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arXiv:cond-mat/0312274 · Physical Review Letters

Nondemolition Measurements of a Single Quantum Spin using Josephson Oscillations

Lev N. Bulaevskii, Marina Hruška, Alexander Shnirman, Darryl Lyle Smith, Yu. Makhlin

Published Apr 27, 2004• 23 citations
arXivHTMLPDF

Abstract

We consider a single localized spin-1/2 between the singlet superconducting leads of a Josephson junction (e.g., a superconducting STM). For the spin subject to a dc magnetic field B parallel z, we study the spin dynamics and the possibility to measure the spin state via transport through the junction embedded in a dissipative circuit. Turning on the tunneling or a voltage bias induces oscillations of the Josephson current, with an amplitude sensitive to the initial value of the z component of the spin, S(z)=+/-1/2. At low temperatures, when effects of quasiparticles are negligible, this procedure realizes a quantum nondemolition measurement of S(z).

DOI
10.1103/physrevlett.92.177001

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arXiv:cond-mat/0501153•Applied Physics Letters•Dec 27, 2004•19 citations
We consider a single localized spin-1/2 between the singlet superconducting leads of a Josephson junction (e.g., a superconducting STM). For the spin subject to a dc magnetic field B parallel z, we study the spin dynamics and the possibility to measure the spin state via transport through the junction embedded in a dissipative circuit. Turning on the tunneling or a voltage bias induces oscillations of the Josephson current, with an amplitude sensitive to the initial value of the z component of the spin, S(z)=+/-1/2. At low temperatures, when effects of quasiparticles are negligible, this procedure realizes a quantum nondemolition measurement of S(z).
We consider a single localized spin-1/2 placed between singlet superconducting leads of a Josephson junction inserted in a superconducting ring, subject to a dc magnetic field B || z. Turning on the tunneling or a time-dependent flux in a superconducting ring, induces oscillations of the Josephson current, with an amplitude sensitive to the initial value of the z-component of the spin, Sz = ±1/2, which allows for a measurement of the initial spin state. At low temperatures when effects of quasiparticles are negligible, this procedure realizes a quantum-non-demolition (QND) measurement of Sz.
We show that the S/F/S Josephson ${\ensuremath{\varphi}}_{0}$ junction permits detection of macroscopic quantum tunneling and quantum oscillation of the magnetic moment by measuring the ac voltage across the junction. Exact expression for the tunnel splitting renormalized by the interaction with the superconducting order parameter is obtained. It is demonstrated that magnetic tunneling may become frozen at a sufficiently large ${\ensuremath{\varphi}}_{0}$. The quality factor of quantum oscillations of the magnetic moment due to finite ohmic resistance of the junction is computed. It is shown that magnetic tunneling rate in the ${\ensuremath{\varphi}}_{0}$ junction can be controlled by the bias current, with no need for the magnetic field.
Conventional tunnel Josephson junctions form the basic building blocks of superconducting electronics. Their operation is based on comparatively simple dynamics where the superconducting phases across the junctions is the only dynamical degree of freedom. The goal of the project on which this thesis is based, is to understand the physics and develop a consistent theoretical description of the quantum dynamics of unconventional Josephson structures: spin active junctions, junctions containing low energy quasiparticles, and junctions composed of ddd-wave superconductors. Spin active Josephson junctions involve the additional degree of freedom of quasiparticle spin. Here we theoretically investigate the spin-structure of the current carrying interface bound states - Andreev Bound States (ABS), and induced ground state spin polarization of a short (shorter than the superconducting coherence length) nanowire junction containing a localized magnetic moment. We show that temporal variation of the superconducting phase difference and magnetic moment induce rotations in spin polarized and unpolarized subspaces respectively, which is manifested by temporal oscillation of the Josephson current.The interlevel transitions obey a selection rule that forbids manipulations in a certain region ofexternal parameters and results from specific properties of Andreev bound states in magnetic contacts where, in a certain regime of phase bias and strength of magnetic scatterer, ABS belong to different eigenstates of the combined charge and parity inversion symmetry operator.A general framework is developed to include low energy quasiparticle states into the dynamics of Josephson junctions. Such states exist in e.g. constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. The existence of such states prevent the separation of energy scales which in conventional tunnel junctions freezes out the quasiparticle degrees of freedom. We show that the resonant interaction with such low energy states rather than the Josephson potential defines the nonlinear Josephson dynamics at small amplitudes.The framework is applied to high temperature Josephson junctions, whose unconventional order parameter admits ABS with energies in the middle of the superconducting gap - Mid Gap States (MGS). In addition to the non-linear dynamics induced by the MGS, we identify a reentrance effect in the transition between thermal activation and macroscopic quantum tunneling associated with the MGS, and connect this phenomenon to experimental observations.
Abstract. Superconducting circuits with Josephson tunnel junctions are interesting systems for research on quantummechanical behavior of macroscopic degrees of freedom. A particular realization is a small superconducting loop containing three Josephson junctions. Close to magnetic frustration 1=2, the physics of this system corresponds to a double well, whose minima correspond to persistent currents of opposite sign. We present DC measurements of the flux indicating a smooth transition close to the degeneracy point even at very low temperatures. Furthermore, microwavespectroscopy experiments allow for the excitation to the next excited state. The dependence of the energy of the resonance on the applied flux clearly indicates the nature of these states as tunneling-splitted superpositions of flux states. We theoretically analyze the system using a generalized master-equation formulation of the spin-boson model. We address the nature of the measuring process by a switching DC SQUID and the possible interpretation of the spectroscopy data in terms of quantum coherence. We discuss these aspects in the context of further applications as a quantum bit.
Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong backaction. We show that the backaction of a dc-switching detector can be considerably reduced by limiting the switching voltage and using a fast cryogenic amplifier, such that a single readout can be completed within 25 ns at a repetition rate of 1 MHz without loss of contrast. Based on a sequence of two successive readouts we show that the measurement has a clear quantum nondemolition character, with a QND fidelity of 75%.
Critical current fluctuations with a 1∕f spectral density (f is frequency) are potentially a limiting source of intrinsic decoherence in superconducting quantum bits (qubits) based on Josephson tunnel junctions. Prior measurements of this noise were made at nonzero voltages whereas qubits are operated in the zero voltage state. We report measurements of 1∕f noise in a dc superconducting quantum interference device first, coupled to a resonant tank circuit and operated in a dispersive mode at zero voltage, and, second, operated conventionally with a current bias in the voltage regime. Both measurements yield essentially the same magnitude of critical current 1∕f noise.