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Optics Letters

Exact dissipation model for arbitrary photonic Fock state transport in waveguide QED systems

Zihao Chen, Yao Zhou, Jung‐Tsung Shen

Published Feb 14, 2017• 53 citations
Publisher

Abstract

We present an exact dissipation model for correlated photon transport in waveguide QED systems. This model rigorously incorporates the infinitely many degrees of freedom of the full three-dimensional photonic scattering channels in the non-excitable ambient environment. We show that the photon leakages to the scattering channels can be accounted for by a reduced Hamiltonian and a restricted eigen-state, with a resultant atomic dissipation. This model is valid for arbitrary photonic Fock and coherent states.

DOI
10.1364/ol.42.000887

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We present an exact dissipation model for correlated photon transport in waveguide QED systems. This model rigorously incorporates the infinitely many degrees of freedom of the full three-dimensional photonic scattering channels in the non-excitable ambient environment. We show that the photon leakages to the scattering channels can be accounted for by a reduced Hamiltonian and a restricted eigen-state, with a resultant atomic dissipation. This model is valid for arbitrary photonic Fock and coherent states.
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We propose an exact analytical approach to study the single-photon spontaneous emissions in waveguide quantum electrodynamic (QED) systems. Using the ab initio evolution technique, our approach provides a universal framework to investigate the full spatiotemporal dynamics of the atomic response, the cavity response, and the emitted photonic wave functions. The validity of the analytical approach is numerically confirmed. Our rigorous approach can be extensively applied to more complicated waveguide QED architectures. Moreover, such an approach can readily incorporate the effects of dissipations and has the potential to tremendously facilitate the design of spontaneous emission-driven quantum nanophotonic devices in the dissipative regime.
Using an entanglement-preserving approach, we theoretically study the reservoir-induced photonic dissipations in waveguide quantum electrodynamic (wQED) systems coupled to an excitable reservoir consisting of oscillators. For the single-photon case, we show that the effects of dissipation can be described by a reduced Hamiltonian and a restricted eigenstate. For the multiphoton case, we show that the reduced Hamiltonian approach is, in general, not valid. Nonetheless, we identify a weak-reservoir condition for the reduced Hamiltonian approach to be approximately valid, which applies to the majority of current experiments. In addition, we apply the density matrix approach to investigate the same physical system and show that the Markovian density matrix approach can describe only the lowest-order dissipative effect. The deviations from the weak-reservoir scenario are suggested to be observable in an engineered excitable reservoir consisting of optical cavities.
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At the quantum many-body level, atom-light interfaces generally remain challenging to solve for or understand in a nonperturbative fashion. Here we consider a waveguide quantum electrodynamics model, where two-level atoms interact with and via propagating photons in a one-dimensional waveguide, and specifically investigate the interplay of atomic position disorder, multiple scattering of light, quantum nonlinear interactions, and dissipation. We develop qualitative arguments and present numerical evidence that such a system exhibits a many-body localized (MBL) phase, provided that atoms are less than half excited. Interestingly, while MBL is originally formulated with respect to closed systems, this system is intrinsically open. However, as dissipation originates from transport of energy to the system boundaries and the subsequent radiative loss, the lack of transport in the MBL phase makes the waveguide QED system look essentially closed and makes applicable the notions of MBL. Conversely, we show that if the system is initially in a delocalized phase due to a large excitation density, then rapid initial dissipation can leave the system unable to efficiently transport energy at later times, resulting in a dynamical transition to an MBL phase. These phenomena can be feasibly realized in state-of-the-art experimental setups.