Denis Konstantinov, Leonid Abdurakhimov,

William Powell

Development of a cryogenic spectrometer

for experiments with electrons on helium

Electrons on Helium 2014, Kazan, May 3-7

Quantum Dynamics Unit, OIST Graduate University

Cryogenic Lab.

Quantum Dynamics Unit

OIST Graduate University

Okinawa Institute of Science and Technology - OIST

One of the goals – development of

Collaborartion with Sergey Vasiliev, Turku

a cryogenic spectrometer for ESR

- Nonliner NMR in solid antiferromagnets

Other activities

Magneto-transport under excitation -

Collaboartion with Yu. Bunkov, CNRS Grenoble

Talks by A. Badrutdinov and L. Abdurakhimov

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

T=740 mK -25 dBm

-20 dBm

-15 dBm

-10 dBm

-5dBm

0 dBm

5 dBm

10 dBm

15 dBm

18 dBm

4Q

B0 (T)

Electron transport through constriction -

Collaboration with David Rees

- Spectroscopy of surface and spin states

- Fabry-Perot cavities, preliminary experiments

Talk (Part 1)

(D. Konstantinov)

(W. Powell)

Standard method

MW

+ VB

InSb

fref

PSD

mod

B

signal δVV

AδV

VB

δVmod

δVsignal

Grimes and Brown, PRL 1974

Collin et al., PRL 2002

Previous experiments in RIKEN

H. Isshiki, DK et al. J. Phys. Soc. Jpn. 2008

Power absorption

22

0

2

21)(

5.0)(

nnPa

Asymmetric “Fano” shape

Photo-induced phenomena in transport

- Bistabiliti and hysteresis

- Photo-conductivity and electron heating

DK at al. PRL 2009

DK et al. PRB 2012

DK and Kono, PRL 2009, PRL 2010

DK at al, PRL 2013

DK et al. PRL 2007

- Magneto-transport and ZRS

90 95 100

0.4

0.5

0.6

0.7

F (V/cm)

-1 (

M

)

T=0.5 K

4 5 6 7 8 90

5

10

15

xx (

10

-11

-1)

/c

Electron spins on liquid helium

[S. A. Lyon, Phys. Rev. A, 74,

052338]

Trap

[D. I. Shuster et al. PRL 105, 040503

(2010)]

- Spin qubits with long coherence time (S. Lyon)

- c-QED and SC-spin hybrid system (D. Shuster et al.)

- Multi-spin system for quantum memory storage

Spin resonance?

Power absorption

2

2

0

2

221

)(1

5.0)(

T

TnnPa

1HB - Rabi frequency

High MW power

2TNPa

- absorption saturation

Absorption saturation

E1

E2

E1

E2

E1

E2

121 /1 TA 12B 21B

µV 1TNPa

Absorption signal from 107 electrons

s 7

1 10T - for surface states

s 2

1 10T - for spin states

DK and Kono, J. Phys. Soc. Jpn. 2013 Need 1015 electrons!

Reflection from cavity

cavity

detector

Z0 C

L

R

0

0

ZZ

ZZ

V

V

L

L

in

out

Reflection coefficient -

Effect of sample - )41( LL

jQ

jQ

L

L

41

)1(4 1

0

0

0

Pin

Power the detector -

in

L

L PjQ

jQP

2

det41

4

jwhere

Reflection from cavity

jAt the resonance

in

Le

L PQTTH

QP

2

''

max21

2

1

2

''

maxdet

41

4

From Bloch equations 21

2

1

2200

21

2

1

2

''

max

1

1

2

1

1 TTHT

TTH ee

s 10021 TT

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

1012

cm-2

1011

cm-2

1010

cm-2

Pd

et (

pW

)

Pin (pW)

109 cm

-2

Q=10 000

Use theoretical estimate

Heterodyne detection

S. Vasiliev et al. Rev. Sci. Instrum. 75, 94 (2004)

- Cryogenic mixers

conversion losses 10 dB

noise temperature 100 K

- Fabry-Perot resonator

- Down-conversion to 100 MHz

Spectroscopy of surface states

Z0

C L R 0

0

ZZ

ZZ

V

V

L

L

in

out

Reflection coefficient -

Effect of sample - )41( eCC

where electrical susceptibility EED e4

Electrical dipole moment 222221121111

2121)()( zeeztezttjtj

2

1

22

0

)(

0*

2112

2

1

22

0

2

11122

)(

))((

2

1

)(1

0

T

ej

T

T

tj

From optical Bloch equations

Reflection from cavity

2

1

22

0

2

12''

2

1

22

0

02

12'

)(

)(

)(

)()(

T

ezn

T

ezn

e

e

Complex electrical susceptibility

in

L

L PQT

QP

2

''

max

21

1

''

maxdet

41

4

s 7

1

1 10 T

100

101

102

103

104

105

10-3

10-2

10-1

100

101

102

103

104

105

108 cm

-2

107 cm

-2

106 cm

-2

Pd

et (

pW

)

Pin (pW)

105 cm

-2

Q=10 000

A. Badrutdinov et al. Eur. Phys. Lett. 2013

Use experimental estimate

Back to asymmetric “Fano” shape

H. Isshiki, DK et al. J. Phys. Soc. Jpn. 2008

Asymmetric “Fano” shape

)( '''

det eeel

j

refoutelrefout jVeVVVVVV

2'''

det )(1 ee

j jeP - mixture of absorption

and dispersion response

H. Isshiki, DK et al. J. Phys. Soc. Jpn. 2008

“Fano” lineshape

“Mixture” lineshape

22

0

0

)(

)(sin)cos1()(

F

13 14 15 16

-10

0

10

20

30 4He: T=900 mK

VInSb

=20-35 mV

160.99 GHz

160.9 GHz

159.9 GHz

V (V

)

Vbottom

(V)

159.5 GHz

GHz 85.024

1 f

Lf

Back to asymmetric “Fano” shape

24 26 28 30 32

-2

-1

0

1

fitting

dA

/dE

(a

rb.

un

it)

bias voltage VB (V)

620 mK

Changes with frequency (test of the model)

Good agreement!

Talk (Part 2)

- Spectroscopy of surface and spin states

- Fabry-Perot cavities, preliminary experiments

(D. Konstantinov)

(W. Powell)

Fabry-Perot resonator

coupling hole

spacer for frequency

adjustment

spherical mirrors

• Spectrometer uses bandpass filter

centered at 140 GHz

• Aim to tune resonance frequency to this

value

• Take into account dependence on

temperature and presence of dielectric in

cavity

• First, identify modes

Fabry-Perot resonator

• Modes given by

• Easier to identify if we consider only

TEM00 modes

• Achieved experimentally by placing

electrode within resonator cavity

Cavity modes

Cavity size (m)

Res

on

an

t fr

eq

ue

ncy (

Hz)

Cavity modes

Cavity Size (m)

Res

on

an

t fr

eq

ue

ncy (

Hz)

TEM00 modes

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

134 136 138 140 142 144 146

Sig

nal

(V)

Frequency (GHz)

Resonator Modes - Closed vs Open Geometry

Closed Geometry

Open Geometry

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

134 136 138 140 142 144 146

Sig

nal

(V)

Frequency (GHz)

Effect of Electrode on Resonator Modes

Electrode Present

Electrode Missing

Cavity Size (m)

Res

on

an

t fr

eq

ue

ncy (

Hz)

TEM00 modes

• Cooling reduces size of resonator cavity

increasing resonant frequency of modes

• Tested at liquid nitrogen temperature

• Observed 500 MHz shift in resonant

frequency

Working mode

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

139.5 140 140.5 141 141.5 142 142.5

Sig

nal

(V)

Frequency (GHz)

Effect of Cooling on Resonator Modes

Uncooled Resonator

Cooled Resonator

• Difficult to determine effect of dielectric

• Naïve approximation expect to see

resonance somewhere between cavity full

of dielectric and empty

• Calculated to fall roughly 3 GHz

Working mode

0

0.002

0.004

0.006

0.008

0.01

0.012

134 136 138 140 142 144 146

Sig

nal

(V)

Frequency (GHz)

Tuning Size of Resonator Cavity

4.43mm Spacer

4.34mm Spacer

4.30mm Spacer

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

143.4 143.45 143.5 143.55 143.6 143.65 143.7 143.75 143.8

Bo

lom

ete

r S

ign

al

(V)

Frequency (GHz)

Resonance shift and QF drop

1.15E-01

1.15E-01

1.16E-01

1.16E-01

1.17E-01

1.17E-01

1.18E-01

1.18E-01

1.19E-01

143.55 143.6 143.65 143.7 143.75 143.8 143.85 143.9 143.95

Bo

lom

ete

r S

ign

al

(V)

Frequency (GHz)

Resonance before He Condensation

• In fridge see small drop in resonant

frequency and large decrease in quality

factor

• Fixing frequency at resonance and

sweeping pressing field brings electrons

into resonance

• Derivative of absorption signal detected

using lock-in amp

Working mode

0

0.000002

0.000004

0.000006

0.000008

0.00001

0.000012

0.000014

0 5 10 15 20 25 30 35

Bo

lom

ete

r S

ign

al

(V)

Electrode Voltage (V)

Signal of electrons at cavity resonance frequency

• Unusual noise appears when TBS vacuum

pump is attached to cell

• Noise depends on level of liquid Helium

• Mechanical vibration caused by vibrating

liquid Helium?

Opto-mechanical effect

1.15E+00

1.15E+00

1.15E+00

1.16E+00

1.16E+00

1.16E+00

1.16E+00

1.16E+00

1.17E+00

143.4 143.45 143.5 143.55 143.6 143.65 143.7 143.75 143.8

Bo

lom

ete

r S

ign

al

(V)

Frequency (GHz)

Noise from Turbo-pump System

1.15E+00

1.15E+00

1.15E+00

1.16E+00

1.16E+00

1.16E+00

1.16E+00

1.16E+00

1.17E+00

143.4 143.45 143.5 143.55 143.6 143.65 143.7 143.75 143.8

Bo

lom

ete

r S

ign

al

(V)

Frequency (GHz)

Cavity Resonance SIgnal

1.37E+00

1.38E+00

1.39E+00

1.40E+00

1.41E+00

1.42E+00

1.43E+00

1.44E+00

1.45E+00

1.46E+00

141 141.5 142 142.5 143 143.5 144 144.5

Bo

lom

ete

r S

ign

al

(V)

Frequency (GHz)

Reducing Helium level Reduces TBS Noise

1.35E+00

1.36E+00

1.37E+00

1.38E+00

1.39E+00

1.40E+00

1.41E+00

1.42E+00

1.43E+00

141 141.5 142 142.5 143 143.5 144 144.5

Bo

lom

ete

r S

ign

al

(V)

Frequency (GHz)

1.34E+00

1.35E+00

1.36E+00

1.37E+00

1.38E+00

1.39E+00

1.40E+00

1.41E+00

141 141.5 142 142.5 143 143.5 144 144.5

Bo

lom

ete

r S

ign

al

(V)

Frequency (GHz)

- Heterodyne detection of ESR in electrons on

Summary

- Can be useful for studying D1-transitions as well

- Employment of open Fabry-Perot resonators

helium is under development

could be useful