Novel Self-Sustained Oscillations And Giant Nonlinearity .

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Novel Self-Sustained Oscillationsand Giant Nonlinearity inSuperconducting ResonatorsEran Arbel-Segev

Novel Self-Sustained Oscillationsand Giant Nonlinearity inSuperconducting ResonatorsRESEARCH THESISSUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OF MASTER OFSCIENCE IN ELECTRICAL ENGINEERINGEran Arbel-SegevSUBMITTED TO THE SENATE OF THE TECHNION - ISRAELINSTITUTE OF TECHNOLOGYSHVAT 5766HAIFAFEBRUARY 2006

This Research Thesis Was Done Under TheSupervision of Doctor Eyal Buks in the Faculty ofElectrical Engineering.THE GENEROUS FINANCIAL HELP OF ALEXAND GERTRUDEZELIG FELLOWSHIP AND THE TECHNION IS GRATEFULLYACKNOWLEDGED.

Contents1 Introduction52 Circuit Design and Fabrication2.1 Circuit Design . . . . . . . . . . . . . . . . . . . . . .2.2 Fabrication Process . . . . . . . . . . . . . . . . . . .2.A Fabrication Processes . . . . . . . . . . . . . . . . . .2.A.1 Introduction . . . . . . . . . . . . . . . . . . .2.A.2 Step by step fabrication process . . . . . . . .2.A.3 Examples of unsuccessful fabrication processes2.A.4 Electron Beam lithography (EBL) . . . . . . .2.B Sputtering Machine Characteristics . . . . . . . . . .3 Stationary Behavior3.1 Introduction . . . . . . . . . . . . . . . . . . . . . .3.2 DC I-V Measurements . . . . . . . . . . . . . . . .3.3 DC I-V Effect on the Resonance Lineshape . . . . .3.4 Resonance Frequency Shift Modeling . . . . . . . .3.4.1 Field solution . . . . . . . . . . . . . . . . .3.4.2 Model stationary parameters. . . . . . . . .3.4.3 Model Results . . . . . . . . . . . . . . . . .3.5 IR Illumination Effect on the Resonance Lineshape3.6 Summary . . . . . . . . . . . . . . . . . . . . . . .3.A Damping Rate Extraction . . . . . . . . . . . . . .3.A.1 First Order Extraction . . . . . . . . . . . .3.A.2 Second Order Extraction . . . . . . . . . . .779101011131422.252526283030313134343435364 Self-Sustained Oscillations4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .4.2 Common Self-Modulation Characteristic Behavior . . . .4.2.1 Collapsing Resonance Curves . . . . . . . . . . .4.2.2 HFSM Characterization in the Frequency Domain4.2.3 HFSM Characterization in the Time Domain . . .4.3 Unique Self-Modulation Characteristic Behavior . . . . .4.3.1 Self-Modulation at Two Distinct Power Ranges .4.3.2 SM at low powers . . . . . . . . . . . . . . . . . .4.3.3 Noncontinuous Amplification at Threshold Power.37373838394346464851i.

iiCONTENTS4.4 Low Frequency Self-Sustained Oscillations . . . . . . .4.4.1 Introduction . . . . . . . . . . . . . . . . . . . .4.4.2 Low Frequency Self-Oscillation Characterization4.4.3 Discussion . . . . . . . . . . . . . . . . . . . . .4.4.4 Summary . . . . . . . . . . . . . . . . . . . . .4.5 Theoretical Model . . . . . . . . . . . . . . . . . . . . .4.5.1 Steady State Solutions . . . . . . . . . . . . . .4.5.2 Fluctuation . . . . . . . . . . . . . . . . . . . .4.5.3 Evolution between transitions . . . . . . . . . .4.5.4 Numerical results . . . . . . . . . . . . . . . . .4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . .5 Giant Nonlinear Phenomenons5.1 Introduction . . . . . . . . . . . . . . . . . . .5.2 Self-Stimulation of Resonance Modes . . . . .5.3 Intermodulation . . . . . . . . . . . . . . . . .5.3.1 Introduction . . . . . . . . . . . . . . .5.3.2 Experimental results . . . . . . . . . .5.3.3 Summary . . . . . . . . . . . . . . . .5.4 Period doubling of various orders . . . . . . .5.4.1 Introduction . . . . . . . . . . . . . . .5.4.2 Experimental results . . . . . . . . . .5.4.3 Summary . . . . . . . . . . . . . . . .5.5 Noise squeezing - Phase sensitive amplification5.5.1 Introduction . . . . . . . . . . . . . . .5.5.2 Experimental results . . . . . . . . . .5.5.3 Summary . . . . . . . . . . . . . . . .5.6 Optical and RF Signal Mixing . . . . . . . . .5.6.1 Introduction . . . . . . . . . . . . . . .5.6.2 Experimental results . . . . . . . . . .5.6.3 Single photon detection . . . . . . . . .5.6.4 Discussion . . . . . . . . . . . . . . . .5.6.5 Summary . . . . . . . . . . . . . . . .5.7 Summary . . . . . . . . . . . . . . . . . . . 8789898990939494946 SummaryA Fresnel Zone PlateA.1 Introduction . . . . . . . . .A.2 Fresnel Zone Plate Theory .A.3 Fresnel Zone Plate Design .A.4 Preliminary results. . . . . .A.A Gaussian Beam PropagationA.B Beam intensity . . . . . . .97.101101101103105105107

List of Figures2.1 Device layout and optical microscope images of the HED.2.2 Several S11 measurements, of the Faraday package, asfrequency and input power . . . . . . . . . . . . . . . . .2.3 Optical pictures of meander-shape photon detectors . . .2.4 AlN sputtering-machine characteristics. . . . . . . . . . . . . . . . .function of. . . . . . . . . . . . . . . . . . .3.1 Setup used for reflection measurements. . . . . . . . . . . . . . . . . .3.2 Basic I-V characteristic of the HED meander stripline . . . . . . . . .3.3 Several S11 measurements as a function of frequency, for various HEDresistance values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.4 Several S11 measurements as a function of frequency. The measurements are obtained while applying variable current. . . . . . . . . . .3.5 Resonator transmission line model. . . . . . . . . . . . . . . . . . . .3.6 Resonance frequency and loss factor as a function of the HED resistance, for various initial values of HED inductance. . . . . . . . . . .3.7 Resonance frequency and unloaded damping rate as a function of theHED resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.8 Normalized voltage amplitudes as a function of the ring’s angular location3.9 Several S11 measurements as a function of frequency, while applyingsub-critical current, with and without IR illumination. . . . . . . . .4.14.24.34.44.54.64.74.84.94.104.11Several S11 measurements as function of pump frequency and powerSetup used for SM reflection measurements. . . . . . . . . . . . . . . S11 measurement as a function of pump frequency and power . . . .Reflected power measured in a frequency band of 200MHz around n3resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Reflected power, in a frequency band around n3 resonance, as a function of pump power . . . . . . . . . . . . . . . . . . . . . . . . . . . .Reflected power, in a frequency band around n3 resonance, as a function of pump frequency. . . . . . . . . . . . . . . . . . . . . . . . . .Self-modulation frequency as a function of the pump power and frequency.Reflected power as a function of time . . . . . . . . . . . . . . . . . .Several low power S11 measurements as function of pump frequencyand power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Self-modulation at low pump power . . . . . . . . . . . . . . . . . . .Several S11 measurements as function of pump frequency and 4748

ivLIST OF FIGURES4.12 Several S11 curves as a function of pump power and increasing ordecreasing pump frequency sweeps. . . . . . . . . . . . . . . . . . . .4.13 Reflected power measured in a frequency band of 200MHz around n2resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.14 Self-modulation frequency as a function of the pump frequency andincreasing or decreasing pump power sweeps. . . . . . . . . . . . . . .4.15 self-modulation at the time domain. . . . . . . . . . . . . . . . . . . .4.16 Several S11 measurement of E13 resonator, as a function of frequency.4.17 Reflected power in a frequency band around n4a resonance as a functionof pump power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.18 Setup used for low-frequency self-oscillation measurements. . . . . . .4.19 Type 2 low frequency self-sustained oscillations, measured at E13. . .4.20 Type 1 low frequency self-sustained oscillations, measured at E13. . .4.21 Type one low frequency self-sustained oscillations, measured at E13. .4.22 Type 1, regular, low frequency self-sustained oscillations, measured atE13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.23 Type 1 low frequency self-sustained oscillations, where no SM exist,measured at E13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.24 Low frequency self-oscillations of type 2, measured at E15. . . . . . .4.25 Low frequency self-oscillations of type 2, measured at E15. . . . . . .4.26 Low frequency self-oscillations of type 2, measured at E15. . . . . . .4.27 Low frequency self-oscillations of type 3, measured at E15. . . . . . .4.28 Low frequency self-oscillation, of various time scales coupled together.4.29 Low frequency self-oscillation, of various time scales coupled together.4.30 Resonator model, coupled to a test port and a linear dissipation port.4.31 Numerical solution of the theoretical model . . . . . . . . . . . . . . 155.16Self-Excitation measurement. . . . . . . . . . . . . . . . . . . . . . .Setup used for intermodulation reflection measurements. . . . . . . .2D Intermodulation measurement. . . . . . . . . . . . . . . . . . . . .Intermodulation Signal gain. . . . . . . . . . . . . . . . . . . . . . . .Intermodulation Idler gain. . . . . . . . . . . . . . . . . . . . . . . . .Intermodulation Signal gain and self-modulation frequency as a function of pump power. . . . . . . . . . . . . . . . . . . . . . . . . . . .Period doubling measurement . . . . . . . . . . . . . . . . . . . . . .Setup used for phase sensitive amplification measurement. . . . . . .2D phase sensitive amplification measurement. . . . . . . . . . . . . .3D phase sensitive amplification measurement . . . . . . . . . . . . .Squeezing factor as a function of frequency and pump power. . . . . .Setup used for optical and RF signal mixing. . . . . . . . . . . . . . .RF and optical signal mixing measurement. . . . . . . . . . . . . . .ORSM detection level compared to SM frequency as a function of pumppower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Noise equivalent power for various optical modulation frequencies. . .Single photon detection . . . . . . . . . . . . . . . . . . . . . . . . . 38486878888899091929293

LIST OF FIGURESA.1 Fresnel block diagram. . . . . . . . . . . . . . . . . . . . . . . . . . .A.2 Gaussian beam propagation. . . . . . . . . . . . . . . . . . . . . . . .A.3 Fresnel zone plate optical image. . . . . . . . . . . . . . . . . . . . . .v102103106

viLIST OF FIGURES

List of Tables2.12.22.32.42.52.62.72.82.9Device Parameters . . . . . . . .Sputtering Parameters . . . . . .EBL Liftoff Parameters - I . . . .EBL Liftoff Parameters-II . . . .EBL Direct-Write Parameters - IEBL Direct-Write Parameters-II .EBL Direct-Write Parameters-IIIEBL Direct-Write Parameters-IVEBL Direct-Write Parameters-V .710181919191920203.1 Resonance Frequency Characteristics . . . . . . . . . . . . . . . . . .324.1 Numerical Model Parameters . . . . . . . . . . . . . . . . . . . . . .76vii.

viiiLIST OF TABLES

AbstractWe study microwave superconducting stripline resonators made of NbN on Sapphiresubstrate. A section in the resonator is made of a narrow and thin meander strip.A continuous wave at frequency close to one of the resonances is injected into theresonator and the reflected power off the resonator is measured. Novel, self-sustainedoscillations of the reflected power, at frequencies of down to 0.01 Hz and up to 60 MHzare observed. To the best of our knowledge such oscillations were not reported beforein similar systems.Near the onset of these oscillations the device exhibits a chaotic like behaviorand is characterizes by giant nonlinearity. Intermodulation characterization performedin this state yields extremely high intermodulation gain (about 30dB), which is accompanied by a very strong noise squeezing (about 45dB squeezing factor) and perioddoubling of various orders. We also study the response of the device to IR (1550 nmwavelength) illumination impinging on the meander strip. To characterize the response time of the system we modulate the impinging optical power with a varyingfrequency. We observe extremely fast (modulation frequencies of up to 8 GHz) andsensitive (optical power below 100 fW) response near the onset of the self-sustainedoscillations.To account for our findings we propose a theoretical model according to whichthe self-sustained oscillations are originated by thermal instability in the meanderstrip.1

2ABSTRACT

SESMSMASYNNEPThree dimensional flat viewAluminium-NitrideContinuous waveDe-ionizedData-Translation digital to analog boardDevice number iElectron beam lithographyElectron cyclotron resonanceExposure doseHot-electron detectorHigh frequency self modulationsIntermodulationLow frequency self oscillationsLow-pass filterNetwork analyzerNiobium NitrideNormal conductingN-Methyl-2-PyrrolidoneOptical and RF signal mixingTime domain oscilloscopePeriod doubling bifurcationPhase sensitive amplificationPolyMethylMethacrylateReeactive ion etchingSpectrum onsSubMiniature version ASynthesizerNoise equivalent power3

4GLOSSARYList of Symbols and abbreviation:Z0cr S11 SF6AlCl2H2O2CrN2ArAlVCn(ω), f(ω 0 ), f0(ω p ), fpγ1γ2PpumpfpumpPref lfSMnixGIMsigCharacteristic impedanceSpeed of light in vacuumDielectric constant of SapphirePower reflection coefficientSulfur mNitogenArgonAluminiumCritical voltage number n(Angular) Frequency(Angular) Resonance frequency(Angular) Pump frequencyCoupling constant between the resonator and the feedlineunloaded damping rate of the resonancePump powerPump frequencyReflected powerSelf-modulation frequencyResonance mode number i, index xSignal intermodulation gain

Chapter 1IntroductionResonance parametric amplifiers are characterized by very low noise, high gain, andphase sensitive amplification. Parametric resonance in superconducting (SC) resonators [20] may allow some intriguing applications such as quantum squeezing [59],quantum non-demolition measurements [49], photon creation by the so-called dynamical Casimir effect [18], and more.Parametric excitation occurs when the resonance frequency of an oscillator variesin time. The first parametric resonance occurs when the excitation is performed periodically at twice the resonance frequency f0 , namely f (t) f0 [1 ξ cos (4πf0 t)] [34].The system’s response to such an excitation depends on the dimensionless parameterξQ , where Q is the quality factor of the resonator. When ξQ 1 the system is saidto be in the subthreshold region, while above threshold, when ξQ 1, the systembreaks into oscillation. Achieving parametric gain where ξQ 1 requires that theshift in the resonance frequency exceeds the width of its peak [23].Spirited by this motivation, we have designed and manufactured (chapter 2) several novel SC devices, that integrates a hot-electron detector (HED) into a SC ringresonator. The HED is used as an optically tuned, lumped element, that changes theboundary conditions of the resonator [48], and thus manipulates its resonance frequencies. Several external constrains, such as dc voltage and current, RF power, andIR illumination can be applied on the HED. The switching time in superconductorsis usually limited by the relaxation process of high-energy quasi-particles, also called’hot-electrons’, giving their energy to the lattice, and recombining to form Cooperpairs. Recent experiments with photodetectors, based on a thin layer of SC niobiumnitride (NbN), have demonstrated an intrinsic switching time on the order of 30 psand a counting rate exceeding 2 GHz (see [24] and references therein).The resulting effect of applied dc voltage and current as well as continuous wave(CW) IR illumination on the resonance frequencies of the resonators is investigated(chapter 3) and found to be promising. Applying external constrains indeed shiftsthe resonance frequencies, and the parametric gain threshold condition is achieved ina CW illumination measurement. Moreover, the results are shown to be in a goodagreement with a theoretical modeling.The outcome of the integrated devices is discovered to be much more fruitfulthan expected. A wide variety of nonlinear phenomenons occur in the devices. Phenomenons such as strong intermodulation gain, quantum squeezing, period doubling5

6CHAPTER 1. INTRODUCTIONbifurcation and optical and RF signal mixing, are all coexist and observed in all devices (chapter 5). They are all governed by and correlated to novel, self-sustainedoscillations of the reflected power, at frequencies of down to 0.01Hz and up to 60MHz,that are a robust behavior, which characterizes our devices (chapter 4). To accountfor our findings we propose a theoretical model according to which the self-sustainedoscillations are originated by thermal instability in the HED.The outmost goal of achieving parametric gain has not been achieved in thisresearch. The probable cause is insufficient illumination intensity impinging on theHED (subsection 5.6.4), due to dispersion of the laser beam, traveling in free spacetowards the HED. Future devices, which integrates a Fresnel lens back to back withthe HED, would hopefully solve this problem. This devices are already planed, andthe Fresnel lenses are in preliminary manufacture stages (A).

Chapter 2Circuit Design and Fabrication2.1Circuit DesignThe research is done using three devices, named E13, E15, and E16, which differ interms of width, layout, and optical detector design, as summarized in table 2.1.Thecircuit layouts are illustrated in Fig. 2.1(a) for E15, E16 and 2.1(b) for E13. E16(E13, E15) device is made of 8 nm (200 nm) thick NbN stripline, fabricated on aSapphire wafer, with dimensions of 34 30 1 mm3 . The design integrates threecomponents. The first is a SC ring resonator and its feedline. Ring configuration is asymmetric and compact geometry, which is generally suitable for applications, whichrequire resonance tuning [9]. The first few resonance frequencies are designed for theS&C bands (2 8 GHz). The resonator is weakly coupled to its feedline, where thecoupling gaps are 0.35 mm, 0.45 mm, 0.4 mm for E13, E15, and E16 respectively. Thestripline width is set to 347 μm, to obtain a characteristic impedance of Z0 50 Ω.The second component is a hot electron detector (HED), which is monolithicallyintegrated into the ring structure. Its angular location, relative to the feedline couplinglocation, maximizes the RF current amplitude flowing through it, and thus maximizesits coupling to the resonator. E16’s HED, shown in Fig. 2.1(c), has a 4 4 μm2meander structure, consists of nine NbN SC strips. Each strip has a characteristicarea of 0.15 4 μm2 and the strips are separated one from

4.19 Type 2 low frequency self-sustained oscillations, measured at E13. . . 56 4.20 Type 1 low frequency self-sustained oscillations, measured at E13. . . 57 4.21 Type one low frequency self-sustained oscillations, measured at E13. . 58 4.

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