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Nonlinearities and parametric amplification in superconducting coplanar waveguide resonators
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.ORCID iD: 0000-0003-0493-7792
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
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2007 (English)In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 90, no 25, 253509- p.Article in journal (Refereed) Published
Abstract [en]

Experimental investigations of the nonlinear properties of superconducting niobium coplanarwaveguide resonators are reported. The nonlinearity due to a current dependent kinetic inductanceof the center conductor is strong enough to realize bifurcation of the nonlinear oscillator. Whendriven with two frequencies near the threshold for bifurcation, parametric amplification with a gainof +22.4 dB is observed.

Place, publisher, year, edition, pages
2007. Vol. 90, no 25, 253509- p.
Keyword [en]
Nonlinear oscillator, Parametric amplification
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-11550DOI: 10.1063/1.2750520ISI: 000247468900098Scopus ID: 2-s2.0-34547281367OAI: oai:DiVA.org:kth-11550DiVA: diva2:277679
Note

QC 20100812

Available from: 2009-11-20 Created: 2009-11-19 Last updated: 2017-12-12Bibliographically approved
In thesis
1. 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
2. Fabrication and Characterization of Superconductive Coplanar Waveguide Resonators: Fabrication and Characterization of Superconductive Coplanar Waveguide Resonators
Open this publication in new window or tab >>Fabrication and Characterization of Superconductive Coplanar Waveguide Resonators: Fabrication and Characterization of Superconductive Coplanar Waveguide Resonators
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The objective of this thesis is to evaluate a generic process for fabrication and characterization of the Superconductive coplanar waveguide (CPW) resonators. Superconductive CPW resonators with various lengths and shapes are designed to investigate their electrical and magnetic properties as well as resonance properties and sensitivities. In the first part of thesis, two different models are introduced in order to estimate the nonlinear kinetic inductance of a superconducting CPW resonator. The first model is based on Bean critical-state model and the second one is based on current dependence of London penetration depth. The existence of a shift in resonant frequency  of Superconductive CPW resonator caused by a non-linear kinetic inductance is also shown experimentally. Simulations were carried out to estimate the nonlinear kinetic inductance due to the self- induced magnetic field penetration.

The rest of the thesis is concerned with development of very smooth Aluminum (Al) thin films with RMS (Root Mean Square) roughness 1~nm and CAD (Computer Aid Design) of superconductive CPW resonators. Experimental investigation of a generic fabrication technique for superconductive CPW resonator is carried out. Many resonators are fabricated with different design parameters, such as centerline or gap width, film thickness and gap capacitors length. The fabrication process is described in detail. Electron Beam Lithography is used to fabricate Nb and Al CPW resonators which are coupled to outer conductors via gap capacitors. We have fabricated GHz frequency CPW resonators with quality factors, Q up 5X10^5.

Place, publisher, year, edition, pages
Stockholm: Universitetsservice US AB, 2009. vi, 91 p.
Series
Trita-FYS, ISSN 0280-316X ; 2009:15
Keyword
Coplanar, Waveguide, Resonator, Superconductive, Fabrication, Characterization
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-10419 (URN)978-91-7415-315-6 (ISBN)
Presentation
2009-05-29, A2:1041, Roslagstullsbacken 21, AlbaNova Universitetscentrum, 15:30 (English)
Opponent
Supervisors
Available from: 2009-05-18 Created: 2009-05-12 Last updated: 2010-10-11Bibliographically approved
3. Nonlinear dynamics of Josephson Junction Chains and Superconducting Resonators
Open this publication in new window or tab >>Nonlinear dynamics of Josephson Junction Chains and Superconducting Resonators
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis presents the results of the experimental studies on two kindof Superconducting circuits: one-dimensional Josephson junction chains andsuperconducting coplanar waveguide (CPW) resonators. One-dimensionalJosephson junction chains are constructed by connecting many Superconducting quantum interference devices (SQUIDs) in series. We have studied DC transport properties of the SQUID chains and model their nonlineardynamics with Thermally Activated Phase-Slips (TAPS). Experimental andsimulated results showed qualitative agreement revealing the existence of auniform phase-slipping and phase-sticking process which results in a voltage-independent current on the dissipative branch of the current-voltage char-acteristics (IVC). By modulating the effective Josephson coupling energy ofthe SQUIDs (EJ ) with an external magnetic field, we found that the ratio EJ /EC is a decisive factor in determining the qualitative shape of theIVC. A quantum phase transition between incoherent Quantum Phase Slip, QPS (supercurrent branch with a finite slope) to coherent QPS (IVC withwell-developed Coulomb blockade) via an intermediate state (supercurrentbranch with a remnant of Coulomb blockade) is observed as the EJ /EC ratio is tuned. This transition from incoherent QPS to the intermediate-statehappens around R0 ∼ RQ (RQ = h/4e^2 = 6.45kΩ). We also fabricated structured chains where a SQUID at the middle of the chain (central SQUID) has different junction size and loop area compared to other SQUIDs in the chain. Results showed that with these structured chains it is possible to localize andtune the amplitude of both TAPS and QPS at the central SQUID.

The second part of the thesis describes the fabrication process and themeasurement results of superconducting CPW resonators. Resonators withdifferent design parameters were fabricated and measured. The transmissionspectra showed quality factors up to, Q ∼ 5 × 10^5 . We have observed bendingof the resonance curves to the lower frequencies due to existence of a nonlinear kinetic inductance. The origin of the nonlinear kinetic inductance isthe nonlinear relation between supercurrent density, Js, and superfluid veloc-ity, vs , of the charge carriers on the center line of the resonators. A simplemodel based on the Ginzburg-Landau theory is used in order to explain ob-served nonlinear kinetic inductance and estimates using this model showedgood agreement with the experimental results.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. vi, 119 p.
Series
Trita-FYS, ISSN 0280-316X ; 13:52
Keyword
Superconductivity, Josephson Junction, SQUID, Superconducting Resonators
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-132238 (URN)978-91-7501-869-0 (ISBN)
Public defence
2013-11-28, FA32, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Projects
SCOPE
Funder
EU, FP7, Seventh Framework Programme
Note

QC 20131030

Available from: 2013-11-04 Created: 2013-10-24 Last updated: 2013-11-04Bibliographically approved

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