Temperature Dependent
Energy Levels of Electrons
on Liquid Helium
Royal Holloway
University of London
Bill Bailey, Parvis Fozooni, Phil Glasson, Peter Frayne,
Khalil Harrabi, Mike Lea.
+ Eddy Collin, Grenoble
Microwave absorption
Sweep DC
Modulation AC
WaveguidePutley detector
(InSb bolometer)
Cell
56 mm2.1
mm
Electrodes
Lock-in
1 kHz
Ez
+
CW microwaves
(165 GHz - 220 GHz)
ERF
e-
Cell
2
Segmented
Corbino
Polarising
Grid
Microwave System 1Microwaves for Electrons on Helium
Rydberg
resonance
190 GHz
Ez = 10.7 kV/m
PIN
modulator
90 7.5 GHz
30 mW
Phase locked
to 10 MHz
180 15 GHz
5 mW2 ns risetime
Isolator Amplifier Attenuator
Mechanical
Chopper
300 Hz
Cryostat
WR10
Waveguide
WR5
Mode transformer
+ 7dBTuning
WR28
SS
3
Frequency
Doubler
Reference
Cavity
Tuning
Gunn
Oscillator
Peter Frayne
Royal Holloway
Microwave System 2Microwaves for Electrons on Helium
CellFundamental
Waveguide
WR 5
Bandpass
Filter
f = 1 GHz
1 dB loss
Mylar
window
+ In O-ring
Glass/metal
seal
Tuning
1.3 K
0.1 K
0.6 K
4.2 K
WR28
SS
Options
• Thermal filter
• Thermal break
WR 5
Microwaves
Cryostat
WR28
SS
4
Chip
Rydberg states – liquid 4He
5
2m
1m
0for
0for )(4
)(
0
0
2
0
zV
zbz
ZezU
f12 = 119.3 GHz0for 4
)(0
2
0
zz
ZezU
Image charge
)(4
Z
2m
RE e
m
Stark tuning U(z) = U0(z) + eEzz
Experiment for Ez = 0:
f12 = 125.9 GHz at 1.2 K
Grimes et al:
Stark Tuning Resonance
Brown, Grimes,
Zipfel, 1976
120
140
160
180
200
220
240
0 5 10 15 20
Ez
(kV/m)
189.6 GHz
10.6 kV/m
5.06 GHz/(kV/m)
f 12
(GH
z)
1.5 K
Low power
Resonant frequency f12 increases with EZ
Ground state to first excited Rydberg state
6
4He
Temperature dependent resonance
Low temperatures
Inhomogenous broadening
Medium temperatures
Inhomogenous broadening
convoluted with a Lorentzian
High temperatures
Lorentzian
Resonance frequency decreases
as the temperature increases
7
0
0.2
0.4
0.6
0.8
1
21.8 22 22.2 22.4 22.6
Collin et al (2005)Figure 8
Absorp
tion
V (volts)
1.004 K
0.855 K
0.553 K
0.304 K
1 GHz
189.6 GHz
Inhomogeneous broadening
8
100 MHz
0.1 0.08 0.06 0.04 0.02 00
0.2
0.4
0.6
0.8
1
Voltage/V
Abso
rpti
on
Disk
LorentzianDisk + edges
Data at 0.25 K
• Lineshape independent
of T < 0.5 K
• Inhomogeneous broadening
Peaks from Ez variation (0.3%)?
• Non-parallel disk electrodes:
Parabolic lineshape
• 8 m across 50 mm
• = 0.17 mrad = 35” arc
• Lorentzian contribution small?
Non-parallel electrodes
21.8 21.9 22 22.1 22.20
0.2
0.4
0.6
0.8
1
Convolution
9
Lorentzian Cell
-response
Measured
21.8 21.9 22 22.1 22.20
0.2
0.4
0.6
0.8
1
21.8 21.9 22 22.1 22.20
0.2
0.4
0.6
0.8
1
vvLvVGVS d),()()(G(V)Inhomogeneous
broadeningIntrinsic
linewidth
Convolution
Output = Lorentzian L(V) Cell response G(V)
0.9 K0.3 KFit
volts volts volts
Fit γ = 106 MHz
22
/),(
vvL
v=V-V0
Use lineshape at 0.3 K as a template
Convolute with a Lorentzian
Fit linewidth to data (T)
Microwave absorption at 189.6 GHz
10
Convolution
21.9 21.95 22 22.050
0.2
0.4
0.6
0.8
1
T = 0.498 K
= 0.001 V
= 2.9 MHz
volts
4He
0.3 K
21.9 21.95 22 22.050
0.2
0.4
0.6
0.8
1
T = 0.602 K
= 0.0026 V
= 7.6 MHz
volts
0.3 K
21.85 21.95 22.05 22.150
0.2
0.4
0.6
0.8
1
T = 0.855 K
= 0.0165 V
= 49 MHz
0.3 K
21.7 21.9 22.1 22.30
0.2
0.4
0.6
0.8
1
T = 1.004 K
= 0.098 V
= 288 MHz
volts 0.3 K
Microwave linewidth (T)
11
Theory:
T. Ando, J.Phys.Soc Japan, 44,765 (1976)
gasβbNaT Ripplon Gas atom
Scattering
β = 1.6
[H. Isshiki et al.J.Phys.Soc Japan (2007):
β = 2.1 (3He); 1.6 (4He)]
β = 1
4He
Temperature dependent linewidth
12
H. Isshiki et al.J.Phys.Soc Japan 76, 094704 (2007)
β = 2.1 (3He); 1.6 (4He)
gasβbNaT
Temperature dependent resonance f12
f12 (T) = f12 (0) f12 (T)
800 MHz at 1 K
f12 (T) T5/2 or
T7/3
b
13
Ripplons?
f12 = 189.6 GHz
Low power limit
4He
Temperature dependent resonance
2-ripplon processes:
Lamb shift
Ripplon induced Lamb shift
14
Theory:
Mark Dykman,
Denis Konstantinov
et al (2010)
Electron density
0.67 1011 m–2 (▲)
1.0 (▼)
1.5 (♦)
1.7 (●)
2.4 (■)
● - various
4He
f12 (T) = f12 (0) f12 (T)
+ Vapour
Theory
Density dependence of holding field
15
)ε/(
)2(
)1ε(ε)ε/( 0 ddD
dDne
ddD
VE z
z
Dd
Vz
D -2d =
D -2d =
Extrapolated to T = 0
Temperature dependence of f12
16
RIKEN4He 3He
Microwave absorption - Coulomb shift
Resonance frequency shifts with
• Power absorbed
• Excited state population
• Electron temperature Te
• Electron density
17
D. Konstantinov et al. PRL 103, 096801 (2009)
D. Konstantinov et al. PRL 98, 235302 (2007)
Ultra-hot Electrons on Liquid 3He: Te < 27 K
Power frequency Rabi
3He
3He
za
f12
Optical bistability in microwave absoprtion
18
D. Konstantinov et al. PRL 103, 096801 (2009)
High-powers: Hysteresis in conductivity
( zzz
m
dVVVV )()(1
)'Im(
High-powers: A.C. modulation (10 mV at 1 – 10 kHz)
Complex microwave lineshape
Vmod
t
0.9 0.95 1 1.05 1.10
0.1
0.2
0.3
0.4
0.5
Vz
)( zV
)( zV
3He
Differential
absorption
α‛ = dα/dVz
α
f12 = 189.6 GHz
1.3 K
α
α
Hysteresis Complex Lineshape
21.4 21.6 21.8 22 22.2 22.40.001
0
0.001
0.002
T = 0.9 K Re()
Im()
21.4 21.6 21.8 22 22.2 22.40.001
0
0.001
0.002
Vz (V)
T = 0.5 K
Re()
Im()
19
0
0.05
0.1
0.15
0.97 0.98 0.99 1 1.01 1.02 1.03
E
Re(Line)
Im(Line)
( zzz
m
dVVVV
V
)()(
21
2)Im( off
mV
VV
21)Im( max
off
MHz 50 mV 202 mV
0
1
2
3
1 10 100 1000
o
ff
Power (mV)
)Re( off
)Im( off
T = 0. 5K4He
Inhomogeneous power broadening
Inhomogeneous Coulomb broadening
4He
Conclusions
20
• Temperature dependent Rydberg levels
• Inhomogeneous broadening
• Enhanced Ando linewidth
• Microwave absorption bistability (hysteresis)
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