Download Current Measurement by Real-Time Counting of Single Charges

Chalmers University of Technology
Current Measurement by Real-Time
Counting 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 Delsing
Nature 434, 361 (2005)
LT 24 (2005), ISEC (2005)
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Measuring current by counting single electrons
Normal current
measurement
The COUNTer:
Measurement of a voltage drop
across a resistor
Counts the electrons one by one
that are passing through a circuit
Can be coupled in parallel
Referenced to quantum Hall
resistance and Josephson voltage
I
V
I=V/R
fSET=I/e
1-10Hz<f<10MHz
1aA<I<1pA
I
-e
V=e/C
Suggestions for electron counters by Likharev, Visscher, Teunissen et al.
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Coupling the array to the SET
As charge in the array approaches the SET the current in the SET is modulated.
Directly coupled counter
Capacitively coupled counter
1D-array
1D-array
Single
Electron
Transistor
Single
Electron
Transistor
V
V
V
V
Capacitive coupling, more linear
Direct coupling gives full e charge
and thus better Signal to noise
Eliminates back tunneling
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Mixer
RF-source
The Radio-Frequency
Single Electron Transistor
Output
~
LO
RF
SET-bias
20
Warm
Amplifier
15
Cold
Amplifier
10
RSET=44.1k
C=370 aF
Cg20aF
Directional
Coupler
I (nA)
5
0
Vdc
-5
Vac
-10
Bias-Tee
-15
Single
Electron
Transistor
-20
-1.5
Tank circuit
-1.0
-0.5
0.0
0.5
1.0
1.5
V (mV)
L
Very high speed: 137 MHz
R. Schoelkopf, et al. Science (98)
C
Charge sensitivity: Q= 3.2 e/ Hz
Aassime et al., APL 79, 4031 (2001)
C
Per Delsing
Quantum Device Physics
Chalmers University of Technology
The 1D-array
Placing a single electron on
one of the electrodes polarizes
the array and gives rise to a
“Charge soliton”
eC
C0
These charge solitons repel
each other and thus line up in a
1D quasi Wigner lattice
1.0
e i k / i =
e
Ceff
i (-e/Ceff)
0.8
0.6
0.4
0.2
0.0
-20
-10
0
i-k
10
20
Spatial correlation transfers to
time correlation
Soliton size
C
=
C0
Bakhvalov et al, Zh. Eksp. Teor. Fiz. (1989))
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Simulations
We expect to see a time signal at the
output of the SET which has a frequency
fSET=I/e, i.e. SET-oscillations.
6.0 10-10
0.08
5.0 10-10
50 junctions
I= 250 fA
T=0
0.06
2
SQQ [e /Hz]
4.0 10
3.0 10-10
2.0 10-10
1.0 10-10
0.0 100
0
Q(t) [e]
0.04
-10
0.02
Capacitive
coupling
0.00
-0.02
-0.04
0
10
20
30
40
50
t [s]
1
2
3
4
5
f [MHz]
Per Delsing
Quantum Device Physics
Chalmers University of Technology
The Single Electron Counter
Tripple angle evaporation,
direct coupling
Array coupled directly
to SET, i.e. R-SET
configuration
Tri-angle evaporation
RSET=30k
Rarray=940k/jcn
Charge solitons line up
as a train in the array
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Current-Voltage Characteristics of the Array
Rjcn=940k
EC2.2K
EJ6mK
Sharp onset of current
in the normal state
Smooth onset in the
superconducting state
Per Delsing
Counting in the
SC-state gives a
more stable
current.
B=475mT
Bc=650mT
Quantum Device Physics
Chalmers University of Technology
Counting in Time and Frequency Domain
Direct observation of
the SET-oscillations
fSET=I/e
Time resolved
counting of single
electrons
Ben-Jacob, Gefen
Phys. Lett. (1985)
Averin, Likharev
JLTP (1986)
Bylander, Duty, Delsing
Nature 434, 361 (2005)
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Comparing Current with Frequency
The red ridge
corresponds to the
peak in the frequency
spectra
Peak heights have
been normalized
White line is fSET=I/e
5fA to 1pA
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Comparing Room Temperature
measurement with counter
Counter
Room temp am-meter
Keithley Calibrator/source
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Line width of the oscillations
Measurement
Normalized line width
The line width is can be well fitted to a
Lorentzian shape.
The measured line width agrees very well
with the simulated line width.
At low current there is an additional
broadening, probably due to uncertainty in
the bias.
Simulation
Per Delsing
Quantum Device Physics
Chalmers University of Technology
The capacitively coupled counter
Response is more linear,
Signal to noise is not so good.
I
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Crossover from electron to Cooper-pair counting
Power spectra for several different
magnetic fields 200-500 mT
Qcount = Current divided by fpeak
Single electron
tunneling
Incoherent
Cooper-pair
tunneling
EJ/kB 5 mK
T 150 mK
EJ<kBT
Duty, Bylander, Delsing in preparation
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Crossover from electron to Cooper-pair counting
Whether electrons or Cooper-pairs tunnel in the array depends on the threshold
voltage. When the voltage is higher than both thresholds, the rates become important.
The threshold voltages depend on
magnetic field (and background charge)
1.5
When the voltage exceeds both injection
thresholds, the tunneling probablities
will start to be important.
2e-threshold
e
=?
2e
e-threshold
Vt [mV]
1.0
The Tunnel probabilities depend on
energy gap and (subgap-) resistance,
and on back ground charges ….
0.5
0.0
0
100
200
300
400
500
600
B [mT], Bc=650mT
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Crossover from electron to Cooper-pair counting
<n> = I/ef
Peak width /fpeak
2
400
2e
1.6
300
1e
200
1.4
1.2
100
100
500
5
400
4
300
3
1.8
current [fA]
current [fA]
500
200
300
400
500
2
200
1
100
1
100
200
300
400
500
0
B|| [mT]
B|| [mT]
1e both at low voltage and high field
Per Delsing
1e peaks are more narrow
Quantum Device Physics
Chalmers University of Technology
Upper and lower current limits
Minimum counting rate
Maximum counting rate
At low currents only one electron is
present in the array, spatial and thus
temporal correlation is lost
To maintain time correlation the current
needs to be low, typically I < 0.03 e/RC
Current stability will smear the peak in
the frequency domain.
Speed of the RF-SET, in our case
~10MHz.
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Future 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)…
Per Delsing
Quantum Device Physics