Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato, Tatsuo Suzuki, Yukako Wada
In this letter the explicit form of evolution operator of the Tavis-Cummings model with three and four atoms is given. This is an important progress in quantum optics or mathematical physics.
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In this letter the explicit form of evolution operator for the four atoms Tavis-Cummings model is given.
In this letter the explicit form of evolution operator of three atoms Tavis-Cummings model is given, which is a generalization of the paper quant-ph/0403008.
We study in detail the relationship between the Tavis-Cummings Hamiltonian of quantum optics and a family of quasi-exactly solvable Schrödinger equations. The connection between them is stablished through the biconfluent Heun equation. We found that each invariant $n$-dimensional subspace of Tavis-Cummings Hamiltonian corresponds either to $n$ potentials, each with one known solution, or to one potential with $n$-known solutions. Among these Schrödinger potentials appear the quarkonium and the sextic oscillator.
In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between near-integrable and chaotic systems. Here we propose to describe the off-equilibrium dynamics of the Tavis-Cummings model by an underlying classical Hamiltonian system, which can be analyzed using the powerful tools of classical theory of motion. We show that scattering in the classical phase space can drive the quantum model close to thermal equilibrium. Interes…
The explicit form of evolution operator of the three atoms Tavis-Cummings Model is given.
We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and …
The purpose of this paper is to present a comprehensive study of the Tavis-Cummings model from a system-theoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems (TLSs) that are collectively coupled to a common cavity resonator. The associated quantum linear passive system is proposed, whose canonical form reveals typical features of the Tavis-Cummings model, including $\sqrt{N}$- scaling, dark states, bright states, single-excitation superradiant and subradiant states. The passivity of this linear system is related to the…
In this work we study the properties of the atomic entanglement in the eigenstates spectrum of the inhomogeneous Tavis-Cummings Model. The inhomogeneity is present in the coupling among the atoms with quantum electromagnetic field. We calculate analytical expressions for the concurrence and we found that this exhibits a strong dependence on the inhomogeneity.
In this paper we consider the two atoms Tavis--Cummings model and give an explicit form to the solution of this model which will play a central role in quantum computation based on atoms of laser--cooled and trapped linearly in a cavity. We also present a problem of three atoms Tavis--Cummings model which is related to the construction of controlled--controlled NOT operation (gate) in quantum computation.
Choreño et al. [J. Math. Phys. 59, 073506 (2018)] reported analytic solutions to the resonant case of the Tavis-Cummings model, obtained by mapping it to a Hamiltonian with three bosons and applying a Bogoliubov transformation. This comment points out that the Bogoliubov transformation employed is not unitary, cannot be inverted, and cannot enforce the symmetries of the model.
The influence of dipole-dipole interaction on the entanglement between two atoms with different initial entangled W-like states in Tavis-Cummings model with degenerate two-photon transitions has been investigated. The results show that the entanglement between two atoms can be increased by means of dipole-dipole interaction and for some initial states the entanglement sudden death effect can be weakened.
We present a method of generating collective multi-qubit entanglement via global addressing of an ion chain following the guidelines of the Tavis-Cummings model, where several qubits are coupled to a collective motional mode. We show that a wide family of Dicke states and irradiant states can be generated by single global laser pulses, unitarily or helped with suitable postselection techniques.
The model describing interaction between two-level atoms and a single mode field in an optical cavity enclosed by a medium with Kerr nonlinearity is considered in our paper. We study the model within the framework of the analytical solution obtained by application of the quantum inverse method (QIM). The dynamic correlation functions are calculated and transition elements of photons are represented in the determinant form. The obtained answers depend on the solutions of Bethe equations. We provide the numerical solutions of these equations for the different parameters of the model and study th…
A criterion for strong coupling between two quantum emitters and a single resonant light mode in a cavity is presented. The criterion takes into account the escape of cavity photons and the spontaneous emission of the emitters, which are modeled as two level systems. By using such criterion, the dissipative Tavis-Cummings ladder of states is constructed, and it is shown that the inclusion of one more emitter with respect to the Jaynes-Cummings (single emitter) case increases the effective parameter region in which $n^{\text{th}}$ order Rabi splitting is observed.
We study the Tavis-Cummings model with three modes of oscillation by using four different algebraic methods: the Bogoliubov transformation, the normal-mode operators, and the tilting transformation of the $SU(1,1)$ and $SU(2)$ groups. The algebraic method based on the Bogoliubov transformation and the normal-mode operators let us obtain the energy spectrum and eigenfunctions of a particular case of the Tavis-Cummings model, while with the tilting transformation we are able to solve the most general case of this Hamiltonian. Finally, we compute some expectation values of this problem by means o…
An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.
Observation of Photon Blockade in a Tavis-Cummings System
本文在包含超导腔与最多3个transmon量子比特的Tavis-Cummings系统中观察到了微波光子阻塞，并利用光子数分辨光谱学证实了极化激元形成及亚泊松光子统计。
In this paper we develop a general method to obtain the Berry phase of time-dependent Hamiltonians with a linear structure given in terms of the $SU(1,1)$ and $SU(2)$ groups. This method is based on the similarity transformations of the displacement operator performed to the generators of each group, and let us diagonalize these Hamiltonians. Then, we introduce a trilinear form of the Tavis-Cummings model to compute the $SU(1,1)$ and $SU(2)$ Berry phases of this model.
To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\otimes a+S_{-}\otimes a^{\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\equiv S_{+}\otimes a+S_{-}\otimes a^{\dagger}$ diagonal to calculate ${e}^{-itgA}$ and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is first nontrivial examples as far as we know, and reproduce the calculations of ${e}^{-itgA}$ given in quant-ph/0404034. We also give a hint t…
A double Tavis-Cummings model (DTCM) is developed to simulate the entanglement dynamics of realistic quantum information processing where two entangled atom-pairs $AB$ and $CD$ are distributed in such a way that atoms $AC$ are embedded in a cavity $a$ while $BD$ are located in another remote cavity $b$. The evolutions of different types of initially shared entanglement of atoms are studied under various initial states of cavity fields. The results obtained in the DTCM are compared with that obtained in the double Jaynes-Cummings model (DJCM) [J. Phys. B \textbf{40}, S45 (2007)] and an interact…
The influence of the dynamical Stark shift on the thermal entanglement and the efficiency of the quantum Otto cycle is studied for the su(1,1) Tavis-Cummings system. It is shown that the degree of the thermal entanglement becomes larger as the dynamical Stark shift increases. In contrast, the efficiency of the Otto cycle is degraded with an increase of the values of dynamical Stark shift. Expressions for the efficiency coefficient are derived. Using those expressions we identify the maximal efficiency of the quantum Otto cycle from the experimentally measured values of the dynamical Stark shif…
The interaction of an ensemble of $N$ two-level atoms with a single mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by $g_N = \sqrt{N} \bar{g}_1$, where $\bar{g}_1$ is the ensemble-averaged single-atom coupling strength. Formerly, this model has been employed to describe and to analyze numerous cavity-based experiments. Here, we show that this is only justified if the effective scattering rate into non-cavity modes is negligible compared to the cavity's free-spectral range. In terms of experimental pa…
The entanglement of two dipole-coupled atoms with nondegenerate two-photon transitions interacting with two-mode field in lossless cavity has been investigated. It shows that the entanglement is dependent on the initial atomic states. The possibility of considerable growth of atomic entanglement due atomic coherence and dipole-dipole interaction is shown in the case of great mean values of thermal photons.
We study the collective effects of an ensemble of organic molecules confined in an optical cavity based on Holstein-Tavis-Cummings model. By using the quantum Langevin approach and adiabatically eliminating the degree of freedom of the vibrational motion, we analytically obtain the expression of the cavity transmission spectrum to analyze the features of polaritonic states. As an application, we show that the dependence for the frequency shift of the lower polaritonic state on the number of molecules can be used in the detection of the ultra-cold molecules. We also numerically analyze the fluo…
The role of dephasing for dark state coupling in a molecular Tavis-Cummings model
本研究针对分子Tavis-Cummings模型中暗态难以被光学访问的问题，通过含纯退相位与光子衰减的Lindblad方程建模，发现退相位速率和粒子数对暗态布居有显著影响。
We theoretically investigate the emission spectrum of an optomechanical Tavis-Cummings model: two dipole-dipole interacting atoms coupled to an optomechanical cavity (OMC). In particular, we study the influence of dipole-dipole interaction (DDI) on the single-photon spectrum emitted by this hybrid system in the presence of a strong atom-cavity as well as strong optomechanical interaction (hereinafter called the strong-strong coupling). We also show that our analysis is amenable to inclusion of mechanical losses (under the weak mechanical damping limit) and single-photon loss through spontaneou…
We propose a scheme to realize optical nonreciprocal response and conversion in a Tavis-Cummings coupling optomechanical system, where a single cavity mode interacts with the vibrational mode of a flexible membrane with an embedded ensemble of two-level quantum emitters. Due to the introduction of the Tavis-Cummings interaction, we find that the phases between the mechanical mode and the optical mode, as well as between the mechanical mode and the dopant mode, are correlated with each other, and further give the analytical relationship between them. By optimizing the system parameters, especia…
We study the dynamics of two qubits interacting with a single mode of a harmonic oscillator beyond the rotating wave approximation in the ideally degenerate regime. Exact analytic expressions are obtained for state properties of interest, including qubit entanglement for a certain class of initial states of the oscillator and the qubits. Qualitative differences and similarities in the evolution of the qubits in the degenerate regime when the oscillator is treated quantum mechanically and classically are discussed.
A study of the quasi-probability distributions of the Tavis-Cummings model under different quantum channels
本文利用准概率分布和二阶相干函数研究了Tavis-Cummings模型在不同量子信道下的自旋与腔场动力学，揭示了噪声对光子数、自旋激发及腔辐射聚束特性的影响。
Superradiance is the enhanced emission of photons from quantum emitters collectively coupling to the same optical mode. However, disorder in the resonant frequencies of the quantum emitters can perturb this effect. In this paper, we study the interplay between superradiance and spectral disorder in a dynamically modulated Tavis-Cummings model. Through numerical simulations and analytical calculations, we show that the effective cooperativity of the superradiant mode, which is always formed over an extensive number of emitters, can be multiplicatively enhanced with a quantum control protocol mo…
We show that a set of N identical qubits coupled to a single cavity resonator can be decomposed into a set of independent subsystems, which can be thought of as higher pseudospin generalisations of the Jaynes-Cummings model. We derive and analyse the solutions to the equations of motion and demonstrate unusual beating behaviour resulting from a new form of square-root-n-type non-linearity appearing within a pseudospin ladder. Furthermore, we propose a relative phase shift transformation which allows one to switch/initiate the multi-qubit state in a desired pseudospin configuration, and show ho…
The enormous progress in controlling quantum optical and atomic systems has prompted ideas for new experimental realizations of strongly correlated many-body systems operating with light. These systems consist of photons confined in optical cavities, which interact strongly with atoms or atomiclike structures. Due to the interaction between the two particle species optical nonlinearities appear, leading to a quantum phase transition from Mott to superfluid phase. Here, we address the Tavis-Cummings lattice model, which describes light-matter systems containing multiple atomiclike structures in…
A cavity quantum electrodynamical scenario is proposed for implementing a Schrödinger microscope capable of amplifying differences between non orthogonal atomic quantum states. The scheme involves an ensemble of identically prepared two-level atoms interacting pairwise with a single mode of the radiation field as described by the Tavis-Cummings model. By repeated measurements of the cavity field and of one atom within each pair a measurement-induced nonlinear quantum transformation of the relevant atomic states can be realized. The intricate dynamical properties of this nonlinear quantum trans…
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 quality of controlling a system of optical cavities in the Tavis-Cummings-Hubbard (TCH) model is estimated with the examples of quantum gates, quantum walks on graphs, and of the detection of singlet states. This type of control of complex systems is important for quantum computing, for the optical interpretation of mechanical movements, and for quantum cryptography, where singlet states of photons and charges play an essential role. It has been found that the main reason for the decrease of the control quality in the THC model is due to the finite width of the atomic spectral lines, which…
We investigate the dynamics of a two-mode laser system by extending the two-mode Tavis-Cummings model with dissipative channels and incoherent pumping and by applying the mean-field approximation in the thermodynamic limit. To this end we analytically calculate up to four possible non-equilibrium steady states (fixed points) and determine the corresponding complex phase diagram. Various possible phases are distinguished by the actual number of fixed points and their stability. In addition, we apply three time-delayed Pyragas feedback control schemes. Depending on the time delay and the strengt…
We show that an excellent approximation to the exact quantum solution of the ground state of the Tavis-Cummings model is obtained by means of a semi-classical projected state. This state has an analytical form in terms of the model parameters and, in contrast to the exact quantum state, it allows for an analytical calculation of the expectation values of field and matter observables, entanglement entropy between field and matter, squeezing parameter, and population probability distributions. The fidelity between this projected state and the exact quantum ground state is very close to 1, except…
The entanglement character including the so-called sudden death effect between atoms in the non-degenerate two photons Tavis-Cummings model is studied by means of concurrence. The results show that the so-called sudden death effect occurs only for some kind of initial states. In other words, the phenomenon is sensitive to the initial conditions. One can expect the resurrection of the original entanglement to occur in a periodic way following each sudden death event. The length of the time interval for the zero entanglement is dependent on not only the degree of entanglement of the initial stat…
Qubit-qubit interactions can significantly boost quantum coherence times for Bell states. The coherence-time-enhancements are however not monotonic and there exists a phase where further increasing the interaction is unhelpful. A resonator in a suggested circuit QED type implementation of the Tavis-Cummings(Dicke) model, is shown to shift this transition point depending on the number of loaded photons. This allows the resonator to amplify the coherence enhancements in certain regimes. The interactions also induce unusual collapse and revival type behavior for the entanglement dynamics. A new a…
Individual members of an ensemble of identical systems coupled to a common probe can become entangled with one another, even when they do not interact directly. We investigate how this type of multipartite entanglement is generated in the context of a system consisting of two two-level atoms resonantly coupled to a single mode of the electromagnetic field. The dynamical evolution is studied in terms of the entanglements in the different bipartite partitions of the system, as quantified by the I-tangle. We also propose a generalization of the so-called residual tangle that quantifies the inhere…
We study the adiabatic limit for the sequential passage of atoms through a high-Q cavity, in the presence of frequency chirps. Despite the fact that the adiabatic approximation might be expected to fail, we were able to show that for proper choice of Stark-pulses this is not the case. Instead, a connection to the resonant limit is established, where the robust creation of entanglement is demonstrated. Recent developments in the fabrication of high-Q cavities allow fidelities for a maximally entangled state up to 97%.
The elementary optical excitations of a two-dimensional electron or hole system have been identified as exciton-Fermi-polarons. Nevertheless, the connection between the bound state of an exciton and an electron, termed trion, and exciton-polarons is subject of ongoing debate. Here, we use an analogy to the Tavis-Cummings model of quantum optics to show that an exciton-polaron can be understood as a hybrid quasiparticle -- a coherent superposition of a bare exciton in an unperturbed Fermi sea and a bright collective excitation of many trions. The analogy is valid to the extent that the Chevy An…
Engineering near-unitary one-axis twisting evolution via a driven Tavis-Cummings model
本文通过驱动的Tavis-Cummings模型实现近单位元一轴扭曲演化，克服了传统方法中光-原子纠缠导致的单位性破坏问题，并在不同驱动条件下提升了OAT演化精度与抗退相干能力。
Quantum metric and metrology with parametrically-driven Tavis-Cummings models
本研究针对参数驱动的Tavis-Cummings模型，解析求解本征态并数值模拟临界行为，用量子度量表征超辐射相变临界特性，提出基于该临界行为的量子计量方案以提升测量精度。
We theoretically study the conditions under which two laser fields can undergo Coherent Perfect Absorption (CPA) when shined on a single-mode bi-directional optical cavity coupled with two two- level quantum emitters (natural atoms, artificial atoms, quantum dots, qubits, etc.). In addition to being indirectly coupled through the cavity-mediated field, in our Tavis-Cummings model the two quantum emitters (QEs) are allowed to interact directly via the dipole-dipole interaction (DDI). Under the mean-field approximation and low-excitation assumption, in this work, we particularly focus on the imp…
We study the quantum phase transition (QPT) in a non-Hermitian Tavis-Cummings (TC) model of experimentally accessible parameters, which is engineered with two drive fields applied to an ensemble of two-level systems (TLSs) and a cavity, respectively. When the two drive fields satisfy a given parameter-matching condition, the coupled cavity-TLS ensemble system can be described by an effective standard TC Hamiltonian in the rotating frame. In this ideal Hermitian case, the engineered TC model can exhibit the super-radiant QPT with spin conservation at an experimentally accessible critical coupli…
Approaching the double-Heisenberg scaling sensitivity in the Tavis-Cummings model
本文证明Tavis-Cummings模型借助相干平均机制可在平均光子数和原子数上同时实现双重海森堡标度灵敏度，并通过量子压缩在实验上实现，为腔QED和超导电路提供计量应用。
Quantum metrology enhanced by the $XY$ spin interaction in a generalized Tavis-Cummings model
提出含 $XY$ 自旋相互作用的广义 Tavis-Cummings 模型，建立 QFI 与自旋涨落的关系，证明自旋各向异性可实现弱磁场估计的 Heisenberg 标度并揭示标度转变。
Pure and Mixed State Entanglement Dynamics in Tavis-Cummings Model with Squeezed Coherent Thermal States
研究在Tavis-Cummings模型中，通过纯态和混合态的纠缠动力学比较，探讨压缩相干热态对纠缠行为的影响。
We derive an analytical approximate solution of the time-dependent state vector in terms of material Bell states and coherent states of the field for a generalized two-atom Tavis-Cummings model with nonlinear intensity dependent matter-field interaction. Using this solution, we obtain simple expressions for the atomic concurrence and purity in order to study the entanglement in the system at specific interaction times. We show how to implement entangling atomic operations through measurement of the field. We illustrate how these operations can lead to a complete Bell measurement. Furthermore, …
We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, which is the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave re…
Extending the Tavis-Cummings model for molecular ensembles -- Exploring the effects of dipole self energies and static dipole moments
本文扩展了分子系综的 Tavis-Cummings 模型，证明静态偶极矩和偶极自能对极化子化学中光-物质相互作用的准确描述至关重要，并构建了可模拟更大分子系综的高效两能级系统方法。
We present an ideal realization of the Tavis-Cummings model in the absence of atom number and coupling fluctuations by embedding a discrete number of fully controllable superconducting qubits at fixed positions into a transmission line resonator. Measuring the vacuum Rabi mode splitting with one, two and three qubits strongly coupled to the cavity field, we explore both bright and dark dressed collective multi-qubit states and observe the discrete square root of N scaling of the collective dipole coupling strength. Our experiments demonstrate a novel approach to explore collective states, such…
Symplectic split-operator method for the time-dependent unitary Tavis-Cummings model
本文提出一种超越旋波近似的辛分裂算子方法，可高效模拟含时酉Tavis-Cummings模型，计算复杂度与系统总维数呈线性关系，适用于哈密顿项可转化为三对角形式的闭合量子系统模拟。
Ergodic and chaotic properties in Tavis-Cummings dimer: quantum and classical limit
该研究利用Tavis-Cummings二聚体平台，探究自俘获与可积性/混沌的关系，通过随机矩阵诊断和Lyapunov指数分析，揭示了经典-量子对应及开放系统中的混沌特性。
The Tavis-Cummings model for more than one qubit interacting with a common oscillator mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the frequencies of the qubits are much smaller than the oscillator frequency and the coupling strength is allowed to be ultra-strong. The application of the adiabatic approximation, introduced by Irish, et al. (Phys. Rev. B \textbf{72}, 195410 (2005)), for a single qubit system is extended to the multi-qubit case. For a two-qubit system, we identify three-state manifolds of close-lying dressed energy levels…
Quantum phase transitions play an important role in many-body systems and have been a research focus in conventional condensed matter physics over the past few decades. Artificial atoms, such as superconducting qubits that can be individually manipulated, provide a new paradigm of realising and exploring quantum phase transitions by engineering an on-chip quantum simulator. Here we demonstrate experimentally the quantum critical behaviour in a highly-controllable superconducting circuit, consisting of four qubits coupled to a common resonator mode. By off-resonantly driving the system to renor…
Multifractality in the interacting disordered Tavis-Cummings model
该研究分析相互作用无序Tavis-Cummings模型，发现其多重分形本征态与泊松统计共存，缺乏热化，但引入可积性破缺微扰后系统转为遍历近完美导体，并提出了冷原子实现方案。
Quantum phase transitions and observables of interest of the ground state in the Tavis-Cummings model are analyzed, for any number of atoms, by using a tensorial product of coherent states. It is found that this "trial" state constitutes a very good approximation to the exact quantum solution, in that it globally reproduces the expectation values of the matter and field observables. These include the population and dipole moments of the two-level atoms and the squeezing parameter. Agreement in the field-matter entanglement and in the fidelity measures, of interest in quantum information theory…
We revisit the problem of the dynamics of quantum correlations in the exact Tavis-Cummings model. We show that many of the dynamical features of quantum discord attributed to dissipation are already present in the exact framework and are due to the well known non-linearities in the model and to the choice of initial conditions. Through a comprehensive analysis, supported by explicit analytical calculations, we find that the dynamics of entanglement and quantum discord are far from being trivial or intuitive. In this context, we find states that are indistinguishable from the point of view of e…
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