The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum systems with an extensive number of local constraints and play a central role in high energy physics, condensed matter and quantum information. Whereas recent experimental progress points towards the feasibility of large-scale quantum simulation of Abelian gauge theories, the quantum simulation of non-Abelian gauge theories appears still elusive. In this paper we present minimal non-Abelian lattice gauge theories, whereby we introduce the necessary formalism in well-known Abelian gauge theories, such as the Jaynes-Cumming model. In particular, we show that certain minimal non-Abelian lattice gauge theories can be mapped to three or four level systems, for which the design of a quantum simulator is standard with current technologies. Further we give an upper bound for the Hilbert space dimension of a one dimensional SU(2) lattice gauge theory, and argue that the implementation with current digital quantum computer appears feasible.
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…
The Jaynes-Cummings model is a cornerstone of light-matter interactions. While finite, the model provides an illustrative example of renormalisation in perturbation theory. We show, however, that exact renormalisation reveals a rich non-perturbative structure, and that the model provides a physical example of a theory with a chaotic coupling trajectory and multi-valued beta-function. We also construct an exact Wilsonian-like renormalisation group flow for the effective scattering matrix, and show how multi-valued features arise in the flow. Our results shed light on non-perturbative aspects of…
We investigate spin squeezing (SS) and the quantum Fisher information (QFI) for the Jaynes-Cummings Dicke (JC-Dicke) model in a two component atomic Bose-Einstein condensate (BEC) inside an optical cavity. Analytical expressions for spin squeezing and the reciprocal of the quantum Fisher information per particle (RMQFI) are derived using the frozen spin approximation. It is shown that in the superradiant phase near the critical point, maximum squeezing and maximum quantum entanglement occurs. The present study is relevant to quantum information processing and precision spectroscopy.
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.
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…
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 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…
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.
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 …
