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Acta Physica Polonica A

Dynamics of a Charge Qubit Encoded in a Double Quantum Dot

Jakub Łuczak, Bogdan R. Bułka

Published Mar 1, 2018• 4 citations
Publisher

Abstract

We study the short time dynamics of a charge qubit encoded in two coherently coupled quantum dots connected to external electrodes.In the regime of sequential tunneling the waiting time distribution is used to investigate in details statistics of the tunneling events and their correlations.We show that the coherent rotation of the qubit state on the Bloch sphere can be seen in tunneling events when an electron is injected and leave the system.Decoherence, relaxation of the qubit state as well as leakage processes are studied by means of transient currents.

DOI
10.12693/aphyspola.133.748

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We study the short time dynamics of a charge qubit encoded in two coherently coupled quantum dots connected to external electrodes.In the regime of sequential tunneling the waiting time distribution is used to investigate in details statistics of the tunneling events and their correlations.We show that the coherent rotation of the qubit state on the Bloch sphere can be seen in tunneling events when an electron is injected and leave the system.Decoherence, relaxation of the qubit state as well as leakage processes are studied by means of transient currents.
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In this paper, we develop a nonperturbation 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 backreaction 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{T}_{1}T1​ and dephasing time T2{T}_{2}T2​ are analyzed in detail.
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We have analyzed and measured the quantum coherent dynamics of a circuit containing two coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two qubits are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation ofthe qubit circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each qubit by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup the measured pulse-induced probe currents are proportional to the probability for each qubit to have an extra Cooper pai1r after the manipulation. As expected from theory and observed experimentally the measured pulse-induced current in each probe has two frequency components whose position on the frequency axis can be externally controlled. This is a result ofthe inter-qubit coupling which is also responsible for the avoided level crossing that we observed in the qubits' spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape the system remains entangled most ofthe time reaching maximally entangled states at certain instances.