Page 199 - Principles and Applications of NanoMEMS Physics

4. NANOMEMS APPLICATIONS: CIRCUITS AND SYSTEMS 187

control of macroscopic quantum states in a single-Cooper-pair box was
reported by Nakamura, et al. [209]. In these experiments, the superposition
of two charge states (i.e. states with different number of Cooper pairs N) was
detected by a tunneling current through a probe junction. In particular, a
normal electron escaped through the probe junction every time the system
adopted the one state. Control of the state of the qubit was effected by
varying the length of the voltage pulse, with the probability of the system
returning to the zero or one state oscillating in proportion to it. The major
source of decoherence was found to be the probe junction itself, which
limited the coherence time to 2 ns [206].
Nakamura et al.’s [206] approach was improved by the quantronium
device demonstrated by Vion et al.’s [112] see Fig. 4-23. In this device, the
Josephson junction of the Cooper pair is split into two small parallel
Josephson junctions which are characterized by their energy E cos ( /δ ) 2 ,
J
where δ is the superconducting phase difference across the series
combination of the two junctions. These junctions, in turn, are shunted by a
larger Josephson junction, characterized by an energy E ≈ 20 E and by a
0 J J
phase γ , thus forming a loop. A current I applied to an adjacent coil
φ
produces a flux Φ that passes through the loop, with the consequence that it
induces a phase φ that now links the loop phases as follows, δ = γ + φ ,
where φ = e 2 Φ = / . This action entangles the state of the box, N, via δ ,

with the phase γ , see Fig. 4-23(a). The quantum state of the qubit is
manipulated by applying a microwave pulse of frequency
ν ≅ ν 01 ~ 16 5 . GHz , the transition frequency between charge levels in the
box corresponding to the zero and one states. Depending on the pulse
duration, any state Ψ = α 0 + β 1 can be prepared. Reading the state

exploits the fact that a current pulse I () t , see Fig. 4-23(b), of peak
b
amplitude slightly below the critical current of the large junction,
I = 2 eE = / , causes a supercurrent to develop in the loop that is
0 0 J
proportional to N. In particular, when there is no extra charge in the box, this
supercurrent elicits a clockwise current in the loop formed by the two
junctions, whereas when there is an extra charge in the box, the current is
counterclockwise. In the former case, the current adds to the bias current in
the large junction with the result that, for precisely adjusted amplitude and
duration of the () tI pulse, it switches to a finite voltage for a state one and
b