We present a fast, memory-efficient, unitarity-preserving numerical method beyond the rotating-wave approximation for the closed Tavis-Cummings model in which a multilevel spin system interacts with a cavity mode. This model can describe the interaction of an ensemble of spins with a cavity mode in which the spin frequency and other parameters are time-dependent. The method exploits the fact that, while the Tavis-Cummings model is not tri-diagonal, it can be brought into tri-diagonal form by a change of basis that can be implemented purely by re-indexing (permuting basis elements), which is a fast operation. By truncating the Fock basis of the cavity mode, the computational complexity of the method is linear in the total dimension of the coupled system, both in time and memory. The method can be employed to simulate any closed quantum system whose Hamiltonian terms can be brought into tri-diagonal form.
We present a fast, memory-efficient, unitarity-preserving numerical method beyond the rotating-wave approximation for the closed Tavis-Cummings model in which a multilevel spin system interacts with a cavity mode. This model can describe the interaction of an ensemble of spins with a cavity mode in which the spin frequency and other parameters are time-dependent. The method exploits the fact that, while the Tavis-Cummings model is not tri-diagonal, it can be brought into tri-diagonal form by a change of basis that can be implemented purely by re-indexing (permuting basis elements), which is a fast operation. By truncating the Fock basis of the cavity mode, the computational complexity of the method is linear in the total dimension of the coupled system, both in time and memory. The method can be employed to simulate any closed quantum system whose Hamiltonian terms can be brought into tri-diagonal form.
We present a comprehensive theoretical and computational study of the Tavis–Cummings model in the collective-spin basis, addressing both its static spectral properties and dynamic behavior under unitary and open-system evolution. By exploiting the commutation of the total-excitation operator with the Hamiltonian, we construct block-diagonal representations for systems of two-level molecules coupled to a single quantized cavity mode. We derive analytic expressions for the degeneracies, block dimensions, and secular polynomials, introducing a family of orthogonal “Félix–Sanz-Vicario” new class of orthogonal polynomials (here baptized Félix-Sanz-Vicario polynomials) whose roots furnish the energy eigenvalues and whose finite-degree structure allows precise control over photon-number truncation in small manifolds. Numerical implementations in Python (QuTiP) confirm exact agreement with the original Tavis–Cummings solution in each excitation manifold, while also highlighting the role of lower-spin subspaces—absent in the bosonized highest-spin description—in mediating configurational molecular interactions via a rank-1 spherical tensor operator. Time-dependent simulations compare dynamics under the rotating wave aproximation (Tavis-Cummings model) and without it (Dicke model), demonstrating population transfer, Rabi oscillations, and collapse–revival phenomena. The dynamics of open quantum system, via a Lindblad master equation, illustrate cavity-loss effects on photon-number decay, von Neumann entanglement entropy, and coherent exchange under dissipation. Our results establish that the collective-spin framework, using a set of solutions in terms of orthogonal polynomials, provides both analytical insight and computational efficiency for spectroscopic modeling, ultrastrong coupling studies, and the design of low-photon-number quantum simulations.
The purpose of this article 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 noninteracting 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, includingN- scaling, dark states, bright states, single-excitation superradiant, and subradiant states. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon in Tavis–Cummings systems. On the basis of the linear model, an analytic form is presented for the steady-state output state of the Tavis–Cummings model driven by a single-photon state. Master equations are used to study the excitation properties of the Tavis–Cummings model in the multiexcitation scenario. Finally, in terms of the transition matrix for a linear time-varying system, a computational framework is proposed for calculating the state of the Tavis–Cummings model, which is applicable to the multiexcitation case.
Hybrid quantum systems consisting of a collection of N spin- 1 / 2 particles uniformly interacting with an electromagnetic field, such as one confined in a cavity, are important for the development of quantum information processors and will be useful for metrology, as well as tests of collective behavior. Such systems are often modeled by the Tavis-Cummings model, and having an accurate understanding of the thermal behaviors of this system is needed to understand their behavior in realistic environments. We quantitatively show in this work that the Dicke subspace approximation is at times invoked too readily. Specifically, we show that there is a temperature above which the degeneracies in the system become dominant and the Dicke subspace is minimally populated. This transition occurs at a lower temperature than previously considered. In such a temperature regime, the key constants of the motion are the total excitation count between the spin system and cavity and the collective angular momentum of the spin system. These enable perturbative expansions for thermal properties in terms of the energy shifts of dressed states, called Lamb shifts herein. They enable efficient numeric methods that scale in terms of the size of the spin system. Notably the runtime to obtain certain parameters of the system scales as O ( N ) , and is thus highly efficient. These provide methods for approximating, and bounding, properties of these systems as well as characterizing the dominant population regions, including under perturbative noise. In the regime of stronger spin-spin coupling, the perturbations outweigh the expansion series terms, and inefficient methods must likely be employed, removing the computational efficiency of simulating such systems. The results in this work can also be used for related systems such as coupled-cavity arrays, cavity-mediated coupling of collective spin ensembles, and collective spin systems.
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 ultrastrong. The application of the adiabatic approximation introduced by Irish et al. [Phys. Rev. B 72, 195410 (2005)] for a single-qubit system is extended to the multiqubit case. For a two-qubit system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intramanifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-qubit dynamics that are different from the single-qubit case, including calculations of qubit-qubit entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.
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-resonance with the field frequency and the interaction strengths reach the ultra-strong coupling regime. The two-qubit TC model is quasi-exactly solvable because part of the spectra can be determined exactly in the homogeneous coupling case with two identical qubits or with symmetric(asymmetric) detuning. By means of the fidelity of quantum states we identify several nontrivial level crossing points in the same parity subspace, which implies that homogeneous coupled two-qubit TC model with ω1=ω2 or ω1±ω2=2ωc is integrable. We further explore the time evolution of the qubit's population inversion and the entanglement behavior taking two qubits as an example. The analytical methods provide unexpectedly accurate results in describing the dynamics of the qubit in the present experimentally accessible coupling regime, showing that the collapse-revival phenomena emerge, survive, and are finally destroyed when the coupling strength increases beyond the ultra-strong coupling regime. The suggested procedure applies readily to the multiple qubits system such as the GHZ state entanglement evolution and quantum entanglement between a single photon and superconducting qubits of particular experiment interest.
The open Tavis-Cummings model consists of N quantum emitters interacting with a common cavity mode, accounts for losses and decoherence, and is frequently explored for quantum information processing and designing quantum devices. As N increases, it becomes harder to simulate the open Tavis-Cummings model using traditional methods. To address this problem, we implement two quantum algorithms for simulating the dynamics of this model in the inhomogeneous, nonresonant regime, with up to three excitations in the cavity. We show that the implemented algorithms have gate complexities that scale polynomially, as O ( N 2 ) and O ( N 3 ) , while the number of qubits used by these algorithms (space complexity) scales linearly as O ( N ) . One of these algorithms is the sampling-based wave matrix Lindbladization algorithm, for which we propose two protocols to implement its system-independent fixed interaction, resolving key open questions of Patel and Wilde []. We benchmark our results against a classical differential equation solver in a variety of scenarios and demonstrate that our algorithms accurately reproduce the expected dynamics.