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arXiv:0809.1887 · Physical Review B

Detector backaction on the self-consistent bound state in quantum point contacts

Y. Yoon, Min-Sung Kang, Takahiro Morimoto, Lev G. Mourokh, Nobuyuki Aoki, John L. Reno, F. Bird, Y. Ochiai

Published Mar 10, 2009• 23 citations
arXivHTMLPDF

Abstract

Bound-state (BS) formation in quantum point contacts (QPCs) may offer a convenient way to localize and probe single spins. In this Rapid Communication, we investigate how such BSs are affected by monitoring them with a second QPC, which is coupled to the BS via wave-function overlap. We show that this coupling leads to a unique detector backaction, in which the BS is weakened by increasing its proximity to the detector. We also show, however, that this interaction between the QPCs can be regulated at will by using an additional gate to control their wave-function overlap.

DOI
10.1103/physrevb.79.121304

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Bound-state (BS) formation in quantum point contacts (QPCs) may offer a convenient way to localize and probe single spins. In this Rapid Communication, we investigate how such BSs are affected by monitoring them with a second QPC, which is coupled to the BS via wave-function overlap. We show that this coupling leads to a unique detector backaction, in which the BS is weakened by increasing its proximity to the detector. We also show, however, that this interaction between the QPCs can be regulated at will by using an additional gate to control their wave-function overlap.
We study the dynamics of two electron spins in coupled quantum dots (CQDs) monitored by a quantum point contact (QPC) detector. Their quantum state can be measured by embedding the QPC in an LC circuit. We derive the Bloch-type rate equations of the reduced density matrix for CQDs. Special attention is paid to the numerical results for the weak measurement condintion under a strong Coulomb interaction. It is shown that the evolution of QPC current always follows that of electron occupation in the right dot. In addition, we find that the output voltage of the circuit can reflect the evolution of QPC current when the circuit and QPC are approximately equal in frequency. In particular, the wave shape of the output voltage can be improved by adjusting the circuit resonance frequency and bandwidth.
We study theoretically transitions of a double quantum-dot qubit caused by nonequilibrium charge fluctuations in a nearby quantum point contact (QPC) used as a detector. We show that these transitions are related to the fundamental Heisenberg backaction associated with the measurement, and use the uncertainty principle to derive a lower bound on the transition rates. We also derive simple expressions for the transition rates for the usual model of a QPC as a mesoscopic conductor, with screening treated at the RPA level. Finally, numerical results are presented which demonstrate that the charge noise and shot noise backaction mechanisms can be distinguished in QPCs having nonadiabatic potentials. The enhanced sensitivity of the charge noise to the QPC potential is explained in terms of interference contributions similar to those which cause Friedel oscillations.
One-way quantum computing [1, 2] is an important approach for quantum computation based on a series of one-qubit measurements starting from a cluster state of a qubit array. Cluster states are highly-entangled states involving all qubits and are typically generated from an Ising-like Hamiltonian, starting from an initial product state |Ψ0〉 ≡ |Ψ(t = 0)〉 = Πi=1|+〉i , where |±〉i = (|0〉i±|1〉i)/ √ 2. Here, |0〉i and |1〉i are the two states of the i-th qubit in an N -qubit system. In ref. [3], we showed that cluster states in charge qubits[4–17] can be created by applying a single gate bias pulse, right after preparing the initial product state (one-step generation method), and are more robust against nonuniformities among qubits than decoherence-free (DF) states [18, 19] under a noise environment generated by a quantum point contact (QPC) detector, which is a sensitive detector of electric charge distribution[20, 21]. However, trap sites are often unavoidable in solid-state qubits owing to their small fabrication size and several experiments show that trap states significantly affect electric transport properties of nanoscale devices[22–25]. Here, we model the trap site as the island (discrete energy state) between double QPCs (DQPC) and investigate robustness of cluster states in charge qubits measured by the DQPC detector (Fig. 1). The charge qubits are based on quantum dots (QD), in which the position of the excess charge in a qubit affects the QPC current electrically, resulting in detection of charged state. Owing to this additional external degrees of freedom, this setup is considered to be a harsher and more realistic condition for qubits than that of ref .[3]. Here, we calculate a time-dependent fidelity of four charge qubits with DQPC by solving density matrix (DM) equations.
Entanglement between a particle and a detector is known to be inherent in the measurement process. Gurvitz recently analyzed the coupling of an electron in a double dot (DD) to a quantum point contact (QPC) detector. In this paper we examine the dynamics of entanglement that result between the DD and QPC. The rate of entanglement is optimized as a function of coupling when the electron is initially in one of the dots. It decreases asymptotically towards zero with increased coupling. The opposite behavior is observed when the DD is initially in a superposition: the rate of entanglement increases unboundedly as the coupling is increased. The possibility that there are conditions for which measurement occurs versus entanglement is considered.
We solve the master equations of two charge qubits measured by two serially coupled quantum point contacts (QPCs). We describe two-qubit dynamics by comparing entangled states with product states, and show that the QPC current can be used for reading out results of quantum calculations and providing evidences of two-qubit entanglement. We also calculate the concurrence of the two qubits as a function of dephasing rate that originates from the measurement. We conclude that coupled charge qubits can be effectively detected by a QPC-based detector.
Closely related to the quantum information processing in solid states, we study the quantum measurement of single electron state by a mesoscopic charge-sensitive detector, namely the quantum point contact (QPC). We find that the conventional Lindblad-type master equation is not appropriate for describing the underlying measurement dynamics. The treatment developed in this work properly accounts for the energy-exchange between the detector and the measured system, and its role on the detailed-balance relation. A valid description for the QPC measurement dynamics is provided which may have impact on the study of quantum measurement and quantum feedback control in solid states.