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Non-local transport properties of a sextuple quantum dot system in the co-tunneling regime

Fredrik Brange

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Quantum entanglement between electrons in nanostructures is a key concept of quantum information still waiting to be experimentally demonstrated. In this master's thesis we present and analyze the full counting statistics of the charge transfer of a sextuple quantum dot system which works as both entangler and detector of spatially separated electrons. Under certain resonance conditions the system operates in the co-tunneling regime, limiting environment-induced decoherence. By means of a generalized Schrieffer-Wolff transformation the co-tunneling dynamics are obtained from an effective Hamiltonian. Based on these results, a master equation is derived for the reduced density operator of the open sextuple dot system and used to compute the full counting statistics. We find that the system displays quantum coherent non-local transport properties and violates Bell's inequality. Consequently, the sextuple dot system could potentially be used to experimentally demonstrate entanglement between electrons as intended.

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Quantum entanglement between electrons in nanostructures is a key concept of quantum information still waiting to be experimentally demonstrated. In this master's thesis we present and analyze the full counting statistics of the charge transfer of a sextuple quantum dot system which works as both entangler and detector of spatially separated electrons. Under certain resonance conditions the system operates in the co-tunneling regime, limiting environment-induced decoherence. By means of a generalized Schrieffer-Wolff transformation the co-tunneling dynamics are obtained from an effective Hamiltonian. Based on these results, a master equation is derived for the reduced density operator of the open sextuple dot system and used to compute the full counting statistics. We find that the system displays quantum coherent non-local transport properties and violates Bell's inequality. Consequently, the sextuple dot system could potentially be used to experimentally demonstrate entanglement between electrons as intended.
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.
We present electron spin entanglers-devices creating mobile spin-entangled electrons that are spatially separated-where the spin-entanglement in a superconductor present in form of Cooper pairs and in a single quantum dot with a spin singlet groundstate is transported to two spatially separated leads by means of a correlated two-particle tunneling event. The unwanted process of both electrons tunneling into the same lead is suppressed by strong Coulomb blockade effects caused by quantum dots, Luttinger liquid effects or by resistive outgoing leads. In this review we give a transparent description of the different setups, including discussions of the feasibility of the subsequent detection of spin-entanglement via charge noise measurements. Finally, we show that quantum dots in the spin filter regime can be used to perform Bell-type measurements that only require the measurement of zero frequency charge noise correlators.
Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is illustrated for electron transfer through a quantum-dot spin valve, which combines quantum-coherent spin precession with electron tunneling. We show that by counting the number of transferred electrons as a function of time, it is possible to distill out the coherent dynamics from the counting statistics even in transport regimes, in which other tools such as the frequency-dependent current noise and the waiting-time distribution fail.
We consider two quantum dots described by the Anderson-impurity model with one electron per dot. The goal of our work is to study the decay of a maximally entangled state between the two electrons localized in the dots. We prepare the system in a perfect singlet and then tunnel couple one of the dots to leads, which induces nonequilibrium dynamics. We identify two cases: If the leads are subject to a sufficiently large voltage and thus a finite current, then direct-tunneling processes cause decoherence and the entanglement as well as spin correlations decay exponentially fast. At zero voltage or small voltages and beyond the mixed-valence regime, virtual-tunneling processes dominate and lead to a slower loss of coherence. We analyze this problem by studying the real-time dynamics of the spin correlations and the concurrence using two techniques, namely, the time-dependent density matrix renormalization group method and a master-equation method. The results from these two approaches are in excellent agreement in the direct-tunneling regime for the case in which the dot is weakly tunnel coupled to the leads. We present a quantitative analysis of the decay rates of the spin correlations and the concurrence as a function of tunneling rate, interaction strength, and voltage.
We investigate entanglement transfer from a system of two spin-entangled electron-hole pairs, each placed in a separate single mode cavity, to the photons emitted due to cavity leakage. Dipole selection rules and a splitting between the light hole and the heavy hole subbands are the crucial ingredients establishing a one-to-one correspondence between electron spins and circular photon polarizations. To account for the measurement of the photons as well as dephasing effects, we choose a stochastic Schrödinger equation and a conditional master equation approach, respectively. The influence of interactions with the environment as well as asymmetries in the coherent couplings on the photon entanglement is analysed for two concrete measurement schemes. The first one is designed to violate the Clauser-Horne-Shimony-Holt (CHSH) inequality, while the second one employs the visibility of interference fringes to prove the entanglement of the photons. Because of the spatial separation of the entangled electronic system over two quantum dots, a successful verification of entangled photons emitted by this system would imply the detection of nonlocal spin entanglement of massive particles in a solid state structure.
We consider the counting statistics of electron transport through a double quantum dot with special emphasis on the dephasing induced by a nearby charge detector. The double dot is embedded in a dissipative enviroment, and the presence of electrons on the double dot is detected with a nearby quantum point contact. Charge transport through the double dot is governed by a non-Markovian generalized master equation. We describe how the cumulants of the current can be obtained for such problems, and investigate the difference between the dephasing mechanisms induced by the quantum point contact and the coupling to the external heat bath. Finally, we consider various open questions of relevance to future research.