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The European Physical Journal D

The theory of single photon scattering by a three-level atom in a dissipative coupled cavity array

Lian Hai, Lei Tan, Jin-Shan Feng, Jia Bao, Chun-Hai Lv, Bin Wang

Published Aug 1, 2013• 6 citations
Publisher
DOI
10.1140/epjd/e2013-30675-7

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In this paper, we discuss the transport properties of a single photon, which is in a coupled cavity array system where the two nearest cavities nonlocally couple to a -type three-level atom, under the condition of ideal and dissipation, respectively. By employing the quasi-boson picture, the transmission amplitude of the single photon in an open system is investigated analytically. The system where the coupled cavity array nonlocally couples with the three-level atom demonstrates several advantages. Compared with other systems, this system has many parameters to manipulate the single photon transport properties. Moreover, the system of the coupled cavity array that nonlocally couples with the three-level atom may have a wider range of application because the single photon transmission spectrum in this system has three peaks. Furthermore, it has characteristics of its own. At the same value of Rabi frequency , changing the coupling strength between the atom and one cavity of the coupled cavity array shows that there exists an fixed point where the transmission rate is always 1, and the point is corresponding to the frequency of the photon c-. In the nonideal case, it is shown that the dissipations of the cavity and the atom affect distinctively the transmission of photons in the coupled cavity arrays. When considering only the dissipation of the atom, the atomic dissipation increases the dips of the single photon transport spectrum, while the peaks have no observable changes. When considering only the dissipation of the cavity, the peaks of the single photon transmission amplitude are diminished deeply, while the cavity dissipation does not have any effect on the dips. In addition, with both the cavity dissipation rate and the number of the cavity increasing, the photon transmission spectrum peaks decrease. A comparison of the dissipative cavity case with the dissipative atom case shows that the incomplete reflect near the peak is mostly caused by the cavity dissipation, and that the incomplete reflect near the dip is mostly caused by the three-level atom dissipation. Specifically, when considering both the atom and the cavity dissipation at the same time, the dips of the single photon transport spectrum are affected by both the atomic and the cavity dissipation. Instead, with the cavity dissipation rate increasing, the photon transmission spectrum dips are reduced. But for the peaks of the single photon transport spectrum, the dips are always determined by the cavity dissipation rate and the number of the cavity, while the atomic dissipation has no significant influence on them.
In this paper, a new kind of quasi-boson method is used to eliminate the coordinates of the environment and redescribe the dissipative system by using an effective Hamiltonian; the localized mode and the interaction between cavities can be renormalized. Based on the quasi-boson approach, the single photon transport in one-dimensional coupled cavity array, with a driven cascade-type three-level atom embedded in one of the cavity, is investigated under the influence of the environment. The single-photon transmission and the reflection amplitudes are obtained analytically. And the additional effective potential induced by the interaction between the atom and the cavity is also derived. The effects of the controlling parameters on the reflection and transmission amplitudes are discussed with considering the dissipation. It is shown that the decay rates of the atoms and the cavity both reduce the reflection spectrum. But the dissipation of the atom has a significant influence on the reflection amplitude compared with the cavity decay under the same conditions. Due to the irreversible loss of energy, the photon number is non-conservative. Furthermore, the single-photon can be almost reflected by the three-level atom in the dissipative case when one adjusts the detuning and photon number of the quantized cavity field. The investigation will be of benefit to the realization of photon transport in a real experiment, which is also helpful for manipulating the photons in quantum information and quantum simulation.
We have analysed the effects of dissipations on the single-photon transport in a coupled cavity array, with one of the cavities uncoupled and coupled to a two-level atom, respectively. A new approach analysing the dissipative properties of the coupled cavity arrays is first presented. We show that the coupling to a bath renormalizes the localized mode and the interaction between cavities. This permits us to redescribe the system via an effective Hamiltonian without having to mention the coordinates of the bath and then the single-photon transmission and reflection amplitudes are solved exactly. The theoretical results are in qualitatively good agreement with the experiments (Notomi et al 2008 Nature Photon. 2 741). It is shown that the dissipations of the cavity and of the atom affect distinctively the transmission of photons in the coupled cavity arrays. When the atom and the cavity are in tune, a incomplete reflect near the resonance area is mostly caused by the two-level atom dissipation, while for the large detuned cases, the reduced transmission appears to be mainly controlled by the cavity dissipation. A parameter to scale the quality of the dissipative arrays is also presented.