Single-photon scattering on a strongly dressed atom

Z. H. Wang, Yong Li, D. L. Zhou, C. P. Sun, and Peng Zhang

Phys. Rev. A 86, 023824 – Published 15 August 2012

Abstract

We use the generalized rotating-wave approximation approach [Irish, Phys. Rev. Lett. 99, 173601 (2007)] to study single-photon scattering on a two-level system (TLS) with arbitrarily strong coupling to a local mode in a one-dimensional (1D) coupled-resonator array. We obtain the scattering amplitudes by an analytical method, which works well in a broad parameter region, confirmed by independent numerical results. In particular, when the resonator mode is far off resonance with the TLS, our results appear more reasonable than the ones from the standard adiabatic approximation. The approach is further extended to cases with a 1D resonator array strongly coupled to more than one TLS.

Received 11 December 2011

DOI:https://doi.org/10.1103/PhysRevA.86.023824

Authors & Affiliations

Z. H. Wang¹, Yong Li², D. L. Zhou¹, C. P. Sun^2,3, and Peng Zhang^4,*

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Beijing Computational Science Research Center, Beijing 100084, China
³Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
⁴Department of Physics, Renmin University of China, Beijing 100872, China

^*pengzhang@ruc.edu.cn

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Vol. 86, Iss. 2 — August 2012

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Images

Figure 1
Schematic configuration for the hybrid system of a 1D resonator array interacting with a TLS. The frequency of the photon in each resonator is $ω$ , while the intensity of the photon hopping is $ξ$ . The TLS with frequency $Ω$ is localized at the zeroth resonator and coupled to the photon with coupling strength $λ$ .Reuse & Permissions
Figure 2
The single-photon reflection rate $| r_{k} |^{2}$ given by the GRWA approach with the first- and second-order approximations for $(ξ / ω)$ , i.e., $| r_{k}^{(1)} |^{2}$ (red solid line) and $| r_{k}^{(2)} |^{2}$ (black empty triangles), $| r_{k} |^{2}$ from the rotating-wave approximation (RWA) (green empty circles), $| r_{k} |^{2}$ from the adiabatic approximation (green filled diamonds), and the numerical calculations with cutoff excitation number $C_{p} = 2$ (blue filled circles) and $C_{p} = 3$ (blue empty squares). Here we consider the cases of $ξ = 0.04 ω$ and $Ω = ω, λ = 0.04 ω$ (a), $Ω = 0.4 ω, λ = ω$ (b), $Ω = ω, λ = 1.6 ω$ (c), and $Ω = 0.4 ω, λ = 2 ω$ (d).Reuse & Permissions
Figure 3
The real (a)–(d) and imaginary (e)–(h) parts of the single-photon scattering amplitude $r_{k}$ given by the GRWA approach with the first-order approximation for $(ξ / ω)$ , i.e., $r_{k}^{(1)}$ in Eq. (31) (red solid line), the rotating-wave approximation (green empty circles), and the numerical calculations with cutoff excitation number $C_{p} = 2$ (blue filled circles) and $C_{p} = 3$ (blue empty squares). Here we consider the cases of $ξ = 0.04 ω$ and $Ω = ω, λ = 0.04 ω$ (a),(e), $Ω = 0.4 ω, λ = ω$ (b),(f), $Ω = ω, λ = 1.6 ω$ (c),(g), and $Ω = 0.4 ω, λ = 2 ω$ (d),(h).Reuse & Permissions
Figure 4
The single-photon reflection rate $| r_{k} |^{2}$ in the cases with strong TLS-photon coupling. Here we show the results given by Eq. (36) (red solid line), rotating-wave approximation (green empty circles), and the numerical calculations with cutoff excitation number $C_{p} = 2$ (blue filled circles) and $C_{p} = 3$ (blue empty squares) for the cases with $Ω = ω, λ = 1.6 ω, ξ = 0.002 ω$ (a), $Ω = 0.4 ω, λ = 1.4 ω, ξ = 0.03 ω$ (b), and $Ω = ω, λ = 2 ω, ξ = 0.04 ω$ (c). In the three cases we have $ω_{1 g}^{(0)} / ξ = 15, 1, 0.06$ , respectively.Reuse & Permissions
Figure 5
(a) The energy spectrum of the Hamiltonian $H_{1}$ of the 1D resonator array and the interaction between the resonator array and the TLS. The low-excitation spectrum has clear band structure. The intraband transitions are missed unreasonably in the adiabatic approximation. (b) The energy spectrum of the Hamiltonian $H_{1}$ of a single-mode bosonic field and the interaction between the single-mode bosonic field and a TLS. In such a simple system there is no band structure in the spectrum of $H_{1}$ , and then the adiabatic approximation is applicable when $Ω ≪ ω$ .Reuse & Permissions

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