakage from the cavity, and the loss due to the spontaneous emission through the open surface of the cavity. We have compared our results with the experimental data obtained by Brune et al [Phys. Rev. Lett. 76, 1800 (1996)] in this regard.
We study in detail entanglement properties of the Jaynes-Cummings model assuming a two-level atom (qubit) interacting with the first $N$ levels of an electromagnetic field mode (qudit) in a cavity. In the Jaynes-Cummings model, the number operator is the conserved quantity that allows for the exact diagonalization of the Hamiltonian and thus we study states that commute with this conserved quantity and whose structure is preserved under the Jaynes-Cummings dynamics. Contrary to the common belief, we show that there are bound entangled states that satisfy the symmetries imposed by the conservat…
We investigate a generalized Jaynes-Cummings model with the external field driving the cavity mode. The numerical results for the dynamics of the atom and the cavity field mode are given. Approximated solutions to the Schrodinger equation are supplied, which allow us to predict the kinematics of the Q function in the complex plane.
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.
We study the intensity-dependent and nonresonant Jaynes-Cummings Hamiltonian when the field is described by an arbitrary shape-invariant system. We determine the eigenstates, eigenvalues, time evolution matrix and the population inversion matrix factor.
Impact of atomic initial conditions on nonclassicality of the light in the ladder-type three-level Jaynes-Cummings model
本研究针对梯型三能级Jaynes-Cummings模型，利用薛定谔方程精确解分析原子初始条件对原子能级占据概率、平均光子数及光非经典性的影响，并通过数值模拟验证了结果的稳健性。
In this article we apply algebraic operator ordering property of the basic atom and field operators to construct and prove conservation of the excitation number operator of the anti-rotating (anti-Jaynes-Cummings) component of the quantum Rabi model. The corresponding U(1) and parity symmetry operators have also been derived in explicit form.
Spectral response of a nonlinear Jaynes-Cummings model
本文基于变形场算符推导了非线性 Jaynes-Cummings 模型的时间依赖光谱响应解析表达式，揭示其长时响应与电路 QED 强色散区实验一致，并指出非线性耦合导致光谱固有不对称和有限激发下无法共振。
A nondegenerate two-photon Jaynes-Cummings model is investigated where the leakage of photon through the cavity is taken into account. The effect of cavity damping on the mean photon number, atomic populations, field statistics and both field and atomic squeezing is considered on the basis of master equation in dressed-state approximation for initial coherent fields and excited atom.
We consider two Jaynes-Cummings cavities coupled periodically with a photon hopping term. The semi-classical phase space is chaotic, with regions of stability over some ranges of the parameters. The quantum case exhibits dynamic localization and dynamic tunneling between classically forbidden regions. We explore the correspondence between the classical and quantum phase space and propose a scheme for implementing the system experimentally.
We analyze the Jaynes-Cummings model of quantum optics, in the strong-dispersive regime. In the bad cavity limit and on timescales short compared to the atomic coherence time, the dynamics are those of a nonlinear oscillator. A steady-state non-perturbative semiclassical analysis exhibits a finite region of bistability delimited by a pair of critical points, unlike the usual dispersive bistability from a Kerr nonlinearity. This analysis explains our quantum trajectory simulations that show qualitative agreement with recent experiments from the field of circuit quantum electrodynamics.
We study the algebraic structure of the one-dimensional Dirac oscillator by extending the concept of spin symmetry to a noncommutative case. An SO(4) algebra is found connecting the eigenstates of the Dirac oscillator, in which the two elements of Cartan subalgebra are conserved quantities. Similar results are obtained in the Jaynes--Cummings model.
We present the dissipative dynamics of the field of two-photon Jaynes-Cummings model (JCM) with Stark shift in dispersive approximation and investigate the influence of dissipation on entanglement. We show the coherence properties of the field can be affected by the dissipative cavity when nonlinear two-photon process is involved.
We investigate the dynamics of a four-photon Jaynes-Cummings model for large photon number. It is shown that at certain times the cavity field is in a pure state which is a superposition of two Kerr states, analogous to the Schrödinger cat state (superposition of two coherent states) which occurs in the one and two photon cases.
In this paper, we present a protocol to engineer upper-bounded and sliced Jaynes-Cummings and anti-Jaynes-Cummings Hamiltonians in cavity quantum electrodynamics. In the upper-bounded Hamiltonians, the atom-field interaction is confined to a subspace of Fock states ranging from $\left\vert 0\right\rangle $ up to $\left\vert 4\right\rangle $, while in the sliced interaction the Fock subspace ranges from $\left\vert M\right\rangle $ up to $\left\vert M+4\right\rangle $. We also show how to build upper-bounded and sliced Liouvillians irrespective of engineering Hamiltonians. The upper-bounded and…
Exploring Supersymmetry: Interchangeability Between Jaynes-Cummings and Anti-Jaynes-Cummings Models
本文揭示了量子光学中JC与AJC模型的超对称联系，提出利用超对称技术获取AJC模型可观测量的时间演化及完整光子计数统计的方法，证明了通过控制原子初始状态和频率可工程化场的量子特性。
Recently, it has been known that a quantum entangled state plays an important role in the field ofquantum information theory such as quantum teleportation and quantum computation. The research on quantifying entangled states has been done by several measures. In this letter, we will adopt the method using quantum mutual entropy to measure the degree of entanglement of Jaynes-Cummings model.
We propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model. In this model the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the initial and the searched states. This algorithm behaves like Grover's algorithm; the optimal search time is proportional to the square root of the size of the search set and the probability to find the searched state oscillates periodically in time. In this frame, it is possible to reinterpret the usual Jaynes-Cummings model as a trivial case of the quantum …
In this work we construct an approximate time evolution operator for a system composed by two coupled Jaynes-Cummings Hamiltonians. We express the full time evolution operator as a product of exponentials and we analyze the validity of our approximations contrasting our analytical results with those obtained by purely numerical methods.
In this paper, we develop the notion of the marginal and density atomic Wehrl entropies for two-level atom interacting with the single mode field, i.e. Jaynes-Cummings model. For this system we show that there are relationships between these quantities and both of the information entropies and the von Neumann entropy.
A unitary transformation of the N-ion Jaynes-Cummings hamiltonian is proposed. It is shown that any approximate expression of the evolution operator associated with the transformed hamiltonian retains its validity independently from the intensity of the external driving field. In particular, using the rotating wave approximation, one obtains a solution for the N-ion Jaynes-Cummings model which improves the standard rotating wave approximation solution.
We have experimentally observed the dynamics of a single polariton and two polaritons in a two-ion chain. By driving two trapped ions at a motional blue-sideband transition, we realize the anti-Jaynes-Cummings-Hubbard model. When a single polariton exists in a trapped-ion chain, the polariton hops between the ion sites. On the other hand, when there are single polaritons at each ion site, the hopping of the polaritons is suppressed because of the polariton-polariton interaction induced by the nonlinearity of the anti-Jaynes-Cummings interaction, thereby realizing the blockade of polariton hopp…
The original Jaynes-Cummings model is described by a Hamiltonian which is exactly solvable. Here we extend this model by several types of interactions leading to a nonhermitian operator which doesn't satisfy the physical condition of space-time reflection symmetry (PT symmetry). However the new Hamiltonians are either exactly solvable admitting an entirely real spectrum or quasi exactly solvable with a real algebraic part of their spectrum.
The theory of non-Hermitian systems and the theory of quantum deformations have attracted a great deal of attention in the past decades. In general, non-Hermitian Hamiltonians are constructed by an ad hoc manner. Here, we study the (2+1) Dirac oscillator and show that in the context of the $κ$-deformed Poincaré-Hopf algebra its Hamiltonian is non-Hermitian but has real eigenvalues. The non-Hermiticity stems from the $κ$-deformed algebra. From the mapping in Bermudez et al., Phys. Rev. A 76, 041801(R) (2007), we propose the $κ$-Jaynes-Cummings and $κ$-anti-Jaynes-Cummings models, which describe…
Theoretical realization of a two qubit quantum controlled-not logic gate and a single qubit Hadamard logic gate in the anti-Jaynes-Cummings model
本研究在反-Jaynes-Cummings模型中理论实现了Hadamard门和量子受控非门，通过精确选择相互作用时间，在非正交基态子空间中获得单位成功概率，为量子计算提供了新方案。
Particle-Hole Ansatz in the Jaynes-Cummings-Hubbard Model
本文提出粒子-空穴递推拟设，将 JCHM 约化为玻色子能量依赖跳跃强度的 JCM，从而计算 Mott-超流相变相图及临界跳跃强度随失谐的变化。
We have studied the Jaynes-Cummings-Hubbard model for a chain with the Kerr effect (nonlinear optical effect) through fermionic approximation. We have observed that the Kerr effec does not cause major changes in the energy spectrum. However, the phase transition properties from Mott insulator to superfluid undergoes significant changes due to the Kerr effect.
Jaynes-Cummings interaction with a traveling light pulse
本文提出了一种级联量子系统方法，用于准确描述量子系统与行进光脉冲的相互作用，修正了传统Jaynes-Cummings模型的局限性。
We show that the two-photon Jaynes-Cummings model, feasible of experimental realization in cavity or ion-trap quantum electrodynamics, can approximately produce nonlinear coherent states of the field. We introduce these nonlinear coherent states of the field as $2m$-photon added or subtracted coherent states in terms of raising and lowering field operators, also known as London phase operators or Susskind-Glogower operators.
We study the dynamics of a single control atom and an atomic sample interacting with a nonresonant cavity mode. The control atom is driven by an auxiliary classical field. Under certain conditions, the coherent energy exchange between the control atom and the atomic sample induced by the cavity mode is described by the Jaynes-Cummings model. The idea provides a possibility for quantum-state engineering and reconstruction for collective atomic modes.
In this paper we study the evolution of the two two-level atoms interacting with a single-mode quantized radiation field, namely, two-atom multiphoton Jaynes-Cummings model when the radiation field and atoms are initially prepared in the superpostion of displaced number states and excited atomic states, respectively. For this system we investigate the atomic inversion, Wigner function, phase distribution and entanglement.
A two level system resonantly coupled to a single mode cavity field and subject to ground state occupancy measurement like interaction is considered. For this situation, the solution to the Lindblad master equation for the density matrix is obtained with respect to the Jaynes Cummings eigenstate representation. It is seen that, the rate of decoherence of the superposition of the Jaynes Cummings eigenstates increases monotonically with the increase in the occupancy measurement coupling up to a certain critical value (already reported in the literature in a different context), whereas the rate d…
The regions of independent quantum states, maximally classically correlated states, and purely quantum entangled (supercorrelated) states described in a recent formulation of quantum information theory by Cerf and Adami are explored here numerically in the parameter space of the well-known exactly soluable Jaynes-Cummings model for equilibrium and nonequilibrium time-dependent ensembles.
We develop a theoretical framework to evaluate the energy spectrum, stationary states, and dielectric susceptibility of two Jaynes-Cummings systems coupled together by the overlap of their respective longitudinal field modes, and we solve and characterize the combined system for the case that the two atoms and two cavities share a single quantum of energy.
Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, and in-situ tuning of parameters. We show how to realise strongly correlated states of light in Jaynes-Cummings-Hubbard arrays under the introduction of an effective magnetic field. The effective field is realised by dynamic tuning of the cavity resonances. We demonstrate the existence of Fractional Quantum Hall states by com- puting topological invariants, phase transitions between topologically distinct states, and Laughlin wavefunction overlap.
In this paper we treat the Jaynes-Cummings model with dissipation and give an approximate solution to the master equation for the density operator {\bf under the general setting} by making use of the Zassenhaus expansion.
We provide the first solution of a time-dependent metric operator for the non-Hermitian Jaynes-Cummings Hamiltonian. We use this solution to calculate the entanglement between two identical isolated such Hamiltonians. The presence of a non-Hermitian interaction term leads to a spontaneously broken $\mathcal{PT}$-symmetric regime which manifests itself in the exotic time-evolution of entanglement. When the symmetry is broken, oscillatory modes transition into decay. As such that there is a drastic difference in behaviour between the broken and unbroken regimes.
We study and exactly solve the two-photon and k-photon Jaynes-Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the tilting transformation of the $SU(2)$ group and let us diagonalize the Hamiltonian of these models by properly choosing the coherent state parameters of the transformation. Finally, we explicitly obtain the energy spectrum and eigenfunctions for each model.
We examine the eigenstates of the one-dimensional Jaynes-Cummings-Hubbard (JCH) model in the two-excitation subspace. We discover that two-excitation bound states emerge when the ratio of vacuum Rabi frequency to the tunneling rate between cavities exceeds a critical value. We determine the critical ratio as a function of the quasi-momentum quantum number, and indicate that the bound states carry a strong correlation in which the two polaritons appear to be spatially confined together.
In this paper, we have proposed a q-deformed Jaynes-Cummings(JC) model and constructed the q-SuperCoherent States(q-SCSs) for the q-deformed JC model. We have also discussed the properties of the q-supercoherent states and given the completeness relation expression. The representation of the q-supercoherent states for the q-deformed JC model is studied as well. PACS number(s): 03.65.Nk Key Works: q-deformed JC model, q-supercoherent states,q-SCSs representation.
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