Chalmers University of Technology Current Measurement by ...
Transcript of 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
Chalmers University of Technology
Quantum Device Physics
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
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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))
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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.
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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)
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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
Per Delsing
Chalmers University of Technology
Quantum Device Physics
Comparing Room TemperatureComparing Room Temperaturemeasurement with countermeasurement with counter
CounterRoom temp am-meterKeithley Calibrator/source
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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
Per Delsing
Chalmers University of Technology
Quantum Device Physics
The capacitively coupled counterThe capacitively coupled counter
IResponse is more linear,Signal to noise is not so good.
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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
Per Delsing
Chalmers University of Technology
Quantum Device Physics
Crossover from electron to Cooper-pair countingCrossover from electron to Cooper-pair counting
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 ….
Per Delsing
Chalmers University of Technology
Quantum Device Physics
Crossover from electron to Cooper-pair countingCrossover from electron to Cooper-pair counting
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
Per Delsing
Chalmers University of Technology
Quantum Device Physics
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
Chalmers University of Technology
Quantum Device Physics
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)…