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Physical Review A

Dynamic generation of Bell states in a double-quantum-dot array including electron-phonon interaction

L. Debora Contreras-Pulido, F. Rojas

Published Mar 3, 2008• 6 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.77.032301

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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.
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.
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 investigate the dynamics of a double quantum dot charge qubit which is coupled to piezoelectric acoustic phonons, appropriate for GaAs heterostructures. At low temperatures, the phonon bath induces the non-Markovian dynamical behavior of the oscillations between the two charge states of the double quantum dot. Upon applying the numerically exact quasiadiabatic propagator path-integral scheme, the reduced density matrix of the charge qubit is calculated, thereby avoiding the Born-Markov approximation. This allows a systematic study of the dependence of the QQQ factor on the lattice temperature, on the size of the quantum dots, as well as on the interdot coupling. We calculate the QQQ factor for a recently realized experimental setup and find that it is two orders of magnitudes larger than the measured value, indicating that the decoherence due to phonons is a subordinate mechanism.
We investigate the electronic transport through two parallel double quantum dots coupled both capacitively and via a perpendicularly aligned charge qubit. The presence of the qubit leads to a modification of the coherent tunnel amplitudes of each double quantum dot. We study the influence of the qubit on the electronic steady-state currents through the system, the entanglement between the transport double quantum dots, and the back-action on the charge qubit. We use a Born-Markov secular quantum master equation for the system. The obtained currents show signatures of the qubit. The stationary qubit state may be tuned and even rendered pure by applying suitable voltages. In the Coulomb diamonds, it is also possible to stabilize pure entangled states of the transport double quantum dots.
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.
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.