1. 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

2. 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

3. Microwave Components and Cell
Microwaves for Qubits on Helium
Microwave Components and Cell
Upper microwave cell showing waveguide and coupling pin 3

4. 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

5. Microwave inter-subband absorption
Electrons on Bulk Helium
Microwave inter-subband absorption
Cell
CW microwaves
(165 GHz 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

6. 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

7. 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

8. Temperature dependent linewidth
Electrons on Bulk Helium
Temperature dependent linewidth
E.Collin et al. PRL 89, (2002)
NB not the absolute linewidth Inhomogeneous broadening plus a contribution (T)
Theory: Ando (1976)
gas BN AT + = g
Ripplon Gas atom Scattering
f = GHz
(T)
(MHz)
Grimes et al. (1976) 8

9. 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 = GHz
Low power limit b
T-dependent surface profile and potential well
2-ripplon effects? 9

10. 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

11. Inter-subband transitions
Electrons on Bulk Helium
Inter-subband transitions
Vertical transitions
Microwave absorption/emission  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

12. Coulomb Non-linearity
Electrons on Bulk Helium
Coulomb Non-linearity z a
f12 Vz
 f12 = e2 z2
40ha3 t
Resonance frequency shifts with
Electron density
Power absorbed (excited state population)
Vmod
Finite a.c. voltage
modulation
 f12  34 MHz
n = m-2
2-level saturation 12

13. Hysteresis  Complex Lineshape
Electrons on Bulk Helium
Hysteresis  Complex Lineshape
T = 0.9 K
Re()
Im()
Vz (V)
T = 0.5 K   13

14. 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