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arXiv:1312.3982 · Europhysics Letters (EPL)

Full counting statistics of generic spin entangler with quantum dot-ferromagnet detectors

O. Malkoc, C. Bergenfeldt, Peter Samuelsson

Published Feb 1, 2014• 8 citations
arXivHTMLPDF

Abstract

Entanglement between spatially separated electrons in nanoscale transport is a fundamental property, yet to be demonstrated experimentally. Here we propose and analyse theoretically the transport statistics of a generic spin entangler coupled to a hybrid quantum dot-ferromagnet detector system. We show that the full distribution of charges arriving at the ferromagnetic terminals provides complete information on the spin state of the particles emitted by the entangler. This provides means for spin entanglement detection via electrical current correlations, with optimal measurement strategies depending on the a priori knowledge of ferromagnet polarization and spin-flip rates in the detector dots. The scheme is exemplified by applying it to Andreev and triple dot entanglers.

DOI
10.1209/0295-5075/105/47013

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Entanglement between spatially separated electrons in nanoscale transport is a fundamental property, yet to be demonstrated experimentally. Here we propose and analyse theoretically the transport statistics of a generic spin entangler coupled to a hybrid quantum dot-ferromagnet detector system. We show that the full distribution of charges arriving at the ferromagnetic terminals provides complete information on the spin state of the particles emitted by the entangler. This provides means for spin entanglement detection via electrical current correlations, with optimal measurement strategies depending on the a priori knowledge of ferromagnet polarization and spin-flip rates in the detector dots. The scheme is exemplified by applying it to Andreev and triple dot entanglers.
The work contained in this thesis deals with two closely related topics. Papers I-III deal with charge transport statistics in nanoscale devices to investigate the presence of entanglement in the constituent electrons. We identify the contributions of entangled electron pairs to the current cross-correlations as a signature of entanglement. Paper IV treats the electric control of a quantum dot based spin qubit via Electric Dipole Spin Resonance.In Paper I, we present a spin entanglement detection model in a hybrid nanoscale device, with a general entangler connected to a set of quantum dots and anti-collinear ferromagnetic contacts. Our model allows us to study the implications of a non-ideal detector in an entanglement detection scheme.In Paper II, we investigate a scheme for generating and detecting orbitally entangled states in a device consisting of six quantum dots. The underlying process which enables our proposed scheme is sufficiently fast, even for the rapidly decaying quantum coherence of orbital states defined in a solid.In Paper III, we investigate a minimal entanglement detection scheme based on measurements of current cross correlations. We find a significant reduction in the number of measurements required for an entanglement test.In Paper IV, we investigate the optimisation of electrically controlling an electron spin in a gate defined semiconductor quantum dot. Specifically, we study how the shape of the quantum dot together with the direction of an in-plane magnetic field affect the spin relaxation rate and frequency of the induced Rabi oscillations.
The development of quantum computing in quantum dots systems requires highly ecient and continuous solidstate source of spatially separated spin-entangled electrons.One of the approaches is a use of double quantum dot system connected to superconducting lead, where Cooper pairs provide a source of naturally entangled electrons.Apart from the source, an useful tool for detection of quantum entanglement is needed.We present entanglement detection by the ferromagnetic electrodes using entanglement witness operator method and direct measurement of spin polarized current in the system.We investigate requirements that have to be fullled by ferromagnetic detectors.
We analyze a model of a double quantum dot Cooper pair splitter coupled to two ferromagnetic detectors and demonstrate the possibility of determination of spin correlation by current measurements. We use perturbation theory, taking account of the exchange interaction with the detectors, which leads to complex spin dynamics in the dots. This affects the measured spin and restricts the use of ferromagnetic detectors to the nonlinear current-voltage characteristic regime at the current plateau, where the relevant spin projection is conserved, in contrast to the linear current-voltage characteristic regime, in which the spin information is distorted. Moreover, we show that for separable states the spin correlation can only be determined in a limited parameter regime, much more restricted than in the case of entangled states. We propose an entanglement test based on the Bell inequality.
Abstract Correlations are fundamental in describing many body systems - not only in natural sciences. However, in experiments, correlations are notoriously difficult to assess on the microscopic scale, especially for electron spins. Here, we demonstrate a direct measurement of the spin cross-correlations between the currents of a Cooper pair splitter, an electronic device that emits electrons originating from Cooper pairs in a superconductor. While it is firmly established theoretically that these electron pairs form maximally spin-entangled singlet states with opposite spin projections, no spin correlation experiments have been demonstrated so far. We use ferromagnetic sidegates, compatible with superconducting electronic structures, to individually spin polarize the transmissions of two quantum dots fabricated in the two electronic paths, which act as tunable spin filters. The signals are detected in standard transport and in highly sensitive transconductance experiments. We find that the spin-cross correlation is negative, compatible with spin singlet emission, and deviates from the ideal value mostly due to a finite overlap of the Zeeman split quantum dot states. Our results demonstrate a new route to perform spin auto- and cross correlation experiments in nanometer scaled electronic devices, especially suitable for those relying on magnetic field sensitive superconducting elements, like unconventional, triplet or topologically non-trivial superconductors, or to perform Bell tests with massive particles, like electrons.
We study the production of spatially separated entangled electrons in ferromagnetic leads from Cooper pairs in a superconducting lead. We give a complete description of the elementary charge transfer processes, i) transfer of Cooper pairs out of the superconductor by Andreev reflection and ii) distribution of the entangled quasiparticles among the ferromagnetic leads, in terms of their statistics. The probabilities that entangled electrons flow into spatially separated leads are completely determined by experimentally measurable tunnel conductances and polarizations. Finally, we investigate how currents, noise and cross-correlations are affected by transport of entangled electrons.
Entangled states are essential in basics quantum communication protocols and quantum cryptography.Ferromagnetic contacts can work as a spin detector, giving possibility of converting information about electron spin to the electric charge, and therefore, detection of entangled states with the electric current measurements is possible.Method of conrming entanglement with non-ideal detectors is presented, the impact of decoherence and noise on states and quality of entanglement is discussed.Entanglement witness (EW) operator method is compared with the CHSH inequalities approach.Required spin polarization for the EW is lower than for the CHSH inequalities.System with asymmetric spin polarizations of detectors was analyzed, including the CHSH inequalities and the EW method.