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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Generating and detecting electron spin entangled states in nanostructures

Xuedong Hu, S. Das Sarma

Published May 25, 2004• 0 citations
Publisher

Abstract

We discuss various approaches to create and detect electron spin entanglement, with a special emphasis on the study of the efficiency of a beam splitter as a detector for entangled electron pairs. In particular, we focus on the consequence of considering wavepacket states for the electrons as they enter the beam splitter in order to illustrate their particle characteristics. We then introduce double quantum dot as a possible source of spin entangled electrons. In particular, we show that a double quantum dot turnstile is, in principle, an efficient electron spin entangler or entanglement filter because of the exchange coupling between the dots and the tunable input/output potential barriers.

DOI
10.1117/12.549437

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We discuss various approaches to create and detect electron spin entanglement, with a special emphasis on the study of the efficiency of a beam splitter as a detector for entangled electron pairs. In particular, we focus on the consequence of considering wavepacket states for the electrons as they enter the beam splitter in order to illustrate their particle characteristics. We then introduce double quantum dot as a possible source of spin entangled electrons. In particular, we show that a double quantum dot turnstile is, in principle, an efficient electron spin entangler or entanglement filter because of the exchange coupling between the dots and the tunable input/output potential barriers.
We study the conditions for a double quantum dot system to work as a reliable electron spin entangler and the efficiency of a beam splitter as a detector for the resulting entangled electron pairs. In particular, we focus on the relative strengths of the tunneling matrix elements, the applied bias and gate voltage, the necessity of time-dependent input/output barriers, and the consequence of considering wave packet states for the electrons as they leave the double dot to enter the beam splitter. We show that a double quantum dot turnstile is, in principle, an efficient electron spin entangler or entanglement filter because of the exchange coupling between the dots and the tunable input/output potential barriers, provided certain conditions are satisfied in the experimental setup.
We propose a scheme based on using the singlet ground state of an electron spin pair in a double-quantum-dot nanostructure as a suitable setup for detecting entanglement between electron spins via the measurement of an optimal entanglement witness. Using time-dependent gate voltages and magnetic fields the entangled spins are separated and coherently rotated in the quantum dots and subsequently detected at spin-polarized quantum point contacts. We analyze the coherent time evolution of the entangled pair and show that by counting coincidences in the four exits an entanglement test can be done. This setup is close to present-day experimental possibilities and can be used to produce pairs of entangled electrons "on demand."
If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing and quantum communication, will be possible. We review our proposed spin-quantum dot architecture for a quantum computer and review some recent results on a deterministic source of entanglement generated by coupling quantum dots. Addressing the feasibility of quantum communication with entangled electrons we consider a scattering set-up with an entangler and beam splitter where the current noise exhibits bunching behavior for electronic singlet states and antibunching behavior for triplet states. We show that spin currents can produce noise even in the absence of any charge currents.
We review our recent work towards quantum communication in a solid-state environment with qubits carried by electron spins. We propose three schemes to produce spin-entangled electrons, where the required separation of the partner electrons is achieved via Coulomb interaction. The non-product spin-states originate either from the Cooper pairs found in a superconductor, or in the ground state of a quantum dot with an even number of electrons. In a second stage, we show how spin-entanglement carried by a singlet can be detected in a beam-splitter geometry by an increased (bunching) or decreased (antibunching) noise signal. We also discuss how a local spin-orbit interaction can be used to provide a continuous modulation of the noise as a signature of entanglement. Finally, we review how one can use a quantum dot as a spin-filter, a spin-memory read-out, a probe for single-spin decoherence and, ultimately, a single-spin measurement apparatus.
The goal of this thesis is to investigate theoretically the generation and behaviour of multipartite entanglement for solid-state nanosystems, in particular electron spin quantum bits (so-called 'qubits') in quantum dots. A quantum dot is a tiny potential well where a single electron can be trapped. A quantum bit can be implemented in this system by applying a magnetic field, and thereby lifting the degeneracy of the spin states of the electron. These spins can then be used as single qubits, and engineering many of these quantum dots next to each other gives as a register of qubits. In this scheme, the so-called Loss-DiVincenzo quantum computer, the single spins can be rotated e.g. by applying a time dependent magnetic field, and two spins can interact through controlling the potential barrier between them. A qubit cannot only be in a superposition of the two computational states 0 and 1 at the same time, but an even stranger characteristic arises for multiple qubits: this phenomenon is called entanglement and refers to a strong correlation between two or more qubits, which can not be achieved within the framework of classical physics, and exponentially enlarges the possible states for a N-qubit system as compared to a classical N-bit system. In this thesis we devise algorithms how to generate multipartite entangled states in electron spin qubits in quantum dots. We compare which classes of entangled states can be generated efficiently in this system. Once the states are created, they decay due to a process called decoherence. We compare how entangled states can be generated and detected in a realistic experiment, and which classes of states are the most suitable. Furthermore, we compare which classes conserve the entanglement, and quantify the robustness of various classes of entangled states. In the last chapter, we devise a scheme of how to execute a simple quantum algorithm, the Deutsch-Jozsa algorithm, in a system containing another type of solid-state qubit, the so-called flux qubit.
We report experimental research into the possibility of using shot noise mea-surements to detect the entangled states of electron spins. The study is part of the effort towards the demonstration of the use of electron spins as quantum bits (qubits) for quantum computing and quantum information processing. Electrons are electrically injected into two neighboring quantum dots and interact with each other through the exchange coupling, after which they tunnel out of the dots and are incident on a beam splitter, which introduces quantum interference between electron states. Depending on the state of the electrons exiting the dots, the outgoing states of electrons scattering off the beam splitter are different, corresponding to different shot noise in the electrical currents flowing into the channels after the beam splitter. Our experimental data is consistent with most theoretical predictions and provides initial evidence of electron spin entanglement. A comprehensive study of the shot noise in mesoscopic semiconductor tunnel barriers is also reported. Besides the theoretically predicted full shot noise, sup-pressed and enhanced shot noise are also observed. Normal conductance measure-ments and numerical simulations are done to understand the shot noise deviation. Our study shows that shot noise in mesoscopic systems is extremely sensitive to the microscopic details, such as potential disorder and impurity configuration.