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 parameters, this requires that the optical depth of the ensemble is low, a condition that is violated in several state-of-the-art experiments. We give quantitative conditions for the validity of the Tavis-Cummings model and derive a more general Hamiltonian description that takes into account the cascaded interaction of the photons with all consecutive atoms. We show that the predictions of our model can differ quantitatively and even qualitatively from those obtained with the Tavis-Cummings model. Finally, we present experimental data, for which the deviation from the predictions of the Tavis-Cummings model is apparent. Our findings are relevant for all experiments in which optically dense ensembles of quantum emitters are coupled to an optical resonator.
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.
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.
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.
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 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…
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.
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…
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…
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 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…
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%.
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 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…
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…
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, …
Symplectic split-operator method for the time-dependent unitary Tavis-Cummings model
Akhiezer Institute for Theoretical Physics, NSC KIPT（阿基谢尔理论物理研究所，NSC KIPT）；Advanced Photonic and Electronic Sciences Division, U.S. Army DEVCOM Army Research Laboratory（先进光子与电子科学分部，美国陆军DEVCOM陆军研究实验室）；Department of Physics, University of Massachusetts at Boston（马萨诸塞大学波士顿分校物理系）；Education and Research Institute “School of Physics and Technology”, Karazin Kharkiv National University（克拉辛哈尔科夫国立大学“物理与技术学院”教育与研究所）；Department of Physics and Engineering Physics, Tulane University（杜兰大学物理与工程物理系）
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…
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.
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…
We present an exact method to calculate the electronic states of one electron Hamiltonians with diagonal disorder. We show that the disorder averaged one particle Green's function can be calculated directly, using a deterministic complex (non-Hermitian) Hamiltonian. For this, we assume that the molecular states have a Cauchy (Lorentz) distribution and use the supersymmetric method which has already been used in problems of solid state physics. Using the method we find exact solutions to the states of $N$ molecules, confined to a microcavity, for any value of $N$. Our analysis shows that the wi…
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…
We present the analytical solution of the Tavis-Cummings (TC) model for more than one qubit inhomogeneously coupled to a single mode radiation field beyond the rotating-wave approximation (RWA). The significant advantage of the displaced oscillator basis enables us to apply the same truncation techniques adopted in the single qubit Jaynes-Cummings (JC) model to the multiple qubits system. The derived analytical spectrum match perfectly the exact diagonalization numerical solutions of the inhomogeneous TC model in the parameter regime where the qubits transition frequencies are far off-resonanc…
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.
We study the time evolution of $N_q$ two-level atoms (or qubits) interacting with a single mode of the quantised radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at $\sfrac{t_r}{4}$, halfway between that start of the collapse and the first mini revival peak, where $t_r$ is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an `attractor state'. The set itself is termed the basin of attraction and the features…
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…
In this paper, we investigate the effect of different optical field initial states on the performance of the Tavis-Cummings (T-C) quantum battery. In solving the dynamical evolution of the system, we found a fast way to solve the Bethe ansatz equation. We find that the stored energy and the average charging power of the T-C quantum battery are closely related to the probability distribution of the optical field initial state in the number states. We define a quantity called the number-state stored energy. With this prescribed quantity, we only need to know the probability distribution of the o…
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 …
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…
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…
