Microscopic theory of multiple-phonon-mediated dephasing and relaxation of quantum dots near a photonic band gap

Abstract

We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption line shape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the "colored" electromagnetic vacuum of a photonic band-gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to an enhanced lifetime of a photon-atom bound state in a PBG. This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (breakup of phonons into lower energy phonons) and purely nonradiative decay. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption line shapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.

Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals

“…To describe this effect, we introduce a phenomenological decay in which the time-dependent annihilation and creation phonon operators satisfy b q (t) = b q e −iω q t−γ q |t| and b † q (t) = b † q e iω q t−γ q |t| . From the independent boson model, it can be shown [30] that…”

“…However, this by itself does not force the atomic Bloch vector to reach the ground state in all cases in the long-time limit. It has been shown in a full quantum theory [30] that, even in the presence of complete 3D PBG's, coupling to damped, finite-lifetime acoustic phonons leads to a decay of the atomic excited-state population to zero. In order to recapture the correct physical behavior in our model, we introduce a phenomenological decay rate pop , This parameter is influenced by the polarization decay rate damp but may be smaller than damp due to Frank-Condon displacement of the excited atomic state from its ground state due to the surrounding phonon cloud.…”

“…When J z (r,r ; t) = δ(r − r )S(t) and σ (r) = 0.0 in Eqs. (30) and (31), the electric field in the z direction E z satisfies…”

“…For simplicity, the phonon decay rate is considered constant γ q = γ ph . A more realistic model for phonon lifetime due to lattice anharmonicity and the breakup of high-frequency phonons into lower-energy phonons can be found elsewhere [30,35,36]. Typically, this leads to a damping rate that is proportional to the phonon frequency and strongly temperature dependent.…”

Quantum-dot all-optical logic in a structured vacuum

“…A natural mechanism to erase the memory effects is the coupling of the quantum dots to damped phonons, causing both dephasing and nonradiative decay [40,41]. The deterioration of the QD inversion caused by this interaction could be slowed down if the dephasing and Frank-Condon effects can diminish the QD dipole that drives the population decay [40].…”