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Entanglement and transport through correlated quantum dot

Adam Rycerz

Published Jan 1, 2008• 7 citations
OpenAlex

Abstract

We study quantum entanglement in a single–level quantum dot in the linear– response regime. The results show, that the maximal quantum value of the conductance 2e 2 /h not always match the maximal entanglement. The pairwise entanglement between the quantum dot and the nearest atom of the lead is also analyzed by utilizing the Wootters formula for charge and spin degrees of freedom separately. The coexistence of zero concurrence and the maximal conductance is observed for low values of the dot–lead hybridization. Moreover, the pairwise concurrence vanish simultaneously for charge and spin degrees of freedom, when the Kondo resonance is present in the system.

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We study quantum entanglement in a single–level quantum dot in the linear– response regime. The results show, that the maximal quantum value of the conductance 2e 2 /h not always match the maximal entanglement. The pairwise entanglement between the quantum dot and the nearest atom of the lead is also analyzed by utilizing the Wootters formula for charge and spin degrees of freedom separately. The coexistence of zero concurrence and the maximal conductance is observed for low values of the dot–lead hybridization. Moreover, the pairwise concurrence vanish simultaneously for charge and spin degrees of freedom, when the Kondo resonance is present in the system.
The transport properties of a linear structure of three quantum dots, with the central one connected to leads, are studied using the logarithmic discretization embedded cluster approximation. It is shown that the side dot spins can be ferromagnetically (F) or antiferromagnetically (AF) correlated between them, depending on the charge at the central dot. The system possesses a regime of coexistence of a two stage Kondo effect and the F phase. Ferromagnetism destroys the Kondo ground state when the system is driven to the molecular regime by increasing the interdot interaction above the largest Kondo temperature. Instead, an AF ground state does not compete with the Kondo regime. This remarkable behavior indicates that the measurement of the conductance can be an efficient readout procedure when the system operates as a quantum gate.
Semiconductor double‐quantum dots represent an ideal system for studying the novel spin physics of localized spins. On each quantum dot when the number of electrons is odd and the net spin is 1/2, a strong coupling of this localized spin to conducting electrons in the leads gives rise to Kondo correlation. On the other hand, in the coupled double‐quantum‐dot if the inter‐dot antiferromagnetic interaction is strong, the two spins can form a correlated spin‐singlet state, quenching the Kondo effect. This competition between Kondo and antiferromagnetic correlation is studied in a controlled manner by tuning the inter‐dot tunnel coupling. Increasing the inter‐dot tunneling, we observe a continuous transition from a single‐peaked to a double‐peaked Kondo resonance in the differential conductance. On the double‐peaked side, the differential conductance becomes suppressed at zero source‐drain bias. The observed strong suppression of the differential conductance at zero bias provides direct evidence signaling the formation of an entangled spin‐singlet state. This evidence for entanglement and the tunability of our devices bode well for quantum computation applications.
We study the interplay between strong correlations and Markovian dephasing, resulting from monitoring the charge or spin degrees of freedom of a quantum dot described by a dissipative Anderson impurity model. Using the auxiliary master equation approach, we compute the steady-state spectral function and occupation of the dot and discuss the role of dephasing on Kondo physics. Furthermore, we consider a two-lead setup that allows to compute the steady-state current and conductance. We show that the Kondo steady state is robust to moderate charge dephasing but not to spin dephasing, which we interpret in terms of dephasing-induced heating of low-energy excitations. Finally, we show universal scaling collapse of the nonlinear conductance with a dephasing-dependent Kondo scale.
Pairwise entanglement, calculated separately for charge and spin degrees of freedom, is proposed as a ground-state signature of the Mott transition in correlated nanoscopic systems. Utilizing the exact diagonalization— ab initio , for chains containing hydrogenic-like atoms (at the half filling), we find that the vanishing of the nearest-neighbor charge concurrence indicates the crossover from a partly-localized quantum liquid to the Mott insulator. Spin concurrence remains nonzero at the insulating phase, showing that the decopling of spin and charge degrees of freedom may manifest itself by wavefunctions entangled in spin, but separable in charge coordinates. At the quarter filling, the analysis for shows that spin concurrence vanishes immediately when the charge-energy gap obtained from the scaling with vanishes, constituting a finite-system version of the Mott transition. Analytic derivations of the formulas expressing either charge or spin concurrence in terms of ground-state correlation functions are also provided.
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 study correlated two-level quantum dots, coupled in effective one-channel fashion to metallic leads, with electron interactions including on-level and interlevel Coulomb repulsions, as well as the interorbital Hund's rule exchange favoring the spin-1 state in the relevant sector of the free dot. For arbitrary dot occupancy, the underlying phases, quantum phase transitions (QPTs), thermodynamics, single-particle dynamics, and electronic transport properties are considered, and direct comparison is made to conductance experiments on lateral quantum dots. Two distinct phases arise generically, one characterized by a normal Fermi liquid fixed point (FP) and the other by an underscreened (USC) spin-1 FP. Associated QPTs, which occur in general in a mixed valent regime of nonintegral dot charge, are found to consist of continuous lines of Kosterlitz-Thouless transitions, separated by first-order level-crossing transitions at high symmetry points. A ``Friedel-Luttinger sum rule'' is derived and, together with a deduced generalization of Luttinger's theorem to the USC phase (a singular Fermi liquid), is used to obtain a general result for the T=0T=0T=0 zero-bias conductance, expressed solely in terms of the dot occupancy and applicable to both phases. Relatedly, dynamical signatures of the QPT show two broad classes of behavior, corresponding to the collapse of either a Kondo resonance, or antiresonance, as the transition is approached from the Fermi liquid phase, the latter behavior being apparent in experimental differential conductance maps. The problem is studied using the numerical renormalization group method, combined with analytical arguments.