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Journal of Physics Condensed Matter

Dynamical entanglement formation and dissipation effects in two double quantum dots

L. Debora Contreras-Pulido, F. Rojas

Published Oct 13, 2006• 4 citations
Publisher

Abstract

We study the static and dynamic formation of entanglement in charge states of a two double quantum dot array with two mobile electrons under the effect of an external driving field. We include dissipation via contact with a phonon bath. By using the density matrix formalism and an open quantum system approach, we describe the dynamical behaviour of the charge distribution (polarization), concurrence (measure of the degree of entanglement) and Bell state probabilities (two qubit states with maximum entanglement) of such a system, including the role of dot asymmetry and temperature effects. Our results show that it is possible to obtain entangled states as well as a most probable Bell state, which can be controlled by the driving field. We also evaluate how the entanglement formation based on charge states deteriorates as the temperature or asymmetry increases.

DOI
10.1088/0953-8984/18/43/001

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We study the static and dynamic formation of entanglement in charge states of a two double quantum dot array with two mobile electrons under the effect of an external driving field. We include dissipation via contact with a phonon bath. By using the density matrix formalism and an open quantum system approach, we describe the dynamical behaviour of the charge distribution (polarization), concurrence (measure of the degree of entanglement) and Bell state probabilities (two qubit states with maximum entanglement) of such a system, including the role of dot asymmetry and temperature effects. Our results show that it is possible to obtain entangled states as well as a most probable Bell state, which can be controlled by the driving field. We also evaluate how the entanglement formation based on charge states deteriorates as the temperature or asymmetry increases.
We demonstrate theoretical stationary and dynamical generation of Bell states in a system of two parallel double quantum dots with one mobile electron each (proposed as two charge qubits) driven by an external potential difference applied to the second of the double dots. For coherent dynamics, it is shown that each one of the four Bell states is obtained through a suitable nonentangled initial condition as well as through the control of the time-dependent external electric field. We analyze dissipative effects on such state formation, due to the coupling with a thermal bath of phonons. Via a Markovian master equation approach, which includes the electron-phonon interaction, we found that Bell-state probabilities are preserved for very low temperature but are adversely affected as the temperature increases. In addition, we include concurrence and charge distribution calculations in order to characterize the double-dot array. This electrostatic mechanism could be of interest in quantum-computation, -information, and -communication schemes.
The decoherence dynamics of two charge qubits in a double quantum dot is investigated theoretically. We consider the quantum dynamics of two interacting electrons in a vertically coupled quantum dot driven by an external electric field. We derive the equations of motion for the density matrix, in which the presence of an electron confined in the double dot represents one qubit. A Markovian approach to the dynamical evolution of the reduced density matrix is adopted. We evaluate the concurrence of two qubits in order to study the effect of acoustic phonons on the entanglement. We also show that the disentanglement effect depends on the double dot parameters and increases with the temperature.
We study the dynamics of quantum correlations of two coupled double quantum dots containing two excess electrons. The dissipation is included through the contact with an oscillator bath. We solve the Redfield master equation in order to determine the dynamics of the quantum discord (QD) and the entanglement of formation (EoF). Based on our results, we find that the QD is more resistant to dissipation than the EoF for such a system. We observe that this characteristic is related to whether the oscillator bath is common to both qubits or not and to the form of the interaction Hamiltonian. Moreover, our results show that the QD might be finite, even for higher temperatures in the asymptotic limit.
Quantum information and quantum computation implementation in terms of electron charges and spin has attracted tremendous attention for the development of large-scale quantum information processing [1-5]. Artificial and tunable charge qubits fabricated in a semiconductor nanostructure are suitable for the purpose, since various parameters can be controlled by external gate voltages [6,7]. The rapid control of external gate voltage in two-electron double quantum dots has been demonstrated [8,9].Entanglement has recently emerged as a significant resource in quantum information and other applications. However an important problem is to ensure the robustness of this resource; that is, the ability to maintain it against decay. Decoherence is one of the fundamental limitation in quantum information science, and the understanding and the control of its dynamics appears as a crucial issue for the development of quantum information devices.For charge qubits in quantum dots, the effects of phonons and electromagnetic and background charge fluctuations are important in the decoherence process. The effect of phonons on the dynamics of two charge qubits has been examined [10,11].In this work, we analyze the effect of telegraph noise on the dynamical of two electrons in laterally coupled quantum dots. The resulting qubit is supposed to evolve in the basis spanned by the states |0〉 and |1〉 which describe the electron localized in the left and right dot respectively. We investigate theoretically the quantum dynamics of two interacting electrons driven by an oscillatory electric field. In order to study the effect of the telegraph noise on the entanglement we adopt the concurrence.
Solid state quantum bits are a promising candidate for the realization of a scalable quantum computer, however, they are usually strongly limited by decoherence. We consider a double quantum dot charge qubit, whose basis states are defined by the position of an additional electron in the system of two laterally coupled quantum dots. The coupling of these two states can be controlled externally by a quantum point contact between the two dots. We discuss the decoherence through coupling to the electronic leads due to cotunneling processes. We focus on a simple Gedanken experiment, where the system is initially brought into a superposition and then the inter-dot coupling is removed nonadiabatically. We treat the system by invoking the Schrieffer-Wolff transformation in order to obtain a transformed Hamiltonian describing the cotunneling, and then obtain the dynamics of the density matrix using the Bloch-Redfield theory. As a main result, we show that there is energy relaxation even in the absence of inter-dot coupling. This is in contrast to what would be expected from the Spin-Boson model and is due to the fact that a quantum dot is coupled to two distinct baths.