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arXiv:0707.1171 · New Journal of Physics

Entanglement, measurement, and conditional evolution of the Kondo singlet interacting with a mesoscopic detector

Kicheon Kang, Gyong Luck Khym

Published May 9, 2007• 11 citations
arXivHTMLPDF

Abstract

We investigate various aspects of the Kondo singlet in a quantum dot (QD) electrostatically coupled to a mesoscopic detector. The two subsystems are represented by an entangled state between the Kondo singlet and the charge-dependent detector state. We show that the phase-coherence of the Kondo singlet is destroyed in a way that is sensitive to the charge-state information restored both in the magnitude and in the phase of the scattering coefficients of the detector. We also introduce the notion of the 'conditional evolution' of the Kondo singlet under projective measurement on the detector. Our study reveals that the state of the composite system is disentangled upon this measurement. The Kondo singlet evolves into a particular state with a fixed number of electrons in the QD. Its relaxation time is shown to be sensitive only to the QD-charge dependence of the transmission probability in the detector, which implies that the phase information is erased in this conditional evolution process. We discuss implications of our observations in view of the possible experimental realization.

DOI
10.1088/1367-2630/9/5/121

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We investigate various aspects of the Kondo singlet in a quantum dot (QD) electrostatically coupled to a mesoscopic detector. The two subsystems are represented by an entangled state between the Kondo singlet and the charge-dependent detector state. We show that the phase-coherence of the Kondo singlet is destroyed in a way that is sensitive to the charge-state information restored both in the magnitude and in the phase of the scattering coefficients of the detector. We also introduce the notion of the 'conditional evolution' of the Kondo singlet under projective measurement on the detector. Our study reveals that the state of the composite system is disentangled upon this measurement. The Kondo singlet evolves into a particular state with a fixed number of electrons in the QD. Its relaxation time is shown to be sensitive only to the QD-charge dependence of the transmission probability in the detector, which implies that the phase information is erased in this conditional evolution process. We discuss implications of our observations in view of the possible experimental realization.
We investigate the effect of the charge state measurement of the Kondo singlet in a quantum dot transistor via a capacitively coupled quantum point contact detector. By employing the variational ansatz for the singlet ground state of the quantum dot combined with the density matrix formulation for the coupled system, we show that the coherent Kondo singlet is destroyed by the phase-sensitive as well as the current-sensitive detection in the transmission and reflection coefficients at the quantum point contact. We argue that the phase-sensitive component of the decoherence rate may explain the anomalous features observed in a recent experiment by Avinun-Kalish et al. [Phys. Rev. Lett. 92, 156801 (2004)]. We also discuss the correlations of the shot noise at the quantum point contact detector and the decoherence in the quantum dot.
We investigate the conditional evolution of a charge state coupled to a mesoscopic detector under continuous weak measurement. The state suffers relaxation into a particular state with a definite charge when electrons in a particular output lead are monitored in the detector. The process of the conditional relaxation is not restricted by the shot noise of the detector, unlike the case of the back-action dephasing. As a result, the relaxation of conditional evolution is much faster than the current-sensitive part of dephasing. Furthermore, the direction of the relaxation depends on the choice of the output lead. We propose that these properties can be verified in a two-path interferometer containing a quantum dot capacitively coupled to a detector. In this setup, the current-current correlation between the interferometer and the detector reveals characteristic features of conditional relaxation.
We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.
We study two simple mesoscopic models of interacting two electrons; first one consists of two quantum coherent parallel conductors with long-range Coulomb interaction in some localized region and the other is of an interacting quantum dot (QD) side-coupled to a noninteracting quantum wire. We evaluate exact two-particle scattering matrix as well as two-particle current which are relevant in a two-particle scattering experiment in these models. Finally we show that the on-site repulsive interaction in the QD filters out the spin-singlet two-electron state from the mixed two-electron input states in the side-coupled QD model.
We investigate the entanglement between the spins of two quantum dots that are not connected at once to the same system. Quantum entanglement between localized spins is an essential property for the development of quantum computing and quantum information. It is for this reason that generating and controlling an entangled state between quantum dots received great attention in the later years. In this work, we show that the information on the spin orientation of a quantum dot can be kept, using the Kondo entanglement, in a reservoir of electrons. Then, this information can be transmitted to another dot after the first dot has been uncoupled from the reservoirs. We use a double quantum dot system in a parallel geometry to construct the initial state, where each dot interacts with reservoirs of different symmetries. We chose a phase in the couplings to induce an antiferromagnetic spin correlation between the dots. The time evolution of the initial state has been analyzed using the time-dependent density matrix renormalization group method. We found that a partially entangled state between the dots can be obtained, even if they are not connected at the same time. This entangled state is formed just during the transient and is destroyed in the stationary state. The stability of the state found in the transient is shown. To understand the details of these phenomena, a canonical transformation of the real space is used.
We investigate the entanglement between the spins of two quantum dots that are not simultaneously connected to the same system. Quantum entanglement among localized spins is a crucial property for the advancement of quantum computing and quantum information. Generating and controlling an entangled state between quantum dots have garnered significant attention in recent years for this reason. In this study, we demonstrate that information about the spin orientation of a quantum dot can be preserved, utilizing Kondo entanglement, within a reservoir of electrons. Subsequently, this information can be transmitted to another dot after the initial dot has been decoupled from the reservoirs. We employ a double quantum dot system in a parallel geometry to establish the initial state, where each dot interacts with reservoirs of different symmetries. A specific phase in the couplings is chosen to induce antiferromagnetic spin correlation between the dots. The time evolution of the initial state is analyzed using the time-dependent density matrix renormalization group method. Our findings reveal that a partially entangled state between the dots can be achieved, even when they are not simultaneously connected. This entangled state arises transiently and dissipates in the stationary state. The stability of the state observed during the transient phase is demonstrated. To comprehend the details of these phenomena, we employ a canonical transformation of real space.