Temperature Dependent Energy Levels of Electrons on Liquid Helium

Transcription

1 Royal Holloway University of London Temperature Dependent Energy Levels of Electrons on Liquid lium Bill Bailey, Parvis Fozooni, Phil Glasson, Peter Frayne, Khalil Harrabi, Mike Lea. + Eddy Collin, Grenoble

2 2. mm Microwave absorption CW microwaves (65 GHz - 22 GHz) Cell Sweep DC + Modulation AC Electrodes khz Lock-in Waveguide Polarising Grid e- 56 mm E z E RF Putley detector (InSb bolometer) Cell Segmented Corbino 2

3 Microwaves for Electrons on lium Microwave System Peter Frayne Royal Holloway Tuning Reference Cavity Rydberg resonance 9 GHz E z =.7 kv/m 2 ns risetime 8 5 GHz 5 mw Gunn Oscillator GHz 3 mw Phase locked to MHz Isolator Amplifier Attenuator WR Waveguide + 7dB PIN modulator Mode transformer Mechanical Chopper 3 Hz Tuning Frequency Doubler WR5 WR28 SS Cryostat 3

4 Microwaves for Electrons on lium Mylar window + In O-ring WR28 SS Microwave System 2 Microwaves Cryostat 4.2 K Bandpass Filter f = GHz db loss WR 5.3 K Cell Options Thermal filter Thermal break Tuning Chip WR28 SS.6 K. K Fundamental Waveguide WR 5 Glass/metal seal 4

5 Rydberg states liquid 4 Image charge 2 Ze U( z) for z 4 z Z 4( ) E m R m e 2 f 2 = 9.3 GHz Grimes et al: U ( z) V 2 Ze 4 ( z b) for z for z Experiment for E z = : f 2 = 25.9 GHz at.2 K Stark tuning U(z) = U (z) + ee z z m 2 m 5

6 Stark Tuning Resonance Ground state to first excited Rydberg state Resonant frequency f 2 increases with E Z f 2 (GHz) GHz 5.6 GHz/(kV/m).6 kv/m Brown, Grimes, Zipfel, K Low power E (kv/m) z 6

7 Absorption Temperature dependent resonance Collin et al (25) Figure GHz Low temperatures Inhomogenous broadening.8.34 K.4 K Medium temperatures Inhomogenous broadening convoluted with a Lorentzian.6 High temperatures Lorentzian K Resonance frequency decreases as the temperature increases K V (volts) GHz 7

8 Absorption Inhomogeneous broadening Non-parallel electrodes Lineshape independent of T <.5 K.8 Data at.25 K Inhomogeneous broadening Peaks from E z variation (.3%)? Non-parallel disk electrodes: Parabolic lineshape 8 m across 5 mm =.7 mrad = 35 arc Lorentzian contribution small? Disk + edges Lorentzian Disk Voltage/V MHz 8

9 Convolution Lorentzian Use lineshape at.3 K as a template Convolute with a Lorentzian Fit linewidth to data (T) Cell -response Measured Fit γ = 6 MHz.8 Fit.8.3 K.8.9 K.6.4 v=v-v volts volts volts L( v, ) Intrinsic linewidth / 2 v 2 G(V) Inhomogeneous broadening S( V ) G( V Output = Lorentzian L(V) Cell response G(V) v) L( v, ) dv Convolution 9

10 Microwave absorption at 89.6 GHz Convolution T =.498 K =. V = 2.9 MHz.8.6 T =.62 K =.26 V = 7.6 MHz K volts K volts T =.855 K =.65 V = 49 MHz.8.6 T =.4 K =.98 V = 288 MHz K volts.3 K

11 Microwave linewidth (T) 4 Theory: T. Ando, J.Phys.Soc Japan, 44,765 (976) at Ripplon βbn gas Gas atom Scattering [H. Isshiki et al.j.phys.soc Japan (27): β = 2. ( 3 );.6 ( 4 )] β =.6 β =

12 Temperature dependent linewidth H. Isshiki et al.j.phys.soc Japan 76, 9474 (27) β = 2. ( 3 );.6 ( 4 ) at βbn gas 2

13 Temperature dependent resonance f 2 f 2 (T) = f 2 () f 2 (T) 8 MHz at K 4 b f 2 (T) T 5/2 or T 7/3 Ripplons? f 2 = 89.6 GHz Low power limit 3

14 Ripplon induced Lamb shift Temperature dependent resonance Theory: Mark Dykman, Denis Konstantinov et al (2) 2-ripplon processes: Lamb shift Electron density.67 m 2 ( ). ( ).5 ( ).7 ( ) 2.4 ( ) - various 4 Theory + Vapour f 2 (T) = f 2 () f 2 (T) 4

15 Density dependence of holding field E z Vz ne ( D 2d) ( D d d / ε) ε (ε ) ( D d d / ε) Extrapolated to T = V z D d D -2d = D -2d = 5

16 Temperature dependence of f 2 RIKEN 4 3 6

17 Microwave absorption - Coulomb shift D. Konstantinov et al. PRL 98, (27) Ultra-hot Electrons on Liquid 3 : T e < 27 K 3 Resonance frequency shifts with Power absorbed Excited state population Electron temperature T e Electron density f 2 a z Rabi frequency Power D. Konstantinov et al. PRL 3, 968 (29) 3 7

18 Optical bistability in microwave absoprtion D. Konstantinov et al. PRL 3, 968 (29) High-powers: Hysteresis in conductivity High-powers: A.C. modulation ( mv at khz) Complex microwave lineshape.5 3 α ( V z ) ( V z ). V z α α f 2 = 89.6 GHz.3 K Differential absorption α = dα/dv z Im( ') V m t V mod ( ( Vz ) ( Vz ) dvz 8

19 Hysteresis Complex Lineshape T =.9 K Re() 4 Im() V z (V) T =.5 K Re() Im() off T =. 5K Re(Line) Im(Line) Re( off ) Im( off ) Power (mv) Im( off 2 V ) V ) 2 m ( ( Vz ) ( Vz dvz Inhomogeneous power broadening Inhomogeneous Coulomb broadening E max V V Im( off ) 2V m 2 2 mv 5 MHz V m 9

20 Conclusions Temperature dependent Rydberg levels Inhomogeneous broadening Enhanced Ando linewidth Microwave absorption bistability (hysteresis) 2