Design, Fabrication and Characterization of a Microwave Resonator ...

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5 Measurements5.3 Measurements – Yale DesignFigure 5.12: Overcoupled capacitance ofR21.Measurements based on the Yale design aredone on R21, a resonator designed for a resonancefrequency of 5.85 GHz, on Silicon andSapphire. It is, as well as design 1, overcoupledto the environment (see Figure 5.12).R41 for the probing station (see section 5.1)has the same geometry.5.3.1 R21 on Siliconname design W S length frequency capacitance substrate[µm] [µm] [mm] [GHz] value materialR21 Yale 5 10 9.759 6.0166 overcoupled 7.1 fF SiliconTable 5.8: Description of the resonator R21 on Silicon.At 4.2 K we observed a quality factor of 6000. After cooling to ∼ 1.4 K the quality factorincreased to a value of about 15000. The measurement is shown in Figure 5.13. Whencooling to 17 mK in the new cryostat installed at the Walther-Meißner-Institut no furtherincrease in quality was visible. This is expected, because an increase in the internal qualityfactor influences the overall quality factor weakly in the case of overcoupled resonators (seesubsection 2.3.3).In subsection 2.3.3 on page 19 it was shown that a quality factor of 10 4 is required toperform experiments with qubits. With R21 this condition is fulfilled. With a quality factorhigher than this value the readout becomes more difficult, because the photon lifetime in thecavity is proportional to the quality factor and the photon would stay in the cavity for toolong (see (2.30) and following).When measuring the reflection around the resonance peak, a strange behavior of the resonancedip can be seen (Figure 5.14). Although the S 21 resonance has a quality of tenthousand, the quality in reflection is lower. This is in disagreement with the observationmade on R25 (Figure 5.5 on page 44) where the quality in reflection exceeds the qualityfactor in transmission.In Figure 5.15 the full spectrum with the first and second harmonics is shown.The frequencies of the harmonics again lie almost exactly (the deviation is at the thirddigit) at multiples of the first resonance. The first harmonic again is not as clear as thefundamental resonances and the second harmonic has a quality factor ≈ 2000.We also observed a distortion of the resonance peak with increasing output power above-17 dBm (see Figure 5.16).Figure 5.17 shows the increase of the resonance frequency and the quality factor withdecreasing T . The jump at 4.3 K can be attributed to liquid He in the box.50
5.3 Measurements – Yale DesignFigure 5.13: Transmission S 21 of R21 on Silicon at the resonance frequency at 4 K, below1.3 K and at 17 mK. Comparison of quality factors.Figure 5.14: Transmission S 21 and reflection S 22 and S 11 of R21 on Silicon at 4 K.51
Page 4 and 5: Contents5.2.3 R27 on Silicon . . .
Page 6 and 7: 1 Motivation and Outlinethe antinod
Page 8 and 9: 2 Theoretical Description of a CPW
Page 14: 2 Theoretical Description of a CPW
Page 19 and 20: 2.2 Including Superconductivity in
Page 21 and 22: 2.2 Including Superconductivity in
Page 23 and 24: 2.3 Microwave Resonators2.3.2 Quali
Page 25 and 26: 2.3 Microwave ResonatorsFigure 2.11
Page 27 and 28: 2.3 Microwave ResonatorsFigure 2.13
Page 29 and 30: 2.4 The Scattering MatrixThe first
Page 31 and 32: 3 Designs Procedure for the Resonat
Page 33 and 34: 3.3 ConnectorsFigure 3.1: Coupling
Page 35 and 36: 4 Fabrication and Measurement Setup
Page 37 and 38: 4.2 Measurement SetupDevelop Resist
Page 39 and 40: 4.2 Measurement SetupFigure 4.3: Me
Page 41 and 42: 4.3 Calibration4.3 CalibrationIn or
Page 43 and 44: 5 MeasurementsThe first part of thi
Page 45 and 46: 5.1 First Experimentsname design W
Page 47 and 48: 5.2 Measurements - Design 1Figure 5
Page 49 and 50: 5.2 Measurements - Design 1The adva
Page 51 and 52: 5.2 Measurements - Design 15.2.2 R2
Page 53: 5.2 Measurements - Design 1Figure 5
Page 57 and 58: 5.3 Measurements - Yale DesignFigur
Page 59 and 60: 5.4 Measurement - Design 2: R36 on
Page 61 and 62: 5.5 Discussion of the Experimental
Page 63 and 64: 5.5 Discussion of the Experimental
Page 65 and 66: 6 SimulationsThis chapter gives a b
Page 67 and 68: 6.1 Simulations in SonnetFigure 6.4
Page 69 and 70: 6.1 Simulations in SonnetFigure 6.5
Page 71 and 72: 6.2 Simulations Done at the Institu
Page 73 and 74: 7 Conclusion and OutlookThree centr
Page 75 and 76: A Specimen OverviewDesigns for Rose
Page 77 and 78: B Masks73
Page 79 and 80: B.2 Mask for Probing StationB.2 Mas
Page 81 and 82: Bibliography[1] INFORMATIK: Quanten
Page 83 and 84: List of Figures2.1 Different realiz
Page 85 and 86: List of Figures6.6 Forward and back
Page 87 and 88: List of Tables2.1 Values where (2.1
Page 89: DanksagungVor allem möchte ich mic

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