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arXiv:0909.4343 · Physica Scripta

Tunneling without tunneling: wavefunction reduction in a mesoscopic qubit

James A. Nesteroff, D. V. Averin

Published Dec 1, 2009• 0 citations
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Abstract

The transformation cycle and associated inequality are suggested for the basic demonstration of the wavefunction reduction in a mesoscopic qubit in measurements with quantum-limited detectors. Violation of the inequality would show directly that the qubit state changes in a way dictated by the probabilistic nature of the wavefunction and inconsistent with the dynamics of the Schrödinger equation: the qubit tunnels through an infinitely large barrier. Estimates show that the transformation cycle is within the reach of current experiments with superconducting qubits.

DOI
10.1088/0031-8949/2009/t137/014002

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The transformation cycle and associated inequality are suggested for the basic demonstration of the wavefunction reduction in a mesoscopic qubit in measurements with quantum-limited detectors. Violation of the inequality would show directly that the qubit state changes in a way dictated by the probabilistic nature of the wavefunction and inconsistent with the dynamics of the Schrödinger equation: the qubit tunnels through an infinitely large barrier. Estimates show that the transformation cycle is within the reach of current experiments with superconducting qubits.
Recent experimental demonstrations of quantum coherence of the charge and flux states of Josephson junctions show that the quantum Josephson dynamics can be used to develop scalable quantum logic circuits. In this work, I review the basic concepts of Josephson tunneling and Josephson-junction qubits, and discuss two problems of this tunneling motivated by quantum computing applications. One is the theory of photon-assisted resonant flux tunneling in SQUID systems used to demonstrate quantum coherence of flux. Another is the problem of quantum measurement of charge with the SET electrometer. It is shown that the SET electrometer at the Coulomb blockade threshold is the quantum-limited detector with energy sensitivity reaching ħ/√3 in the resonant-tunneling regime.
We study noninvasive measurement of stationary currents in mesoscopic systems. It is shown that the measurement process is fully described by the Schrödinger equation without any additional reduction postulate and without the introduction of an observer. Nevertheless the possibility of observing a particular state out of coherent superposition leads to collapse of the wave function, even though the measured system is not distorted by interaction with the detector. Experimental consequences are discussed.
We analyze several mechanisms leading to errors in a course of measurement of a superconducting flux-biased phase qubit. Insufficiently long measurement pulse may lead to nonadiabatic transitions between qubit states \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩, before tunneling through a reduced barrier is supposed to distinguish the qubit states. Finite (though large) ratio of tunneling rates for these states leads to incomplete discrimination between \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩. Insufficiently fast energy relaxation after the tunneling of state \ensuremath{\mid}1⟩ may cause the repopulation of the quantum well in which only the state \ensuremath{\mid}0⟩ is supposed to remain. We analyze these types of measurement errors using analytical approaches as well as a numerical solution of the time-dependent Schr\"odinger equation.
In quantum measurement theory it is necessary to show how a quantum source conditions a classical stochastic record of measured results. We discuss mesoscopic conductance using quantum stochastic calculus to elucidate the quantum nature of the measurement taking place in these systems. To illustrate the method we derive the current fluctuations in a two terminal mesoscopic circuit with two tunnel barriers containing a single quasi bound state on the well. The method enables us to focus on either the incoming/ outgoing Fermi fields in the leads, or on the irreversible dynamics of the well state itself. We show an equivalence between the approach of BÜttiker and the Fermi quantum stochastic calculus for mesoscopic systems.
Detecting quasiparticle tunneling events in superconducting circuits provides information about the population and dynamics of non-equilibrium quasiparticles. Such events can be detected by monitoring changes in the frequency of an offset-charge-sensitive superconducting qubit. This monitoring has so far been performed by Ramsey interferometry assisted by a readout resonator. Here, we demonstrate a quasiparticle detector based on a superconducting qubit directly coupled to a waveguide. We directly measure quasiparticle number parity on the qubit island by probing the coherent scattering of a microwave tone, offering simplicity of operation, fast detection speed, and a large signal-to-noise ratio. We observe tunneling rates between 0.8 and 7 s−17~\rm{s}^{-1}7 s−1, depending on the average occupation of the detector qubit, and achieve a temporal resolution below 10 μs10~μ\rm{s}10 μs without a quantum-limited amplifier. Our simple and efficient detector lowers the barrier to perform studies of quasiparticle population and dynamics, facilitating progress in fundamental science, quantum information processing, and sensing.