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)