We address the consequences of backaction in the unidirectional coupling of two cascaded open quantum subsystems connected to the same reservoir at different spatial locations. In the spirit of [H. J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993)], the second subsystem is a two-level atom, while the first transforms from a driven empty cavity to a perturbative QED configuration and ultimately to a driven Jaynes-Cummings (JC) oscillator through a varying light-matter coupling strength. For our purpose, we appeal at first to the properties of resonance fluorescence in the statistical description of radiation emitted along two channels -- those of forwards and sideways scattering -- comprising the monitored output. In the simplest case of an empty cavity coupled to an external atom, we derive analytical results for the nonclassical fluctuations in the fields occupying the two channels, pursuing a mapping to the bad-cavity limit of the JC model to serve as a guide for the description of the more involved dynamics. Finally, we exemplify a conditional evolution for the composite system of a critical JC oscillator on resonance coupled to an external monitored two-level target, showing that coherent atomic oscillations of the target probe the onset of a second-order dissipative quantum phase transition in the source.
We highlight the importance of quantum fluctuations in organizing a dissipative quantum phase transition for the driven Jaynes-Cummings interaction with variable qubit-cavity detuning. The system response presents a substantial difference from the predictions of the semiclassical theory, the extent of which is revealed in the properties of quantum bistability, and visualized with the help of quasi-distribution functions for the cavity field, subject to an appropriate scale parameter. States anticipated by the neoclassical theory of radiation coexist in the quantum picture, following the occurr…
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…
An accurate modeling of a Josephson junction that is embedded in an arbitrary environment is of crucial importance for qubit design. We present a formalism to obtain a Lindblad master equation that describes the evolution of the system. As the qubit degrees of freedom oscillate with a well-defined frequency $ω_q$, the environment only has to be modeled close to this frequency. Different from alternative approaches, we show that this goal can be achieved by modeling the environment with only few degrees of freedom. We treat the example of a transmon qubit coupled to a stripline resonator. We de…
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 …
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 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…
本文研究了腔中二能级原子与电磁场模式的前$N$能级相互作用的Jaynes-Cummings模型的纠缠特性。在Jaynes-Cummings模型中，数算符是允许哈密顿量精确对角化的守恒量，因此我们研究与这个守恒量交换的状态，并且其结构在Jaynes-Cummings动力学下保持不变。与通常的看法相反，我们证明了当$N>3$时，存在满足激发数守恒的对称性的束缚纠缠态。进一步证明了原子与模之间存在\emph{the Jaynes-Cummings interaction can be used to generate bound-entanglement}。
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.
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.
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.
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…
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.
