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Chinese Physics B

Single-photon scattering by two separated atoms in a supercavity

Wei Ming Zhu, Xiao Xiao, Duan-Lu Zhou, Peng Zhang

Published Jun 1, 2016• 1 citation
Publisher

Abstract

We study the single-photon scattering along a one-dimensional cavity array with two distant two-level atoms in a supercavity, which aims to simulate a recent x-ray experiment [ Nature 482 , 199 (2012)]. Without introducing dissipation, we find that when one atom is exactly located at a node of a mode of the supercavity and the other is at the antinode of that mode, no splitting of the reflectivity peak can appear. Nevertheless, the atom at the node significantly changes the positions of the reflectivity valleys. On the other hand, when the atom is shifted a little from the exact node, then the splitting can appear. We also explain these results with an analysis based on the general formal scattering theory. Our result implies the importance of non-resonant modes of the supercavity in our problem.

DOI
10.1088/1674-1056/25/6/064203

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We study the single-photon scattering along a one-dimensional cavity array with two distant two-level atoms in a supercavity, which aims to simulate a recent x-ray experiment [ Nature 482 , 199 (2012)]. Without introducing dissipation, we find that when one atom is exactly located at a node of a mode of the supercavity and the other is at the antinode of that mode, no splitting of the reflectivity peak can appear. Nevertheless, the atom at the node significantly changes the positions of the reflectivity valleys. On the other hand, when the atom is shifted a little from the exact node, then the splitting can appear. We also explain these results with an analysis based on the general formal scattering theory. Our result implies the importance of non-resonant modes of the supercavity in our problem.
We present a microscopic model of cavity quantum electrodynamics based on a one-dimensional (1D) coupled cavity array (CCA), where a supercavity (SC) is composed by a segment of the 1D CCA with relatively smaller couplings with the outsides. The single-photon scattering problem for the SC empty or with a two level atom in it is investigated. We obtain the exact theoretical result on the transmission rate for our system, which predicts that the transmission peaks shall appear near the eigenenergies of the SC. Our numerical results further prove that the SC is a well-defined multimode cavity. When a two level atom resonant with the SC locates at the antinode of the resonant mode, the transmission spectrum shows a clear sign of vacuum Rabi splitting as expected. However, when the atom locates at the node of the resonant mode, we observe a deep valley in the transmission peak, which can be explained by the destructive interference of two transmission channels: one is the resonant mode, while the other is arising from the atom coupling with the nonresonance modes. The effect of nonresonance modes on vacuum Rabi splitting is also analyzed.
We study the one-photon scattering problem for a super-cavity (SC) coupling with two two-level atoms. With atomic decay, photon reflection shows a sudden drop at Δ = 0 only for the two atoms in the node-antinode configuration. The underlying mechanism is attributed to the fact that the scatterer has a configuration-dependent localized dissipated eigen-mode at Δ = 0 . In the node-antinode configuration, the eigen-mode localized at the input side, through which the photon can enter into the SC, then excites the atom at the node and finally leaks into the reservoir due to atomic decay. In this way, a sudden drop emerges at Δ = 0 in photon reflection. In the antinode-node case, however, the eigen-mode is localized at the output side, so the photon is completely reflected at Δ = 0 . A similar phenomenon has been observed in a recent experiment of X-ray quantum optics (R öhlsberger R. et al. , Nature , 482 (2012) 199) but with a complicated explanation due to electromagnetically induced transparency.
We study single-photon transport in an array of coupled microcavities where two two-level atomic systems are embedded in two separate cavities of the array. We find that a single photon can be totally reflected by a single two-level system. However, two separate two-level systems can also create, between them, single-photon quasibound states. Therefore, a single two-level system in the cavity array can act as a mirror while a different type of cavity can be formed by using two two-level systems, acting as tunable ``mirrors,'' inside two separate cavities in the array. In analogy with superlattices in solid state physics, we call this ``cavity inside a coupled-cavity array'' a supercavity. This supercavity is the quantum analog of Fabry-Perot interferometers. Moreover, we show that the physical properties of this quantum supercavity can be adjusted by changing the frequencies of these two-level systems.
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 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.
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.