Circuit QED with qutrits: Coupling three or more atoms via virtual-photon exchange

Peng Zhao, Xinsheng Tan, Haifeng Yu, Shi-Liang Zhu, and Yang Yu

Phys. Rev. A 96, 043833 – Published 13 October 2017

Abstract

We present a model to describe a generic circuit QED system which consists of multiple artificial three-level atoms, namely, qutrits, strongly coupled to a cavity mode. When the state transition of the atoms disobeys the selection rules the process that does not conserve the number of excitations can happen determinatively. Therefore, we can realize coherent exchange interaction among three or more atoms mediated by the exchange of virtual photons. In addition, we generalize the one-cavity-mode mediated interactions to the multicavity situation, providing a method to entangle atoms located in different cavities. Using experimentally feasible parameters, we investigate the dynamics of the model including three cyclic-transition three-level atoms, for which the two lowest energy levels can be treated as qubits. Hence, we have found that two qubits can jointly exchange excitation with one qubit in a coherent and reversible way. In the whole process, the population in the third level of atoms is negligible and the cavity photon number is far smaller than 1. Our model provides a feasible scheme to couple multiple distant atoms together, which may find applications in quantum information processing.

Received 27 June 2017

DOI:https://doi.org/10.1103/PhysRevA.96.043833

Physics Subject Headings (PhySH)

Light-matter interaction Quantum entanglement Quantum gates

Perturbative methods

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Peng Zhao¹, Xinsheng Tan¹, Haifeng Yu^1,2,*, Shi-Liang Zhu^1,2, and Yang Yu^1,2

¹National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
²Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

^*hfyu@nju.edu.cn

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Vol. 96, Iss. 4 — October 2017

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Images

Figure 1
(a) Schematic of the generic circuit QED system which consists of $N$ qutrits strongly coupled to a cavity mode. The qutrits are cyclic three-level systems, and the lowest two levels are treated as qubit states. (b) A schematic of a deformation model for (a) with three qutrits. The 1st and 3rd qutrit are strongly coupled to cavity modes labeled by $L$ and $R$ , respectively. The 2nd qutrit is strongly coupled to the two-cavity modes.
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Figure 2
Calculated energy-level diagram of the system which consists of three nondegenerate qutrits coupled to a cavity mode. Shown here are $E_{6}$ and $E_{7}$ as functions of $ω_{e}^{(1)} / ω_{0}$ . An avoided energy-level crossing resulting from the resonant coupling between $| 0, e, g, g 〉$ and $| 0, g, e, e 〉$ can be observed. The magnitude of the energy splitting is about $1.6 \times 10^{- 4} ω_{0} .$
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Figure 3
(a) Sketch of a typical path which contributes in $2 n th$ -order perturbation theory to the effective coupling between the bare states $| 0, e, g, . . ., g 〉$ and $| 0, g, e, . . ., e 〉$ for the system depicted in Fig. 1. (b) Sketch of the only path which contributes in fourth-order perturbation theory to the effective coupling between the bare states $| 0, 0, e, g, g 〉$ and $| 0, 0, g, e, e 〉$ for the system depicted in Fig. 1, where the virtual transitions involving the two-cavity modes are represented by dotted blue and dashed red arrows, respectively. The dashed arrows denote the virtual transitions that do not conserve the energy, and the dashed black lines represent the intermediate virtual states.
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Figure 4
Numerical simulation of the dynamics under the influence of dissipation. (a) Temporal evolution of the atom mean excitation number $〈 σ_{q}^{+} σ_{q}^{-} 〉$ and the equal-time second-order correlation function $〈 σ_{2}^{+} σ_{3}^{+} σ_{3}^{-} σ_{2}^{-} 〉$ with the system prepared in the state $|0, e, g, g〉$ . (b) The residual population in the third level of the atoms ${| i 〉}_{q} 〈 i |$ and the cavity mode $〈 a^{†} a 〉$ .
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Figure 5
Numerical simulation of the dynamics under the influence of dissipation. (a) Temporal evolution of the atom mean excitation number $〈 σ_{q}^{+} σ_{q}^{-} 〉$ and the equal-time second-order correlation function $〈 σ_{2}^{+} σ_{3}^{+} σ_{3}^{-} σ_{2}^{-} 〉$ with the system prepared in the state $| 0, 0, e, g, g 〉$ . (b) The residual population in the third level of the $2 nd$ atom ${| i 〉}_{2} 〈 i |$ and the two-cavity modes $〈 a_{s}^{†} a_{s} 〉 (L, R)$ .
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Figure 6
Numerical simulation of the dynamics under the influence of dissipation. (a) Temporal evolution of the atom mean excitation number $〈 σ_{q}^{+} σ_{q}^{-} 〉$ and the three-atom correlation function $〈 σ_{2}^{+} σ_{3}^{+} σ_{4}^{+} σ_{4}^{-} σ_{3}^{-} σ_{2}^{-} 〉$ with the system prepared in the state $| 0, e, g, g, g 〉$ . (b) The residual population in the third level of the atoms ${| i 〉}_{q} 〈 i |$ and the cavity mode $〈 a^{†} a 〉$ .
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