Electromagnetically coupled two-level systems play a central role in several condensed matter components being considered for quantum information processing applications. If the states couple to phonon excitations, their electromagnetic response is altered via phonon-assisted transitions and lifetime broadening. The former has been treated extensively for a number of specific two-level systems (e.g., excitons in artificial quantum dots, localized states associated with impurities or defects, etc.), but the latter has received less attention. Here we study a microscopic model of the dipole transition of a two-level system under the influence of both diagonal and nondiagonal interactions with a bath of phonons. Our results capture both the influence of the frequency distribution of phonons on the relative spectral weight of the zero-phonon transition and the phonon sidebands, and the broadening of the zero-phonon line due to nondiagonal electron-phonon coupling. We use a formalism that includes non-Markovian effects related to the feedback mechanism between the two-level system and the phonon bath. For simplified forms of the phonon spectral functions we provide analytical expressions up to second order in the coupling strength that demonstrate the importance of including both forms of electron-phonon coupling in studies of these systems. Our formalism can be generalized to higher orders of coupling and for realistic phonon spectral functions.
Electromagnetically coupled two-level systems play a central role in several condensed matter components being considered for quantum information processing applications. If the states couple to phonon excitations, their electromagnetic response is altered via phonon-assisted transitions and lifetime broadening. The former has been treated extensively for a number of specific two-level systems (e.g., excitons in artificial quantum dots, localized states associated with impurities or defects, etc.), but the latter has received less attention. Here we study a microscopic model of the dipole transition of a two-level system under the influence of both diagonal and nondiagonal interactions with a bath of phonons. Our results capture both the influence of the frequency distribution of phonons on the relative spectral weight of the zero-phonon transition and the phonon sidebands, and the broadening of the zero-phonon line due to nondiagonal electron-phonon coupling. We use a formalism that includes non-Markovian effects related to the feedback mechanism between the two-level system and the phonon bath. For simplified forms of the phonon spectral functions we provide analytical expressions up to second order in the coupling strength that demonstrate the importance of including both forms of electron-phonon coupling in studies of these systems. Our formalism can be generalized to higher orders of coupling and for realistic phonon spectral functions.
We investigate the effect of electron-phonon interactions on the coherence properties of single photons emitted from a semiconductor cavity QED (quantum electrodynamics) system, i.e., a quantum dot embedded in an optical cavity. The degree of indistinguishability, governing the quantum mechanical interference between two single photons, is calculated as a function of important parameters describing the cavity QED system and the phonon reservoir, e.g., cavity quality factor, light-matter coupling strength, temperature, and phonon lifetime. We show that non-Markovian effects play an important role in determining the coherence properties for typical parameter values and establish the conditions under which a Markovian approximation may be applied. The calculations are performed using a recently developed second-order perturbation theory, and the limits of validity are established by comparing to an exact diagonalization approach. We find that for large cavity decay rates the perturbation theory may break down.
The transition from weakly damped coherent motion to localization in the context of the spin-boson model has been the subject of numerous studies with distinct behavior depending on the form of the phonon-bath spectral density $J\left(\ensuremath{\omega}\right)\ensuremath{\propto}{\ensuremath{\omega}}^{s}$. Sub-Ohmic (s<1) and Ohmic (s=1) spectral densities show a clear localization transition at zero temperature and zero bias, while for super-Ohmic (s>1) spectral densities this transition disappears. In this paper, we consider the influence of the phonon-bath spectral density on the nonequilibrium dynamics of a quantum dot with electron-phonon interactions described by the extended Holstein model. Using the reduced density matrix formalism combined with the multilayer multiconfiguration time-dependent Hartree approach, we investigate the dynamic response, the time scales for relaxation, as well as the existence of multiple long-lived solutions as the system-bath coupling changes from the sub- to the super-Ohmic cases. Bistability is shown to diminish for increasing powers of s similar to the spin-boson case. However, the physical mechanism and the dependence on the model parameters such as the typical bath frequency ${\ensuremath{\omega}}_{c}$ and the polaron shift $\ensuremath{\lambda}$ are rather distinct.
A finite coupling generalised master equation theory of the electronic relaxation among electronic eigen-states is presented. When converted into a closed time-convolution form (TCGME) for just diagonal elements of the density matrix, the theory is appreciably non-Markovian with the memory kernel summed partially up to the infinite order in the electron-phonon coupling. On soluble examples, it is shown that: (a), higher-order effects may influence even the lowest-order relaxation rates; (b), weakness of the finite coupling is not sufficient for reducing the theory to the standard lowest-order form; (c), the Markov approximation to the TCGME is in general misleading; (d), the initial condition term may appreciably influence the long-time development of the relaxation; (e), the theory is able to yield quasi-coherent effects (quantum beats) due to the electron coupling to the bath; (f), very effective tunnelling through barriers between equivalent sites appears with non-zero tunnelling currents starting from the second order in the electron-phonon coupling. Limitations from above (below) for the time (frequency) are found for the theory to reduce to the standard lowest-order form.
In this thesis we study the role of nonradiative degrees of freedom on quantum optical properties of mesoscopic quantum dots placed in the structured electromagnetic reservoir of a photonic crystal. We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption lineshape, 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. Phonon sidebands in an ordinary electromagnetic reservoir are recaptured in a simple model of optical phonons using a mean-field factorization of the atomic and lattice displacement operators. Our formalism is then used to treat the non-Markovian dynamics of the same system within the structured electromagnetic density of states of a photonic crystal. 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 enhanced lifetime of a photon-atom bound state in a PBG by (i) dephasing and reducing the transition electric dipole moment of the atom and (ii) reducing the quantum mechanical overlap of the state vectors of the excited and ground state (polaronic shift). 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 (break-up of phonons into lower energy phonons) and purely nonradiative decay. We demonstrate how these additional damping effects limit the extent of the polaronic (Franck-Condon) shift of the atomic excited state. 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 lineshapes. 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.
We investigate the temperature dependence of photon coherence properties through two-photon interference (TPI) measurements from a single quantum dot (QD) under resonant excitation. We show that the loss of indistinguishability is related only to the electron-phonon coupling and is not affected by spectral diffusion. Through these measurements and a complementary microscopic theory, we identify two independent separate decoherence processes, both of which are associated with phonons. Below 10 K, we find that the relaxation of the vibrational lattice is the dominant contribution to the loss of TPI visibility. This process is non-Markovian in nature and corresponds to real phonon transitions resulting in a broad phonon sideband in the QD emission spectra. Above 10 K, virtual phonon transitions to higher lying excited states in the QD become the dominant dephasing mechanism, this leads to a broadening of the zero phonon line, and a corresponding rapid decay in the visibility. The microscopic theory we develop provides analytic expressions for the dephasing rates for both virtual phonon scattering and non-Markovian lattice relaxation.
This work is focused on the optical dynamics of mesoscopic semiconductor heterostructures, using as prototypes zero-dimensional quantum dots and quantum cascade lasers which consist of quasitwo-dimensional quantum wells. Within a density matrix theory, a microscopic many-particle theory is applied to study scattering effects in these structures: the coupling to external as well as local fields, electron-phonon coupling, coupling to impurities, and Coulomb coupling. For both systems, the investigated effects are compared to experimentally observed results obtained during the past years. In quantum dots, the three-dimensional spatial confinement leads to the necessity to consider a quantum kinetic description of the dynamics, resulting in non-Markovian electron-phonon effects. This can be seen in the spectral phonon sidebands due to interaction with acoustic phonons as well as a damping of nonlinear Rabi oscillations which shows a nonmonotonous intensity and pulse duration dependence. An analysis of the inclusion of the self-interaction of the quantum dot shows that no dynamical local field terms appear for the simple two-level model. Considering local fields which have their origin in many quantum dots, consequences for a two-level quantum dot such as a zero-phonon line broadening and an increasing signal in photon echo experiments are found. For the use of quantum dots in an optical spin control scheme, it is found that the dephasing due to the electron-phonon interaction can be dominant in certain regimes. Furthermore, soliton and breather solutions are studied analytically in nonlinear quantum dot ensembles. Generalizing to quasi-two-dimensional structures, the intersubband dynamics of quantum cascade laser structures is investigated. A dynamical theory is considered in which the temporal evolution of the subband populations and the current density as well as the influence of scattering effects is studied. In the nonlinear regime, the scattering dependence and the importance of coherence for Rabi oscillations is investigated. The optically induced charge dynamics is discussed with respect to coherent effects. Calculations of the electronic density and pump-probe signals within a microscopic theory of dephasing show coherent transport effects such as gain oscillations, in agreement with recent experimental results.