SET environmental and real time

1
Radio-frequency single-electron transistor
(RF-SET) as a fast charge and position sensor
11/01/2005
2
Single-Electron Transistor
q, offset charge
qne
q(n-1/2)e
I and RSET sensitive to offset charge q
SET as charge sensor
I
island charge is quantized when
q
n0
n
-1
n
1
and kBTltlt e2/C
3
Limitations of SET Bandwidth
Ideal circuit
R, C
R, C
Intrinsic time scale
output
Cc
V
DUT
Noise-limited bandwidth
Achievable bandwidth in a typical DC setup
4
RF-SET as a Fast Electrometer
Capacitance now part of the characteristic
impedance!
radio-frequency single-electron transistor
inductor L, SET pad stray capacitance Cp, SET
differential resistance Rd(q) form resonant tank
circuit
vr
Z0 50 ?
L
R,C
R,C
Cc
Cp
DUT
V(w0t)
changes in charge modulates the amplitude of the
reflected signal
Dq(wmt)-gtDR(wmt)
q1
q0
q0
Signal at wm detected after demodulation
Schoelkopf, Science, 280, 1238 (1998)
5
Characterization of RF-SET
sine wave modulation applied to the gate
Frequency domain
Time domain
Lu, Nature, 422, 423 (2003)
BW1MHz
6
Experimental Set-up
RF circuit
1.0 GHz carrier w0
HEMT amplifier
circulator
GaAs FET amplifier
Bipolar amplifier
mixer
To digital oscilloscope
directional coupler
LO
w0
L
Cp

SET
QD
Vbias
Cc

Tmix 50 mK
7
RF-SET coupled to QD
top view
depletion gates
side view
Al tunnel junctions
Al AlGaAs GaAs
Cc
QD
QD tunable by gate voltage, capacitively coupled
to SET
SET Excellent electrometer
Charge detector
8
Real time detection of individual electrons
Number of tunneling events a direct measure of
the tunneling rate G
relatively open dot
relatively closed dot
9
Charge Occupation probability
two level system near a charge degeneracy point
dot switching between two charge states
Can directly measure the occupation probability
of the N electron charge state
10
Distribution Function
charge occupation probabilities
Distribution function Thermally broadened Fermi
distribution
Tunneling rate directly measured
Lu, Nature, 422, 423 (2003)
11
RF-SET as fast charge sensor
Can see transition rate pick up as QD
source/drain bias is increased. Can also monitor
charge fluctuations. In principle, can
acquire complete statistical information about
current flow! Great potential applications for
quantum computation, for example.
Lu, Nature, 422, 423 (2003)
12
RF-SET as displacement sensor
RF-SET
Mechanical resonator
Q0CgVg
DQ0VgDCg?VgDd
resonator
Apply fixed voltage Vg to the beam, and the
RF-SET output measures the beams motion (changes
in d)
d
SET
LaHaye, Science, 304, 74 (2004)
13
RF-SET as displacement sensor
LaHaye, Science, 304, 74 (2004)
Ultrasensitive displacement detection achieved
Detect the properties of the resonator by simply
listening, without driving it (a factor of 4.3
away from the quantum limit)
14
High BW particle/cell counter
Wood, APL, 87, 184106 (2005)
RF reflectance data taken for flowing 15 mm beads
through the microfluid channel
BWgt10MHz
Problems associated with large R, Cs solved by
the RF resonant circuit
Millions of beads (cells) can be counted per
second