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arXiv:1112.1491 · Physical Review A

Single-photon scattering on a strongly dressed atom

Zhihai Wang, Yong Li, D. L. Zhou, C. P. Sun, Peng Zhang

Published Aug 15, 2012• 37 citations
arXivHTMLPDF

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.

DOI
10.1103/physreva.86.023824

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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.
The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed beyond the rotating wave approximation using matrix product states. It is found that the scattering is strongly influenced by the single- and multiphoton dressed bound states present in the system. In the ultrastrong coupling regime a new channel for inelastic scattering appears, where an incident photon deposits energy into the qubit, exciting a photon-bound state, and escaping with a lower frequency. This single-photon nonlinear frequency conversion process can reach up to 50% efficiency. Other remarkable features in the scattering induced by counterrotating terms are a blueshift of the reflection resonance and a Fano resonance due to long-lived excited states.
Abstract Recent experiments have pushed the studies on atom–photon interactions to the ultrastrong regime, which motivates the exploration of physics beyond the rotation wave approximation. Here we study the single-photon scattering on a system composed of a coupling cavity array with a two-level atom in the center cavity, which, by varying two outside coupling parameters, corresponds to a model from a supercavity (SC) QED to a waveguide QED with counter rotating wave (CRW) interaction. By applying a time-independent scattering theory based on the bound states in the scattering region, we find that the CRW interaction obviously changes the transmission valley even in the weak atom-cavity coupling regime; in particular, the CRW interaction leads to an inelastic scattering process and a Fano-type resonance, which is directly observed in the crossover from the SC-QED case to the waveguide QED case. Predictably, our findings provide the potential of manipulating the CRW effects in realistic systems and pave the way for the numerical study of very general QED systems.
We study two-photon scattering in a one-dimensional coupled resonator arrays (CRA) by a two-level system (TLS), which is localized as a quantum controller. The SSS-matrix is analytically calculated for various two-photon scattering processes by TLS, e.g., one photon is confined by TLS to form a bound state while the other is in the scattering state. It is discovered from the poles of the SSS-matrix that there exist two kinds of three-body bound states for describing two bound photons localized around TLS.
Single-photon scattering in waveguide-QED systems plays a pivotal role in quantum information processing and communication. We introduce a time-dependent variational approach employing a modified multiple Davydov Ansatz to simulate single-photon dynamics in one-dimensional waveguide-QED systems within the strong-coupling regime. The method is benchmarked across three configurations: a single qubit, two distant qubits, and a ladder-type qutrit coupled to the waveguide. For the single- and two-qubit cases, the variational results exhibit excellent agreement with those derived from a transformed rotating-wave approximation (TRWA). The accuracy of our approach is further verified by an analysis of the local-in-time error, which remains small even under strong coupling, indicating its potential superiority over TRWA in specific regimes. In addition, by contrasting our results with the rotating-wave approximation, we elucidate the significant influence of counter-rotating couplings on scattering dynamics. Our findings establish this variational method as a reliable and versatile tool for investigating single-photon scattering in diverse waveguide-QED systems, particularly in regimes where traditional approximations falter.
A canonical transformation, which diagonalizes the single-mode radiation Hamiltonian in the rotating wave approximation, is exploited to dress a two-level atom by the strong monochromatic driving field in the resonance fluorescence phenomenon. Langevin equations of motion are obtained for dressed atomic operators, and their solutions yield the amplitude of waves scattered into the fluorescence field. The power spectrum of the scattered field is obtained from the first-order correlation functions between dressed atomic operators. The results of the present treatment are compared with others, and advantages and disadvantages of the present method are discussed.
Single-photon scattering properties in a coupled-resonator waveguide (CRW) coupled to a nanocavity embedded with a two-level system are investigated theoretically. Two cases are considered: when the nanocavity is locally coupled to one resonator and when it is nonlocally coupled to two resonators of the CRW. The transmission and reflection amplitudes are obtained for the two cases, respectively. The results show that the position of perfect transmission remains unchanged, while the position of perfect reflection is shifted due to the nonlocal coupling. An asymmetric Fano resonance appears in the transmission spectrum and can be controlled by adjusting the coupling strengths in the nonlocal coupling case. The effects of the coupling strengths and dissipation on the transport properties are also analyzed for the two cases.