Experimental Progress: Solid State Computing on Quantum Dots
huiliu
will benefit us:)
Experimental Realization of Quantum Computing on Quantum Dots (original
title : high sensitivity emectrometer )
Introduction:
Electrons and spins in quantum dots are thought to be candidates for
basic elements of solid quantum computing, and many researches are
performed on the study of the mechanism of electrons or spins in
realizing quantum computing, the generating and detecting of electrons
or spins used for performing quantum computing. In this report, I will
shows the recent progress on the technique of detecting of electrons
and spins in quantum dots.
1. Problems related to detecting electrons in quantum dots
Quantum blockade effect allows us to detect the addition / subtraction
of single electron in quantum dots. And the conditions where quantum
blockade is obvious are important. For any experiment to detect single
electron in quantum dots, any one must consider the followings:
(1) Rt >> h / e2;
(2) Ec = e2 / Cd >> KbT;
where Rt is the tunneling resistance, Ec is Coulomb energy, Cd is
quantum dot capacitance (Here, Rt is used to ensure to localize
electron in reservoir or quantum dot to prevent quantum fluctuation; Ec
to guarantee the suppression of thermal excitation.). The first
condition can be met by weak-coupling between quantum dot and
reservoir. And the second condition can be realized by fabricating
small quantum dots (reduce the capacitance) or lowering the
temperature.
The second problem related to achieve high charge sensitivity is the
impedance mismatch between quantum dot and measurement instrument. So
the successful design of impedance converter is critical to realize
single electron detection. Up to now, the most successful amplifier is
single-electron amplifier with modified output stage. In following, I
will focus on some considerations on such kind of amplifier.
2. Technique details of high charge sensitivity amplifier
2.1. Capacitance technique [1]
[I can not paste figure here, you guys try to get details from refs;]
Technique data:
(1) In order to achieve high frequency measurement rate, the sample
must be designed carefully so that the tunneling frequency (ftunnel = 1
/ (2 * pi * R bottom * C bottom)) must be larger than the max working
frequency.
(2) The excited voltage Vexc is applied across the sample and the
current is measured by reading the voltage across the input impedance
of measurement apparatus. And minimizing the input impedance is
becoming tricky especially when the experiment is conducted in low
temperature.
This problem can be solved by introducing a two-stage amplifier. The
first stage is used to amplify and has low impedance, and the second
stage has unit gain and high output impedance for driving high
impedance cable and data acquiring instrument (see figure 1-3).
Reference data:
Vexc = 100µV;
Capacitance of cable: 300pF;
GaAs / AlGaAs(300nm × 300nm): capacitance of Ctop Cbottom =
0.1 fF;
Lock-in Ref frequency: 600kHz with 4 gain to avoid 1/f noise;
Low input capacitance: 0.3 pF;
Input white noise: 10nV / (Hz)1/2 ( = 0.01 e / (Hz)1/2 );
Summary:
The quantum dot signal is capacitively coupled to an amplifier
that
can detect single electrons tunneling on and off. This max ref
frequency is limited by the sample's tunnel conductance and tunnel
capacitance between quantum dot and electron reservoir.
2.2 single-electron transistor technique [2]
As shown in figure 2-1, the voltage applied to the gate electrode can
raise and lower the height of electrostatic barrier and results in the
variation of tunnel current in SET. Then the charge variation in gate
electrode is reflected in the voltage applied in SET's central island
with the expression: VSET = (CS / Cg )* Vg .
Figure 2-1: (1) SET electrometer configuration with gate electrode
weakly linked to the quantum dots and capacitancely coupled to SET; (2)
Current peaks at different gate voltage shows that electron is
tunneling into quantum dots.
High frequency offers low noise for high charge sensitivity, for
example, avoiding signal degradation due to leakage or decay. The
following SET configuration's cut off frequency can be 1MHz. There
are several reasons limiting the max working frequency, for instance,
the tunneling frequency, max frequency applied to excitation gate
voltage, coax cable cross talking, capacitance and resistance in long
cable for conducting voltage and the lock-in response time. The quantum
limit for SET amplifier is about 10GHz due to RC in tunnel junctions.
Technique Data:
SET load impedance: several fF;
Max working frequency: 1MHz (limited by coax cable);
2.3 radio frequency single-electron transistor technique[3]
Principle:
Unlike the above one, the RF-SET monitors the damping of high frequency
resonance circuit instead of directly measuring current or voltage from
SET. The excited source is adjusted to show resonance with inducer and
pad capacitance. When SET is in blockade state, the reflected RF power
is high due to the maximum of SET resistance. [3]
The RF-SET is more attractive recently and many theoretical and
experimental works are done. And it was used to read a cooper pair [4].
For this kind of RF-SET, the quality factor and sensitivity will
balance the design.
Figure 3-2 Model for RF-SET
Technique Data:
Charge sensitivity: 10-5e / (Hz)1/2;
Working Frequency: 137 MHz;
Reference:
[1]. Charging of Two-Dimensional Electron Puddles, Misha Brodsky,
Thesis, 2000;
[2]. The Aluminum Single-Electron Transistor for Ultrasensitive
Electrometry of Semiconductor Quantum-Confined Systems, David Berman,
Thesis, 1998;
[3]. R.J.Schoelkopf, et al, The Radio-Frequency Single-Electron
Transistor (RF-SET): A Fast and Ultrasensitive Electrometer, Science,
208,1238.1998;
[4]. A. Assime, et al, Radio-Frequency single-Electron as Readout
Device for Qubits: Charge Sensitivity and Backaction, Phys. Rev. Lett,
86,3376,2001;