chalmers university of technology current measurement by

Per Delsing

Chalmers University of Technology

Quantum Device Physics

Current Measurement by Real-TimeCurrent Measurement by Real-TimeCounting of Single ChargesCounting of Single Charges

Introduction, single electron counting

Results

Counting of single electrons

Crossover from electron to Cooper-pair counting

Summary

Jonas Bylander, Tim Duty and Per DelsingNature 434, 361 (2005)LT 24 (2005), ISEC (2005)

Per Delsing



Normal currentmeasurementMeasurement of a voltage dropacross a resistor

Referenced to quantum Hallresistance and Josephson voltage

The COUNTer:Counts the electrons one by onethat are passing through a circuit

Can be coupled in parallel

I V I=V/R

fSET=I/e

1-10Hz<f<10MHz

1aA<I<1pA

V=e/C

I -e

Suggestions for electron counters by Likharev, Visscher, Teunissen et al.

Measuring current by counting single electronsMeasuring current by counting single electrons

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Coupling the array to the SETCoupling the array to the SET

As charge in the array approaches the SET the current in the SET is modulated.

Single

Electron

Transistor

1D-array

V V

Capacitively coupled counter

Single

Electron

Transistor

1D-array

V V

Directly coupled counter

Direct coupling gives full e charge

and thus better Signal to noise

Capacitive coupling, more linear

Eliminates back tunneling

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The Radio-FrequencyThe Radio-FrequencySingle Electron TransistorSingle Electron Transistor

L

C

DirectionalCoupler

Mixer

SET-bias

Tank circuit

Cold

Amplifier

Warm

Amplifier

~RF-sourceOutput

RF

LO

Bias-Tee

C

Single

ElectronTransistor

Very high speed: 137 MHzR. Schoelkopf, et al. Science (98)

Charge sensitivity: Q= 3.2 e/ HzAassime et al., APL 79, 4031 (2001)

-20

-15

-10

-5

0

5

10

15

20

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5I

(nA

)

V (mV)

RSET

=44.1k

C =370 aF

Cg

20aF

Vdc

Vac

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The 1D-arrayThe 1D-arrayPlacing a single electron onone of the electrodes polarizesthe array and gives rise to a“Charge soliton”

These charge solitons repeleach other and thus line up in a1D quasi Wigner lattice

Spatial correlation transfers totime correlation

0.0

0.2

0.4

0.6

0.8

1.0

-20 -10 0 10 20

i (-e

/Cef

f)

i-k

Soliton size

=C

C0

e-

C

C0

i =e

Ceff

e i k /

Bakhvalov et al, Zh. Eksp. Teor. Fiz. (1989))

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SimulationsSimulations

0.0 100

1.0 10-10

2.0 10-10

3.0 10-10

4.0 10-10

5.0 10-10

6.0 10-10

0 1 2 3 4 5

SQ

Q [

e2/H

z]

f [MHz]

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0 10 20 30 40 50

Q(t

) [e

]

t [ s]

50 junctionsI= 250 fAT=0

Capacitivecoupling

We expect to see a time signal at theoutput of the SET which has a frequency

fSET=I/e, i.e. SET-oscillations.

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The Single Electron CounterThe Single Electron Counter

Array coupled directlyto SET, i.e. R-SETconfiguration

Tri-angle evaporation

RSET=30k

Rarray=940k /jcn

Charge solitons line upas a train in the array

Tripple angle evaporation,direct coupling

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Current-Voltage Characteristics of the ArrayCurrent-Voltage Characteristics of the Array

Sharp onset of currentin the normal state

Smooth onset in thesuperconducting state

Rjcn=940kEC 2.2KEJ 6mK

Counting in theSC-state gives amore stablecurrent.B=475mTBc=650mT

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Counting in Time and Frequency DomainCounting in Time and Frequency Domain

Bylander, Duty, DelsingNature 434, 361 (2005)

Direct observation ofthe SET-oscillations

fSET=I/e

Time resolvedcounting of singleelectrons

Ben-Jacob, GefenPhys. Lett. (1985)Averin, LikharevJLTP (1986)

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Comparing Current with FrequencyComparing Current with Frequency

The red ridgecorresponds to thepeak in the frequencyspectra

Peak heights havebeen normalized

White line is fSET=I/e

5fA to 1pA

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Comparing Room TemperatureComparing Room Temperaturemeasurement with countermeasurement with counter

CounterRoom temp am-meterKeithley Calibrator/source

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Line width of the oscillationsLine width of the oscillations

The line width is can be well fitted to aLorentzian shape.The measured line width agrees very wellwith the simulated line width.At low current there is an additionalbroadening, probably due to uncertainty inthe bias.

Measurement

Simulation

Normalized line width

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The capacitively coupled counterThe capacitively coupled counter

IResponse is more linear,Signal to noise is not so good.

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Crossover from electron to Cooper-pair countingCrossover from electron to Cooper-pair counting

Power spectra for several differentmagnetic fields 200-500 mT QQcount count == Current divided Current divided by by ffpeakpeak

IncoherentCooper-pairtunneling

Single electrontunneling

EJ<kBT

Duty, Bylander, Delsing in preparationEJ/kB 5 mKT 150 mK

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0.0

0.5

1.0

1.5

0 100 200 300 400 500 600

Vt [

mV

]

B [mT], Bc=650mT

e-threshold

2e-threshold

Whether electrons or Cooper-pairs tunnel in the array depends on the thresholdvoltage. When the voltage is higher than both thresholds, the rates become important.

The threshold voltages depend onmagnetic field (and background charge)

e

2e

= ?

When the voltage exceeds both injectionthresholds, the tunneling probablitieswill start to be important.

The Tunnel probabilities depend onenergy gap and (subgap-) resistance,and on back ground charges ….

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2e

1e

B|| [mT]

curr

ent [

fA]

<n> = I/ef

100 200 300 400 500

100

200

300

400

500

1

1.2

1.4

1.6

1.8

2

Peak width /fpeak

100 200 300 400 500

100

200

300

400

500

0

1

2

3

4

5

B|| [mT]

curr

ent [

fA]

1e both at low voltage and high field 1e peaks are more narrow

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Upper and lower current limitsUpper and lower current limits

Minimum counting rateMinimum counting rate

At low currents only one electron ispresent in the array, spatial and thustemporal correlation is lost

Current stability will smear the peak inthe frequency domain.

Maximum counting rateMaximum counting rate

To maintain time correlation the currentneeds to be low, typically I < 0.03 e/RC

Speed of the RF-SET, in our case~10MHz.

Per Delsing



Future directionsFuture directions

• Improving signal to noise, Squid amplifier

• Coherent versus incoherent 2e, Bloch oscillations

• Accuracy, how small currents can we measure

• Larger currents, parallel counters

• Looking at other systems, nanotubes, nanowires ….

• Counting statistics, (linear detectors)…

chalmers university of technology current measurement by

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