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Saratov Fall Meeting: Laser Physics, Photonic Technologies, and Molecular Modeling

Generalized Tavis-Cummings models and quantum networks

Alexander V. Gorokhov

Published Apr 26, 2018• 0 citations
Publisher

Abstract

The properties of quantum networks based on generalized Tavis-Cummings models are theoretically investigated. We have calculated the information transfer success rate from one node to another in a simple model of a quantum network realized with two-level atoms placed in the cavities and interacting with an external laser field and cavity photons. The method of dynamical group of the Hamiltonian and technique of corresponding coherent states were used for investigation of the temporal dynamics of the two nodes model.

DOI
10.1117/12.2315914

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The properties of quantum networks based on generalized Tavis-Cummings models are theoretically investigated. We have calculated the information transfer success rate from one node to another in a simple model of a quantum network realized with two-level atoms placed in the cavities and interacting with an external laser field and cavity photons. The method of dynamical group of the Hamiltonian and technique of corresponding coherent states were used for investigation of the temporal dynamics of the two nodes model.
Выполнено теоретическое исследование квантовых сетей, сконструированных на основе обобщенных моделей Тависа-Каммингса. Рассчитан коэффициент передачи информации от одного узла сети к другому в модели сети, реализованной двухуровневыми атомами в высокодобротных резонаторах. Учтено движение атомов через резонаторы и взаимодействие атомов с внешними лазерными полями и резонаторными фотонами. Выполненный расчет хорошо согласуется с результатами последних экспериментов. A theoretical study of quantum networks constructed on the basis of generalized Tavis-Cummings models is performed. The coefficient of information transfer from one node of the network to another in a network model realized by natural or artificial two-level atoms in high-Q resonators is calculated. The motion of atoms through resonators and the interaction of atoms with external laser fields and resonator photons are taken into account. The calculation is in good agreement with the results of the latest experiments.
A coherent dynamics of two-and three-level atoms in the ideal cavity were investigated. In particular, the investigation of the dynamics of three-level atoms (qutrits) interacting with photons in the cavity having two resonant frequencies close to the frequencies of the two allowed atomic transitions were performed. This model generalizes the well-known Tavis-Cummings model. Time dependencies of mean number of the cavity photons and level populations of atoms are computed and entanglement of atoms and photon fields states are discussed.
The interaction of an ensemble of NNN two-level quantum emitters with a single-mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by gN=Ng‾1{g}_{N}=\sqrt{N}{\overline{g}}_{1}gN​=N​g​1​, where g‾1{\overline{g}}_{1}g​1​ is the ensemble-averaged single-emitter coupling strength. 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 noncavity 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 emitters. We show that the predictions of our cascaded 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.
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\sqrt{N}N​- 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.
We have studied entanglement evolution and transfer in a double Tavis-Cumming model where two pairs of entangled two-level atoms AB and CD interact with two single-mode cavity fields a and b. We show that the Bell-like initial state of atoms AB can exhibit entanglement sudden death which should be independent of the initial entanglement of atoms CD. Also, we show that the initial entanglement of one atomic pair can be transferred into another pair, as well as the possible subsystems, that become entangled during evolution.