Recent progress towards realizing quantum emitters (QEs) suitable for integration in quantum information networks stimulates the demand for a self-consistent numerical approach to describe scattering of radiatively limited QEs in complex dielectric environments. As the QE response has to be characterized without the use of phenomenological damping parameters, the divergent nature of the pointlike emitter's in-phase self-field has to be carefully dealt with to avoid unphysical frequency shifts. Here we provide a solution to this problem and show two ways to obtain accurate results in the weak excitation limit using finite-difference time-domain algorithms. One of these approaches lays important groundwork needed for future simulations of nonlinear QE networks. The solution for dealing with the frequency shift reveals that dynamical contributions to the resonant depolarization field of arbitrarily small dielectric objects make crucial contributions to the net dipole moment induced by an external field when radiative scattering is the only source of damping.
Recent progress towards realizing quantum emitters (QEs) suitable for integration in quantum information networks stimulates the demand for a self-consistent numerical approach to describe scattering of radiatively limited QEs in complex dielectric environments. As the QE response has to be characterized without the use of phenomenological damping parameters, the divergent nature of the pointlike emitter's in-phase self-field has to be carefully dealt with to avoid unphysical frequency shifts. Here we provide a solution to this problem and show two ways to obtain accurate results in the weak excitation limit using finite-difference time-domain algorithms. One of these approaches lays important groundwork needed for future simulations of nonlinear QE networks. The solution for dealing with the frequency shift reveals that dynamical contributions to the resonant depolarization field of arbitrarily small dielectric objects make crucial contributions to the net dipole moment induced by an external field when radiative scattering is the only source of damping.
We present an efficient time domain numerical scheme for computing spontaneous emission dynamics in colored vacua. Starting from first principles, we map the unitary evolution of a dressed two-level quantum emitter onto the problem of electromagnetic radiation from a complex harmonic oscillator under self-interaction conditions. This latter oscillator-field system can be efficiently integrated by using finite difference time domain method without the need for calculating the photonic eigenmodes of the surrounding environment. In contrast to earlier investigations, our computational framework provides a unified numerical treatment for both weak and strong coupling regimes alike. We illustrate the versatility of our scheme by considering several different examples.
In this paper, we model the interaction of a quantum emitter with a finite-size dispersive dielectric object in an unbounded space within the framework of macroscopic quantum electrodynamics, using the modified Langevin noise formalism, without any restrictions on the emitter level structure or dipole operator. The quantized electromagnetic field consists of two contributions: the medium-assisted field, which accounts for the electromagnetic field generated by the noise polarization currents of the dielectric, and the scattering-assisted field, which takes into account the electromagnetic field incoming from infinity and scattered by the dielectric. We show that the emitter couples to two distinct bosonic baths: a medium-assisted bath and a scattering-assisted bath, each characterized by its own spectral density. We identify the conditions under which the electromagnetic environment composed of these two baths can be effectively replaced by a single bosonic bath, so that the reduced dynamics of the quantum emitter remain unchanged. In particular, when the initial states of the medium- and scattering-assisted baths are thermal states with the same temperature, we find that a single bosonic bath with a spectral density equal to the sum of the medium-assisted and scattering-assisted spectral densities is equivalent to the original electromagnetic environment.
Using the electromagnetic response function of an electric dipole located within a dielectric geometry, we derive the mathematical equivalence between the classical response and quantum mechanical resonant dipole–dipole interaction between two quantum objects (atoms, quantum dots, etc). Cooperative spontaneous emission likewise emerges from this equivalence. We introduce a practical numerical technique using finite difference time domain for calculating both dipole–dipole interaction and collective spontaneous emission in confined dielectric structures, where strong light–matter coupling might arise. This method is capable of obtaining resonant dipole–dipole interaction over a wide range of frequencies in a single run. Our method recaptures the results of quantum mechanical second order perturbation theory for weak light–matter coupling. In strong coupling situations such as near a photonic band edge, second order Rayleigh–Schrödinger perturbation theory leads to divergences, and instead Brillouin–Wigner perturbation theory is required. This is equivalent to the use of a variational wavefunction to describe the exciton transfer between initial and final states. We introduce a system of coupled classical oscillators, that describes resonant dipole–dipole interaction and vacuum Rabi splitting in the strong-coupling regime, and that provides an effective numerical scheme based on the finite difference time domain method. This includes the effects of quantum entanglement and the correlation of quantum fluctuations. We discuss the crossover to Forster energy transfer when quantum correlations between the dipoles are damped by strong environmental interactions.
Defining a quantum mechanical wavefunction for photons is one of the remaining open problems in quantum physics. Thus quantum states of light are usually treated within the realm of second quantization. Consequently, spontaneous emission (SE) in arbitrary photonic media is often described by Fock space Hamiltonians. Here, we present a real space formulation of the SE process that can capture the physics of the problem accurately under different coupling conditions. Starting from first principles, we map the unitary evolution of a dressed two-level quantum emitter onto the problem of electromagnetic radiation from a self-interacting complex harmonic oscillator. Our formalism naturally leads to an efficient computational scheme of SE dynamics using finite difference time domain method without the need for calculating the photonic eigenmodes of the surrounding environment. In contrast to earlier investigations, our computational framework provides a unified numerical treatment for both weak and strong coupling regimes alike. We illustrate the versatility of our scheme by considering several different examples.
A quantum-electrodynamic theory of spontaneous emission in presence of dielectrics and conductors is developed. The theory makes use of the master-equation techniques and the response-function formalism of part I of this series of papers. Various observable entities such as damping coefficients (lifetimes), Lamb shifts, and frequency shifts are related to the appropriate surface-dependent response functions. The results are valid for arbitrary geometries (involving linear dielectrics) and naturally contain, as a special case, the usual results of spontaneous emission in free space. As explicit examples we consider a two-level atom (also the multilevel atom) in presence of a plane dielectric interface and between two conducting plates. Formulas for the shifts and widths are given and their asymptotic behavior for large and short distances is discussed. The behavior when the atom is embedded inside the dielectric is different than when the atom is outside the dielectric. The origin of coherence in the present model is discussed and the coherence effects in this model are contrasted with those in Dicke's model. The results are also compared with those obtained by the image method. Exact expressions for the operator radiation-reaction fields are obtained in terms of the atomic polarization operators and response functions. Approximate results for such fields are also given. The far-zone behavior of the radiation fields is obtained in terms of response functions and the polarization operators. Some of the normally ordered correlation functions are also calculated. The connection of some of the theoretical results with a recent experimental work of Carniglia, Mandel, and Drexhage is discussed. The effect of anisotropy of the dielectric function on the lifetimes as well as on the far-field correlation functions is also considered. Finally the contribution to the shifts and widths due to the excitation of surface polariton modes is computed and the results are compared with those obtained by the quantization of surface polariton field. It is found that such surface modes contribute significantly to widths.
In this paper, we model the interaction of a quantum emitter with a finite-size dispersive dielectric object in unbounded space within the framework of macroscopic quantum electrodynamics, using the modified Langevin noise formalism. The quantized electromagnetic field consists of two contributions: the medium-assisted field, which accounts for the electromagnetic field generated by the noise polarization currents of the dielectric, and the scattering-assisted field, which takes into account the electromagnetic field incoming from infinity and scattered by the dielectric. We show that the emitter couples to two distinct bosonic reservoirs: a medium-assisted reservoir and a scattering-assisted reservoir, each characterized by its own spectral density. We then use emitter-centered modes to reduce the degrees of freedom of both reservoirs. Eventually, we identify the conditions under which the electromagnetic environment composed of these two reservoirs can be effectively replaced by a single bosonic reservoir so that the reduced time evolution of the quantum emitter remains unchanged. In particular, when the initial states of the medium- and scattering-assisted reservoirs are thermal quantum states at the same temperature, we find that a single bosonic bath with a spectral density equal to the sum of the medium- and scattering-assisted spectral densities is equivalent to the original electromagnetic environment.