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Quantum master equations for the superconductor--dot entangler

Olivier Sauret, D. Feinberg, Thierry Martin

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The operation of a source of entangled electron spins, based on a superconductor and two quantum dots in parallel\cite{loss}, is described in detail with the help of quantum master equations. These are derived including the main parasitic processes in a fully consistent and non-perturbative way, starting from a microscopic Hamiltonian. The average current is calculated, including the contribution of entangled and non-entangled pairs. The constraints on the operation of the device are illustrated by a calculation of the various charge state probabilities.

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The operation of a source of entangled electron spins, based on a superconductor and two quantum dots in parallel\cite{loss}, is described in detail with the help of quantum master equations. These are derived including the main parasitic processes in a fully consistent and non-perturbative way, starting from a microscopic Hamiltonian. The average current is calculated, including the contribution of entangled and non-entangled pairs. The constraints on the operation of the device are illustrated by a calculation of the various charge state probabilities.
The operation of a source of entangled electron spins, based on a superconductor and two quantum dots in parallel, is described in detail with the help of quantum master equations. These are derived including the main parasitic processes in a fully consistent and nonperturbative way, starting from a microscopic Hamiltonian. The average current is calculated, including the contribution of entangled and nonentangled pairs. The constraints on the operation of the device are illustrated by a calculation of the various charge state probabilities.
The detailed operation of an electron spin entangler is studied, using density matrix equations. The device is made of a superconductor, two quantum dots and two normal leads. The treatment takes into account coherent tunneling in a non-perturbative way, and analyzes the various parasitic effects, in addition to the main process (crossed Andreev reflection) : those include singlet pairs passing through a single dot, or cotunneling between dots through the superconductor. The optimum operation of the device is characterized.
Charge and spin current correlations are analyzed in a source of spin-entangled electrons built from a superconductor and two quantum dots in parallel. In addition to the ideal (crossed Andreev) channel, parasitic channels (direct Andreev and cotunneling) and spin flip processes are fully described in a density matrix framework. The way they reduce both the efficiency and the fidelity of the entangler is quantitatively described by analyzing the zero-frequency noise correlations of charge current as well as spin current in the two output branches. Spin current noise is characterized by a spin Fano factor, equal to 0 (total current noise) and -1 (crossed correlations) for an ideal entangler. The violation of the Bell inequalities, as a test of non-locality (entanglement) of split pairs, is formulated in terms of the correlations of electron charge and spin numbers counted in a specific time window τ\tauτ. The efficiency of the test is analyzed, comparing τ\tauτ to the various time scales in the entangler operation.
Charge and spin current correlations are analyzed in a source of spin-entangled electrons built from a superconductor and two quantum dots in parallel. In addition to the ideal (crossed Andreev) channel, parasitic channels (direct Andreev and cotunneling) and spin flip processes are fully described in a density matrix framework. The way they reduce both the efficiency and the fidelity of the entangler is quantitatively described by analyzing the zero-frequency noise correlations of charge current as well as spin current in the two output branches. Spin current noise is characterized by a spin Fano factor, equal to 0 (total current noise) and $\ensuremath{-}1$ (crossed correlations) for an ideal entangler. The violation of the Bell inequalities, as a test of nonlocality (entanglement) of split pairs, is formulated in terms of the correlations of electron charge and spin numbers counted in a specific time window $\ensuremath{\tau}$. The efficiency of the test is analyzed, comparing $\ensuremath{\tau}$ to the various time scales in the entangler operation.
An electron-spin state teleportation scheme is described in detail. It is based on the protocol by Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)], and involves the production and detection by superconductors of entangled pairs of electrons. Quantum dots filter individual electron transitions, and the whole teleportation sequence is selected in a five-dot cell by electrostatic gating in the stationary regime (no time-dependent gate voltages): (i) a normal dot carries the electron-spin state to be teleported, two others carry the ancillary entangled pair; (ii) two superconducting dots, coupled by a superconducting circuit, control the injection of the source electron and the detection of the teleported electron. This teleportation cell is coupled to emitter and receiver reservoirs. In a steady state, a spin-conserving current flows between the reservoirs, most exclusively carried by the teleportation channel. This current is perfectly correlated to a Cooper pair current flowing in the superconducting circuit, and which triggers detection of the teleported electron. This latter current indeed carries the classical information, which is necessary to achieve teleportation. The average teleportation current is calculated using the Bloch equations, for weakly coupled spin reservoirs. A diagnosis of teleportation is proposed using noise correlations.
Devices to generate on-demand non-local spin entangled electron pairs have potential application as solid-state analogues of the entangled photon sources used in quantum optics. Recently, Andreev entanglers that use two quantum dots as filters to adiabatically split and separate the quasi-particles of Cooper pairs have shown efficient splitting through measurements of the transport charge but the spin entanglement has not been directly confirmed. Here we report measurements on parallel quantum dot Josephson junction devices allowing a Josephson current to flow due to the adiabatic splitting and recombination of the Cooper pair between the dots. The evidence for this non-local transport is confirmed through study of the non-dissipative supercurrent while tuning independently the dots with local electrical gates. As the Josephson current arises only from processes that maintain the coherence, we can confirm that a current flows from the spatially separated entangled pair.