Microwaves for Qubits on Helium Microwave System 1 Peter Frayne Royal Holloway University of London Rydberg resonance 190 GHz Ez = 10.7 kV/m Reference Cavity Tuning Gunn Oscillator 180 15 GHz 5 mW 2 ns risetime PIN modulator Frequency Doubler Isolator Amplifier Attenuator + 7dB Tuning WR5 90 7.5 GHz 30 mW Phase locked to 10 MHz WR10 Waveguide Mode transformer WR28 SS Mechanical Chopper 300 Hz Cryostat 1
Microwaves for Qubits on Helium Microwave System 2 Microwaves Peter Frayne Royal Holloway University of London Mylar window + In O-ring Cryostat WR28 SS 4.2 K Bandpass Filter f = 1 GHz 1 dB loss WR 5 1.3 K 0.6 K Options Thermal filter Thermal break WR28 SS 0.1 K Cell Fundamental Waveguide WR 5 Tuning Glass/metal seal Chip 2
Microwave Components and Cell Microwaves for Qubits on Helium Microwave Components and Cell Upper microwave cell showing waveguide and coupling pin 3
Microwave Results and Puzzles Electrons on Bulk Helium Microwave Results and Puzzles Low Microwave Power Stark tuning resonance f12(Ez) Linewidth (T) Temperature dependent resonance f12(T) High Microwave Power Absorption saturation Power broadening Absorption hysteresis 4
Microwave inter-subband absorption Electrons on Bulk Helium Microwave inter-subband absorption Cell CW microwaves (165 GHz - 220 GHz) ERF Sweep DC Modulation AC 1 kHz + Lock-in Electrodes e- 2.1 mm Ez 56 mm Waveguide Putley detector (InSb bolometer) Cell 5
Stark Tuning Resonance Electrons on Bulk Helium Stark Tuning Resonance Ground state to first excited Rydberg state Resonant frequency f12 increases with EZ Our results Brown, Grimes, Zipfel, 1976 120 140 160 180 200 220 240 5 10 15 20 E z (kV/m) 189.6 GHz 10.7 kV/m 5.06 GHz/(kV/m) Theory f 12 (GHz) 1.5 K Low power 6
Temperature dependent absorption Electrons on Bulk Helium Temperature dependent absorption Low temperatures Inhomogenous broadening Medium temperatures Inhomogenous broadening convoluted with a Lorentzian High temperatures Lorentzian broadening Resonance frequency decreases as the temperature increases 7
Temperature dependent linewidth Electrons on Bulk Helium Temperature dependent linewidth E.Collin et al. PRL 89, 245301 (2002) NB not the absolute linewidth Inhomogeneous broadening plus a contribution (T) Theory: Ando (1976) gas BN AT + = g Ripplon Gas atom Scattering f = 189.6 GHz (T) (MHz) Grimes et al. (1976) 8
Temperature dependent resonance Electrons on Bulk Helium Temperature dependent resonance f12 (T) = f12 (0) f12 (T) 800 MHz at 1 K f12 (T) T5/2 or T7/3 f12 = 189.6 GHz Low power limit b T-dependent surface profile and potential well 2-ripplon effects? 9
Absorption Saturation + Power Broadening Electrons on Bulk Helium Absorption Saturation + Power Broadening P = 300 mV 201 mV 150 mV 100 mV 80 mV 20 mV Volts T = 0.90 K Absorption 1 Decay time = T1 BUT: Heating? Higher sub-bands? Bleaching? Microwaves 0 Emission 2-level system? Rabi frequency 2 Power 10
Inter-subband transitions Electrons on Bulk Helium Inter-subband transitions Vertical transitions Microwave absorption/emission 1 2 Energy relaxation E: N 2 1 ; 1 1 (1-ripplon and 2-ripplon) Horizontal transitions Momentum scattering k: N 2 1; 1 1 (1-ripplon + gas atom) Thermal equilibrium Electron-electron scattering ee ee << k << E Microwave energy Very hot electrons Excited sub-bands Bleaching + Population saturation Power broadening + Absorption saturation 11
Coulomb Non-linearity Electrons on Bulk Helium Coulomb Non-linearity z a f12 Vz f12 = e2 z2 40ha3 t Resonance frequency shifts with Electron density Power absorbed (excited state population) Vmod Finite a.c. voltage modulation f12 34 MHz n = 1011 m-2 2-level saturation 12
Hysteresis Complex Lineshape Electrons on Bulk Helium Hysteresis Complex Lineshape T = 0.9 K Re() Im() Vz (V) T = 0.5 K 13
Microwave Results and Puzzles Electrons on Bulk Helium Microwave Results and Puzzles Low Microwave Power Stark tuning resonance f12(Ez) Linewidth (T) Temperature dependent resonance f12(T) High Microwave Power Absorption saturation Power broadening Absorption hysteresis 14