By means of numerical simulations and the input-output formalism, we study photon transport through a chain of coupled nonlinear optical cavities subject to uniform dissipation. Photons are injected from one end of the chain by means of a coherent source. The propagation through the array of cavities is sensitive to the interplay between the photon hopping strength and the local nonlinearity in each cavity. We characterize photon transport by studying the populations and the photon correlations as a function of the cavity position. When complemented with input-output theory, these quantities provide direct information about photon transmission through the system. The position of single-photon and multiphoton resonances directly reflects the structure of the many-body energy levels. This shows how a study of transport along a coupled cavity array can provide rich information about the strongly correlated (many-body) states of light even in presence of dissipation. The numerical algorithm we use, based on the time-evolving block decimation scheme adapted to mixed states, allows us to simulate large arrays (up to 60 cavities). The scaling of photon transmission with the number of cavities does depend on the structure of the many-body photon states inside the array.
By means of numerical simulations and the input-output formalism, we study photon transport through a chain of coupled nonlinear optical cavities subject to uniform dissipation. Photons are injected from one end of the chain by means of a coherent source. The propagation through the array of cavities is sensitive to the interplay between the photon hopping strength and the local nonlinearity in each cavity. We characterize photon transport by studying the populations and the photon correlations as a function of the cavity position. When complemented with input-output theory, these quantities provide direct information about photon transmission through the system. The position of single-photon and multiphoton resonances directly reflects the structure of the many-body energy levels. This shows how a study of transport along a coupled cavity array can provide rich information about the strongly correlated (many-body) states of light even in presence of dissipation. The numerical algorithm we use, based on the time-evolving block decimation scheme adapted to mixed states, allows us to simulate large arrays (up to 60 cavities). The scaling of photon transmission with the number of cavities does depend on the structure of the many-body photon states inside the array.
We consider the quantum transport of multi-photon Fock states in a one-dimensional coupled QED cavity array (CQCA) as a scheme to probe the underlying strongly correlated (many-body) states of the system. To this end, we employ the Lippmann-Schwinger formalism within which an analytical form of the scattering matrix can be found. The latter is evaluated explicitly for the two photon-two site case, from which we calculate the scattering probabilities and auto-correlation functions. The results indicate that the underlying many body structure of the CQCAs can be directly inferred from the probe spectrum and output photon statistics. Our method goes beyond the usual case of using coherent light fields to drive the system and paves the way for CQCAs to serve as a quantum simulator of aspects of quantum transport in strongly correlated bosonic 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.
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.
We study the non-equilibrium behavior of optically driven dissipative coupled resonator arrays. Assuming each resonator is coupled with a two-level system via a Jaynes–Cummings interaction, we calculate the many-body steady state behavior of the system under coherent pumping and dissipation. We propose and analyze the many-body phases using experimentally accessible quantities such as the total excitation number, the emitted photon spectra and photon coherence functions for different parameter regimes. In parallel, we also compare and contrast the expected behavior of this system assuming the local nonlinearity in the cavities is generated by a generic Kerr effect as described by the Bose–Hubbard (BH) model rather than a Jaynes–Cummings interaction. We find that the behavior of the experimentally accessible observables produced by the two models differs for realistic regimes of interactions even when the corresponding nonlinearities are of similar strength. We analyze in detail the extra features available in the Jaynes–Cummings–Hubbard (JCH) model originating from the mixed nature of the excitations and investigate the regimes where the BH approximation would faithfully match the JCH physics. We find that the latter is true for values of the light–matter coupling and losses beyond the reach of current technology. Throughout the study we operate in the weak pumping, fully quantum mechanical regime where approaches such as mean field theory fail, and instead use a combination of quantum trajectories and the time evolving block decimation algorithm to compute the relevant steady state observables. In our study we have assumed small to medium size arrays (from 3 up to 16 sites) and values of the ratio of coupling to dissipation rate g / γ ∼ 20, which makes our results implementable with current designs in circuit QED and with near future photonic crystal set ups.
We discuss the effects of dissipation on the behavior of single photon transport in a system of coupled cavity arrays, with the two nearest cavities nonlocally coupled to a two-level atom. The single photon transmission amplitude is solved exactly by employing the quasi-boson picture. We investigate two different situations of local and nonlocal couplings, respectively. Comparing the dissipative case with the nondissipative one reveals that the dissipation of the system increases the middle dip and lowers the peak of the single photon transmission amplitudes, broadening the line width of the transport spectrum. It should be noted that the influence of the cavity dissipation to the single photon transport spectrum is asymmetric. By comparing the nonlocal coupling with the local one, one can find that the enhancement of the middle dip of single photon transmission amplitudes is mostly caused by the atom dissipation and that the reduced peak is mainly caused by the cavity dissipation, no matter whether it is a nonlocal or local coupling case. Whereas in the nonlocal coupling case, when the coupling strength gets stronger, the cavity dissipation has a greater effect on the single photon transport spectrum and the atom dissipation affection becomes weak, so it can be ignored.
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.