Non-Markovian decoherence theory for a double-dot charge qubit

Abstract

In this paper, we develop a non-perturbation theory for describing decoherence dynamics of electron charges in a double quantum dot gated by electrodes. We extend the Feynman-Vernon influence functional theory to fermionic environments and derive an exact master equation for the reduced density matrix of electrons in the double dot for a general spectral density at arbitrary temperature and bias. We then investigate the decoherence dynamics of the double dot charge qubit with back-action of the reservoirs being fully taken into account. Time-dependent fluctuations and leakage effects induced from the dot-reservoir coupling are explicitly explored. The charge qubit dynamics from the Markovian to non-Markovian regime is systematically studied under various manipulating conditions. The decay behavior of charge qubit coherence and the corresponding relaxation time T1 and dephasing time T2 are analyzed in details.

Non-Markovian dynamics of an open quantum system with initial system-reservoir correlations: A nanocavity coupled to a coupled-resonator optical waveguide

“…In the literature, exact master equations for open systems are mostly derived without initial correlations, such as the systems associated with quantum Brown motions [7][8][9], quantum dot systems in various nanostructures [13,14], and cavity systems coupled to structured reservoirs as well as general non-Markovian reservoirs [16,17,36]. Here we concentrate the exact master equation for the photonic system in the presence of initial Gaussian correlated states.…”

“…Extending the Feynman-Vernon influence functional to other open quantum systems has also achieved great success recently, including the exact master equation for electron systems and the nonequilibrium quantum transport theory in various nanostructures [13][14][15], as well as the exact master equation for micro-or nanocavities in photonic crystals and the quantum transport theory for photonic crystals [16][17][18]. However, in most of these investigations, the system and the reservoir are often assumed to be initially uncorrelated with each other [19].…”

Quantum Zeno and anti-Zeno effect of a nanomechanical resonator measured by a point contact

“…We may deal with relevant energy function of form the densities of states and tunneling amplitudes to take into account the memory effect of the QPC reservoir on the electron transport and the NER system in non-Markovian treatment. For simplicity, we follow several non-Markovian electrontransport studies [19][20][21]23,35 and we consider a Lorentzian spectral density with energy-dependent density of states and tunneling amplitudes as…”

“…The memory effect on the electron transport can be studied in detail by modeling the reservoir spectral densities as Lorentzian functions that has been used in the study of influence of a measuring lead on quantum oscillator coupled to an electron reservoirs. [19][20][21][22][23] We do not make here the so-called wideband approximation ͑energy-independent spectral density of the electric bath, and energyindependent tunnel amplitudes and densities of states of the left and right leads of the QPC tunnel junction͒ as well as the high QPC bias-voltage-limit approximation, normally used 24,25 in the derivation of Markovian dynamical equations. As a consequence, our non-Markovian dynamics of the nanomechanical oscillator is valid for arbitrary QPC lead temperatures, and for arbitrary bias voltages, as long as the perturbation theory that we use holding up to the second order in the system-environment coupling strength.…”

Non-Markovian dynamics of quantum open systems embedded in a hybrid environment

“…For a bosonic bath, a set of powerful tools have been developed to investigate the open system dynamics, such as path integral approach [18,19], master equation approach [20,21,22,23], and Markov and non-Markovian quantum trajectory approach [24,25,26,27,28]. For fermionic bath, similar tools have also been developed, including scattering theory [29], non-equilibrium Green's function approach [30], and fermionic path integral [31,32]. Notably, the fermionic quantum state diffusion equations have been developed recently [33,34,35].…”