Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

Semiconductor Few-Electron Quantum Dots as Spin Qubits 45
the sample heat up due to spurious noise and interference. Several filtering
stages are required for different frequency ranges (see Fig. 11 and Fig. 12). In
the connector box at room temperature, all wires are connected to ground via
0.22 nF “feedthrough capacitors”. At base temperature, all signal wires run
through “copper powder filters” [35]. These are copper tubes filled with copper
powder, in which 4 signal wires with a length of about 2 meters each are
wound. The powder absorbs the high-frequency noise very effectively, leading
to an attenuation of more than −60 dB from a few 100 MHz up to more than
50 GHz [36].
To remove the remaining low-frequency noise, we solder a 20 nF capacitor
between each signal wire and the cold finger ground. In combination with the
∼100 Ω resistance of the wires, this forms a low-pass RC filter with a cut-off
frequency of about 100 kHz (even 10 kHz for the wire connected to the IV
convertor, due to its input resistance of about 1.3 kΩ). These filters are used
for the wires connecting to ohmic contacts (although they were taken out to
perform some of the high-bandwidth measurements described in this work).
For the wires connecting to gate electrodes, a 1:3 voltage divider is present
(consisting of a 20 MΩ resistance in the signal line and a 10 MΩ resistance to
ground). In this way, the gate voltages are filtered by a low-pass RC filter with
a cut-off frequency of about 1 Hz. By combining all these filters, the electrons
in the sample can be cooled to an effective temperature below 50 mK (if no
extra heat loads such as coaxial cables are present).
High-Frequency Signals
High-frequency signals can be applied to gate electrodes via two coaxial cables.
They consist of three parts, connected via standard 2.4 mm Hewlett Packard
connectors (specified up to 50 GHz). From room temperature to 1 Kelvin,
a 0.085 inch semi-rigid Be-Cu (inner and outer conductor) coaxial cable is
used. From 1 Kelvin to the mixing chamber, we use 0.085 inch semi-rigid
superconducting Nb. From the mixing chamber to the sample holder, flexible
tin plated Cu coaxial cables are present. The coaxes are thermally anchored at
4K, 1K, ∼800 mK, ∼100 mK and base temperature, by clamping each cable
firmly between two copper parts. To thermalize also the inner conductor of
the coax, we use Hewlett Packard 8490D attenuators (typically −20 dB) at
1 K. These attenuators cannot be used at the mixing chamber, as they tend
to become superconducting below about 100 mK. We have also tried using
Inmet 50EH attenuators at the mixing chamber, but these showed the same
problem.
To generate the high-frequency signals, we use a microwave source (Hewlett
Packard 83650A) that goes up to 50 GHz (or 75 GHz, in combination with a
“frequency doubler”); a pulse generator (Hewlett Packard 8133A), which generates
simple 10 ns to 1 µs pulses with a rise time of 60 ps; and an arbitrary