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Phase Space Topology of a Switching Current Detector
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
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2006 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 73, 132511- p.Article in journal (Refereed) Published
Abstract [en]

We examine in theory and by numerical simulation, the dynamic process of switching from a zero voltage to a finite voltage state in a Josephson junction circuit. The theoretical model describes small capacitance Josephson junctions which are overdamped at high frequencies, and can be applied to detection of the quantum state of a qubit circuit. We show that the speed and fidelity of the readout are strongly influenced by the topology of the phase space attractors. The readout will be close to optimal when choosing the circuit parameters so as to avoid having an unstable limiting cycle which separates the two basins of attraction.

Place, publisher, year, edition, pages
2006. Vol. 73, 132511- p.
Keyword [en]
josephson-junctions; quantum-state
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-6276DOI: 10.1103/PhysRevB.73.132511ISI: 000237153800028Scopus ID: 2-s2.0-33646232997OAI: oai:DiVA.org:kth-6276DiVA: diva2:10949
Note
QC 20100812Available from: 2006-10-23 Created: 2006-10-23 Last updated: 2010-09-24Bibliographically approved
In thesis
1. Pulse and hold switching current readout of superconducting quantum circuits
Open this publication in new window or tab >>Pulse and hold switching current readout of superconducting quantum circuits
2006 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Josephson junction qubits are promising candidates for a scalable quantum processor. Such qubits are commonly manipulated by means of sequences of rf-pulses and different methods are used to determine their quantum state. The readout should be able to distinguish the two qubit states with high accuracy and be faster than the relaxation time of the qubit. We discuss and experiment with a readout method based on the switching of a Josephson junction from the zero voltage state to a finite voltage state.

The Josephson junction circuit has a non-linear dynamics and when it is brought to a bifurcation point, it can be made arbitrarily sensitive to small perturbations. This extreme sensitivity at a bifurcation point can be used to distinguish the two quantum states if the topology of the phase space of the circuit leads to a quick separation into the final states where re-crossings of the bifurcation point are negligible. We optimize a switching current detector by analyzing the phase space of a Josephson junction circuit with frequency dependent damping.

A pulse and hold technique is used where an initial current pulse brings the junction close to its bifurcation point and the subsequent hold level is used to give the circuit enough time to evolve until the two states can be distinguished by the measuring instrument. We generate the pulse and hold waveform by a new technique where a voltage step with following linear voltage rise is applied to a bias capacitor. The frequency dependent damping is realized by an on-chip RC-environment fabricated with optical lithography. Josephson junction circuits are added on by means of e-beam lithography.

Measurements show that switching currents can be detected with pulses as short as 5 ns and a resolution of 2.5% for a sample directly connected to the measurement leads of the cryostat. Detailed analysis of the switching currents in the RC-environment show that pulses with a duration of 20 us can be explained by a generalization of Kramers' escape theory, whereas switching the same sample with 25 ns pulses occurs out of thermal equilibrium, with sensitivity and speed adequate for qubit readout.

Place, publisher, year, edition, pages
Stockholm: KTH, 2006. viii, 82 p.
Series
Trita-FYS, ISSN 0280-316X ; 2006:61
Keyword
Josephson junction, readout, qubit, detector, frequency dependent damping, quantronium, phase-space, correlation analysis
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-4156 (URN)91-7178-462-4 (ISBN)
Public defence
2006-11-10, FA32, AlbaNova Main Building, Roslagstullsbacken 21, Stockholm, 13:00
Opponent
Supervisors
Note
QC 20100924Available from: 2006-10-23 Created: 2006-10-23 Last updated: 2010-09-24Bibliographically approved
2. Intermodulation in microresonators: for microwave amplification and nanoscale surface analysis
Open this publication in new window or tab >>Intermodulation in microresonators: for microwave amplification and nanoscale surface analysis
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This work explores the effects of weak nonlinearity on harmonic oscillators.Two particular systems are studied experimentally: A superconductingresonator formed from a coplanar waveguide that oscillates at microwave frequencies,and the cantilever of an atomic force microscope (AFM) vibratingat ultrasonic frequencies. Both of these systems are described in the introduction,followed by a theory chapter giving a general theoretical framework for nonlinear oscillators. Basic properties of nonlinear oscillators, such asbifurcation and intermodulation, are explained using simple models. Experimental methods, including cryogenic and microwave measurement techniques,are described in some detail.

The nonlinear superconducting resonator is studied for use as a parametric amplifier. A strong drive tone, called the pump, drives the oscillator nearthe point of bifurcation. A second, much weaker drive signal that is slightlydetuned from the pump, will cause energy to move from the pump to the signal, giving signal amplification. We have measured a signal gain greaterthan 22 dB in a bandwidth of 30 kHz, for a resonator pumped at 7.6 GHz.This type of amplifier is phase-sensitive, meaning that signals in phase withthe pump will be amplified, but signals in quadrature phase of the pump will be deamplified. Phase-sensitivity has important implications on the amplifier’snoise properties. With a parametric amplifier, a signal can be amplified without any additional noise being added by the amplifier, something that is fundamentally impossible for a standard amplifier.

The vibrating AFM cantilever becomes a nonlinear oscillator when it is interacting with a surface. When driven with two frequencies, the amplitudeand phase of the cantilever’s response will develop mixing products, or intermodulation products, that are very sensitive to the exact form of the nonlinearity. Very small changes in the surface properties will be detectable when measuring the intermodulation products. Simultaneously measuring many intermodulation products, or acquiring an intermodulation spectrum,allows one to reconstruct the tip-surface interaction. Intermodulation AFM increases the sensitivity of the measurement or the contrast of the acquiredimages, and provides a means of rapidly measuring the nonlinear tip-surface interaction. The method promises to enhance the functionality of the AFM beyond simple topography measurement, towards quantitative analysis of the chemical or material properties of the surface.

Place, publisher, year, edition, pages
Stockholm: KTH, 2009. v, 106 p.
Series
Trita-FYS, ISSN 0280-316X ; 2009:66
Keyword
Superconductivity, Atomic Force Microscopy, Nonlinear oscillators, Parametric amplification
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11593 (URN)978-91-7415-508-2 (ISBN)
Public defence
2009-12-11, FB54, AlbaNova University Center, Roslagstullsbacken 21,, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20100812

Available from: 2009-12-04 Created: 2009-11-20 Last updated: 2012-08-30Bibliographically approved

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Haviland, David

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