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 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 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.
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.
Cavity qed is the domain of quantum optics which studies the behaviour of single atoms and photons coupled together in an electromagnetic resonator. During the last ten years, various spectacular effects have been observed on such systems, either on the atom’s or on the field’s properties. The presence of a cavity around an atom can produce an alteration of the atomic radiative rates which has been observed in several experiments. Ideally, cavity qed deals with two-level atoms coupled resonantly or nearly resonantly to a single cavity mode. This is of course a simplification of real situations, in which atoms have many levels and the cavity sustains more than one mode. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect.
In previous cavity quantum electrodynamics (QED) systems, atomic gas is usually treated as single atoms, thereby resulting in phenomena such as Rabi splitting, and single-photon blocking. Benefiting from the development of superconducting circuit QED, the superconducting quantum interference devices (SQUIDs) can be regarded as artificial atoms, and the detuned coupling of them through LC harmonic oscillators will constitute an equivalent coherent coupling between artificial atoms. According to this, we study the effect of multiple artificial atoms with coherent coupling on the input and output of a single-mode cavity, and analyze the transmission spectrum from the perspective of decorated state. We find that single-mode cavities containing multiple artificial atoms with coherent coupling have significantly different transmittances from cavities containing single atoms, the transmission spectra of which are correlated with the coherent coupling coefficients between the artificial atoms, and the coupling coefficients between the cavity modes and the artificial atoms, and we also find that both the cavity mode leakage rate and the artificial atom decay rate are related to each other. And as the number of artificial atoms increases, the number of transmission peaks does not increase, and there are only three transmission peaks at most. In order to explain the law of this transmission spectrum, we quantize both artificial atoms and cavity modes, and calculate the eigenvalues and eigenstates of the whole in a single quantum case. In principle, if there are several particles, they will form several decorative states, and there will theoretically appear several transmission peaks. However, we find that there are some decorated states that do not contain the photonic component and thus do not contribute to the transmission peak. From the specific form of these decorated states, many of them have the property of many-body entanglement. Therefore, using such a single-mode cavity containing multiple coherently coupled artificial atoms, we can construct the required many-body entangled state by simply inputting weak monochromatic light, and at the same time, we can sense the forms of multi-body entanglement states in the cavity through the change of transmittance.
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.
Taking nonlinear effect into account, we study theoretically the transmission properties of photons in a one-dimensional coupled cavity, the cavity located at the center of the cavity array being coupled to a two-level system. By using the traditional scattering theory and the mean-field approximation, we calculate the transmission rate of photons along the cavities, and discuss the effect of nonlinearity and the cavity-atom coupling on the photon transport. The results show that the cavity-atom couplings affect the coherent transport of photons. The dynamics of such a system is also studied by numerical simulations, the effect of the atom-field detuning and nonlinearity on the dynamics is shown and discussed.