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Intermodulation in microresonators: for microwave amplification and nanoscale surface analysis
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
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 [en]
Superconductivity, Atomic Force Microscopy, Nonlinear oscillators, Parametric amplification
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-11593ISBN: 978-91-7415-508-2 (print)OAI: oai:DiVA.org:kth-11593DiVA: diva2:277877
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
List of papers
1. Phase Space Topology of a Switching Current Detector
Open this publication in new window or tab >>Phase Space Topology of a Switching Current Detector
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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.

Keyword
josephson-junctions; quantum-state
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-6276 (URN)10.1103/PhysRevB.73.132511 (DOI)000237153800028 ()2-s2.0-33646232997 (Scopus ID)
Note
QC 20100812Available from: 2006-10-23 Created: 2006-10-23 Last updated: 2010-09-24Bibliographically approved
2. Pulse and Hold Strategy for Switching Current Measurements
Open this publication in new window or tab >>Pulse and Hold Strategy for Switching Current Measurements
2007 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 75, no 9, 094515- p.Article in journal (Refereed) Published
Abstract [en]

We investigate by theory and experiment, the Josephson junction switching current detector in an environment with frequency-dependent damping. Analysis of the circuit's phase space shows that a favorable topology for switching can be obtained with overdamped dynamics at high frequencies. A pulse-and-hold method is described, where a fast switch pulse brings the circuit close to an unstable point in the phase space when biased at the hold level. Experiments are performed on Cooper pair transistors and quantronium circuits, which are overdamped at high frequencies with an on-chip RC shunt. For 20 mu s switch pulses the switching process is well described by thermal equilibrium escape, based on a generalization of the Kramers formula to the case of frequency-dependent damping. A capacitor bias method is used to create very rapid, 25 ns switch pulses, where it is observed that the switching process is not governed by thermal equilibrium noise.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-6275 (URN)10.1103/PhysRevB.75.094515 (DOI)000245328500089 ()2-s2.0-34047190361 (Scopus ID)
Note
QC 20100812Available from: 2006-10-23 Created: 2006-10-23 Last updated: 2011-11-07Bibliographically approved
3. Nonlinearities and parametric amplification in superconducting coplanar waveguide resonators
Open this publication in new window or tab >>Nonlinearities and parametric amplification in superconducting coplanar waveguide resonators
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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.

Keyword
Nonlinear oscillator, Parametric amplification
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11550 (URN)10.1063/1.2750520 (DOI)000247468900098 ()2-s2.0-34547281367 (Scopus ID)
Note

QC 20100812

Available from: 2009-11-20 Created: 2009-11-19 Last updated: 2017-12-12Bibliographically approved
4. Intermodulation atomic force microscopy
Open this publication in new window or tab >>Intermodulation atomic force microscopy
2008 (English)In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 92, 153106- p.Article in journal (Refereed) Published
Abstract [en]

A mode of atomic force microscopy ͑AFM͒ is demonstrated where an oscillating AFM cantileverhaving linear response is driven with two frequencies in the vicinity of a resonance. Newfrequencies in the response, known as intermodulation products, are generated when the linearity ofthe cantilever response is perturbed by the nonlinear tip-surface interaction. A rich structure of theintermodulation products is observed as a function of the probe-surface separation, indicating thatit is possible to extract much more detailed information about the tip-surface interaction than ispossible with the standard amplitude and phase imaging methods.

Keyword
Atomic force microscopy, Nonlinear oscillations, Cantilevers; Surfaces; Tip
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11551 (URN)10.1063/1.2909569 (DOI)000255117100081 ()2-s2.0-42349116023 (Scopus ID)
Note

QC 20100812

Available from: 2009-11-20 Created: 2009-11-19 Last updated: 2017-12-12Bibliographically approved
5. Josephson junction transmission lines as tunable artificial crystals
Open this publication in new window or tab >>Josephson junction transmission lines as tunable artificial crystals
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2011 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 83, no 1, 014511- p.Article in journal (Refereed) Published
Abstract [en]

We investigate one-dimensional Josephson junction arrays with generalized unit cells, beyond a single junction or SQUID, as a circuit approach to engineer band gaps. Within a specific frequency range, of the order of the single junction plasma frequency, the dispersion relation becomes gapped and the impedance becomes purely imaginary. We derive the parameter dependence of this gap and suggest designs to lower it to microwave frequencies. The gap can be tuned in a wide frequency range by applying external flux, and persists in the presence of small imperfections. These arrays, which can be thought of as tunable artificial crystals, may find use in applications ranging filters to the protection of quantum bits.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11552 (URN)10.1103/PhysRevB.83.014511 (DOI)000286741100005 ()2-s2.0-79551566674 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20110310 Ändrad från Manuskript (preprint) till Artikel i tidskrift 20110310

Available from: 2009-11-20 Created: 2009-11-19 Last updated: 2017-12-12Bibliographically approved
6. Parametric amplification with weak-link nonlinearity in superconducting microresonators
Open this publication in new window or tab >>Parametric amplification with weak-link nonlinearity in superconducting microresonators
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2009 (English)In: Nobel Symposium 141: Qubits for Future Quantum Information; Gothenburg; 25 May 2009 through 28 May 2009, 2009Conference paper, Published paper (Refereed)
Abstract [en]

Nonlinear kinetic inductance in a high Q superconducting coplanarwaveguide microresonator can cause a bifurcation of the resonance curve. Near thecritical pumping power and frequency for bifurcation, large parametric gain is observedfor signals in the frequency band near resonance. We show experimental results onsignal and intermodulation gain which are well described by a theory of the parametricamplification based on a Kerr nonlinearity. Phase dependent gain, or signal squeezing,is verified with a homodyne detection scheme.

Series
Physica Scripta T, ISSN 0031-8949, E-ISSN 1402-4896
Keyword
Nonlinear oscillators, Parametric amplification
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11556 (URN)10.1088/0031-8949/2009/T137/014019 (DOI)000272834700020 ()2-s2.0-77952866472 (Scopus ID)
Conference
141st Nobel Symposium on Qubits for Future Quantum Information, Gothenburg, Sweden, May 25-28, 2009
Note

Uppdaterad från manuskript till konferensbidrag: 20100812 QC 20100812

Available from: 2009-11-20 Created: 2009-11-20 Last updated: 2017-03-29Bibliographically approved
7. Phase imaging with intermodulation atomic force microscopy
Open this publication in new window or tab >>Phase imaging with intermodulation atomic force microscopy
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2010 (English)In: Ultramicroscopy, ISSN 0304-3991, E-ISSN 1879-2723, Vol. 110, no 6, 573-577 p.Article in journal (Refereed) Published
Abstract [en]

Intermodulation atomic force microscopy (IMAFM) is a dynamic mode of atomic force microscopy (AFM) with two-tone excitation. The oscillating AFM cantilever in close proximity to a surface experiences the nonlinear tip-sample force which mixes the drive tones and generates new frequency components in the cantilever response known as intermodulation products (IMPs). We present a procedure for extracting the phase at each IMP and demonstrate phase images made by recording this phase while scanning. Amplitude and phase images at intermodulation frequencies exhibit enhanced topographic and material contrast.

Keyword
Atomic force microscopy, Nonlinear oscillations
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11557 (URN)10.1016/j.ultramic.2010.02.012 (DOI)000279482900002 ()2-s2.0-77953541578 (Scopus ID)
Note

Uppdaterad från manuskript till artikel: 20100812 QC 20100812

Available from: 2009-11-20 Created: 2009-11-20 Last updated: 2017-12-12Bibliographically approved
8. Reconstructing nonlinearities with intermodulation spectroscopy
Open this publication in new window or tab >>Reconstructing nonlinearities with intermodulation spectroscopy
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2010 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 104, no 5, 050801- p.Article in journal (Refereed) Published
Abstract [en]

We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives, resulting in a complicated spectral response. Analysis of this spectrum allows one to approximate the nonlinearity. The method, which is generally applicable to measurements based on resonant detection, increases the information content of the measurement without requiring large detection bandwidth, and optimally uses the enhanced sensitivity near resonance to extract information and minimize error due to detector noise.

Keyword
Nonlinear oscillations, Atomic force microscopy
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-11558 (URN)10.1103/PhysRevLett.104.050801 (DOI)000274336800009 ()2-s2.0-76249130755 (Scopus ID)
Funder
Swedish Research Council
Note

Uppdaterad från manuskript till artikel: 20100812 QC 20110126

Available from: 2009-11-20 Created: 2009-11-20 Last updated: 2017-12-12Bibliographically approved

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Citation style
  • apa
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