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arXiv:1006.4412

Dissipation Properties of Coupled Cavity Arrays

Ke Liu, Lei Tan

Published Jun 23, 2010• 0 citations
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Abstract

We propose an approach to analyze the dissipation properties of coupled cavity arrays. Employing a kind of quasi-boson, it is shown that the coupling to a bath renormalizes the localized mode and the interaction between cavities. By virtue of without having to mention the coordinates of bath, this approach would be great conceptual and, moreover, computation advantage. Based on the result, a single-photon transport in the array is examined, and the total transmission rate is presented. Besides, we also suggest a parameter to scale quality of the array.

DOI
10.48550/arxiv.1006.4412

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We propose an approach to analyze the dissipation properties of coupled cavity arrays. Employing a kind of quasi-boson, it is shown that the coupling to a bath renormalizes the localized mode and the interaction between cavities. By virtue of without having to mention the coordinates of bath, this approach would be great conceptual and, moreover, computation advantage. Based on the result, a single-photon transport in the array is examined, and the total transmission rate is presented. Besides, we also suggest a parameter to scale quality of the array.
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.
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 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.
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 study the features of superfluid and Mott-insulator states in a two-dimensional array of cavities with a two-level atom embedded in each cavity which is strongly coupled to the cavity field and immersed in a bosonic bath. Employing a different quasiboson approach, we show analytically how the dissipation and decoherence influence the quantum phase transitions from two aspects and find a localized tendency. For the superfluid state, a dynamical instability will lead to a sweeping to a localized state of photons. For the Mott-insulator state, a dissipation-induced fluctuation will suppress the restoring of long-range phase coherence driven by interaction.