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. 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
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 9 7.5 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
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
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
Stark Tuning Resonance Ground state to first excited Rydberg state Resonant frequency f 2 increases with E Z f 2 (GHz) 24 22 2 8 6 4 89.6 GHz 5.6 GHz/(kV/m).6 kv/m Brown, Grimes, Zipfel, 976 4.5 K Low power 2 5 5 2 E (kv/m) z 6
Absorption Temperature dependent resonance Collin et al (25) Figure 8 89.6 GHz Low temperatures Inhomogenous broadening.8.34 K.4 K Medium temperatures Inhomogenous broadening convoluted with a Lorentzian.6 High temperatures Lorentzian.4.855 K Resonance frequency decreases as the temperature increases.2.553 K 2.8 22 22.2 22.4 22.6 V (volts) GHz 7
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?.6.4.2 Disk + edges Lorentzian Disk..8.6.4.2 Voltage/V MHz 8
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.6.4.6.4.2.2.2 volts volts volts 2.8 2.9 22 22. 22.2 2.8 2.9 22 22. 22.2 2.8 2.9 22 22. 22.2 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
Microwave absorption at 89.6 GHz Convolution.8.6 4 T =.498 K =. V = 2.9 MHz.8.6 T =.62 K =.26 V = 7.6 MHz.4.2.3 K volts 2.9 2.95 22 22.5.4.2.3 K volts 2.9 2.95 22 22.5.8.6 T =.855 K =.65 V = 49 MHz.8.6 T =.4 K =.98 V = 288 MHz.4.2.3 K 2.85 2.95 22.5 22.5.4.2 volts.3 K 2.7 2.9 22. 22.3
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 =
Temperature dependent linewidth H. Isshiki et al.j.phys.soc Japan 76, 9474 (27) β = 2. ( 3 );.6 ( 4 ) at βbn gas 2
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
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
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
Temperature dependence of f 2 RIKEN 4 3 6
Microwave absorption - Coulomb shift D. Konstantinov et al. PRL 98, 23532 (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
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.4.3.2 ( V z ) ( V z ). V z.9.95.5. 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
Hysteresis Complex Lineshape.2...2.. T =.9 K Re() 4 Im() V z (V) 2.4 2.6 2.8 22 22.2 22.4 T =.5 K Re() Im() 2.4 2.6 2.8 22 22.2 22.4 off.5..5 3 2 4 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.97.98.99..2.3 E max V V Im( off ) 2V m 2 2 mv 5 MHz V m 9
Conclusions Temperature dependent Rydberg levels Inhomogeneous broadening Enhanced Ando linewidth Microwave absorption bistability (hysteresis) 2