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Entanglement production under electron phonon interaction in a quantum dot

A. LopezE

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We consider the quantum dot entangler device introduced by Oliver et al. [1] coupled to a single phonon mode. While we take the phonon interaction to all orders, we perform a fourth order calculation in electron-dot coupling. Using the Von Neumann entropy we measure the degree of entanglement. We find that the phonon mechanism habilitates single electron processes which manifest themselves as decoherent processes.

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We consider the quantum dot entangler device introduced by Oliver et al. [1] coupled to a single phonon mode. While we take the phonon interaction to all orders, we perform a fourth order calculation in electron-dot coupling. Using the Von Neumann entropy we measure the degree of entanglement. We find that the phonon mechanism habilitates single electron processes which manifest themselves as decoherent processes.
We study the effect of decoherence on a quantum von Neumann measurement process. We discuss the effect of phonon noise on the direct measurement of two-electron spin states in a double quantum dot achieved by monitoring the noise of the current flowing through a quantum point contact coupled to one of the dots. We show that although the decoherence is damaging to the procedure at the extremely low temperatures characteristic of spin-in-quantum-dots experiments, and may even be fatal, increasing the temperature leads to a revival of the usefulness of the protocol: At higher temperatures, when the reservoir becomes an effective source of energy, it can enhance system fluctuations, and under such conditions the decoherence becomes advantageous to the measurement scheme and leads to the enhancement of the distinguishability between the measured states. Hence, the uncontrollable interaction of the measured system with the environment can be either an advantage or a disadvantage for a quantum measurement, depending on the characteristics of the decoherence process.
We study a device for entangling electrons as co-tunneling occurs through a quantum dot where on-site electron-electron interactions U are in place. The main advantage of this device is that single-particle processes are forbidden by energy conservation as proposed by Oliver et al. ( Phys. Rev. Lett. 88 (2002) 7901). Within this model we calculated the two-electron transition amplitude, in terms of the T-matrix, to all orders in the coupling to the dot, and consider a finite lead bandwidth. The model filters singlet entangled pairs with the sole requirement of Pauli principle. Feynman paths involving consecutive and doubly occupied dot interfere destructively and produce a transition amplitude minimum at a critical value of the onsite repulsion U . Singlet filtering is demonstrated as a function of a gate voltage applied to the dot with a special resonance condition when the dot levels are symmetrically placed about the input lead energy.
We describe time-dependent single-electron transport through quantum dots in the Coulomb blockade regime. Coherent dynamics of a single charge qubit in a double quantum dot is discussed with full one-qubit manipulation. Strength of decoherence is controlled with the applied voltage, but uncontrolled decoherence arises from electron–phonon coupling and background fluctuations. Then energy-relaxation dynamics is discussed for orbital and spin degree of freedom in a quantum dot. The electron–phonon interaction and spin–orbit coupling can be investigated as the dissipation problem. Finally, charge detection measurement is presented for statistical analysis of single-electron tunnelling transitions and for a sensitive qubit read-out device.
We investigate decoherence in a triple quantum dot in a ring configuration, in which one dot is coupled to a damped phonon mode while the other two dots are connected to a source and a drain, respectively. In the absence of decoherence, single-electron transport may get blocked by an electron falling into a superposition decoupled from the drain; this is known as a dark state. Phonon-mediated decoherence affects this superposition and leads to a finite current. We study the current and its shot noise numerically within a master equation approach for the electrons and the dissipative phonon mode. A polaron transformation allows us to obtain a reduced equation for only the dot electrons, which provides analytical results in agreement with numerical ones.
We investigate electron charge decoherence in a laterally coupled single-electron semiconductor double quantum dot through electron-phonon interaction. We analytically and numerically evaluate the relaxation and dephasing rates due to electron coupling to both acoustic and optical phonons, and explore the system parameter space in terms of interdot distance, strength of single-dot confinement, and interdot coupling strength. Our numerical results show that the electron scattering rates are strongly dependent on the strength of the electron confinement and the size of the system. In addition, although the most dominant factor that determines the charge decoherence rate is the energy splitting between the charge qubit states, the details of the double dot configuration are also very important.