Page 175 - Principles and Applications of NanoMEMS Physics

4. NANOMEMS APPLICATIONS: CIRCUITS AND SYSTEMS 163

but rather, with the array as a whole. Since the ion trap produces two qubits,
a controlled interaction between them allows the realization of quantum
gates.
In the case of the spin-orientation qubit, the internal spin state of the ion
may be set into the “down” ( ↓ ) or “up” ( ↑ ) states, by application of a
uniform magnetic field. Alternatively, it may be prepared into superposition
states Į ↓ + ȕ ↑ by varying the time duration of applied RF fields.
Further functionality is obtained out of the ion-trap system by coupling its
spin-orientation qubit to its motional qubit. In particular, superposition of a
spatially non-uniform magnetic field along the motional qubit, for instance,
of magnitude + ∆ B at the ion’s left most position and − ∆ B at its right-
most position, causes the ion to experience a field of amplitude B∆ and
frequency equal to the motional oscillation frequency. Under these
circumstances, an exchange of energy between the spin and the motional
states, ↑ 0 → ↓ 1 , ensues if the magnetic field frequency coincides

with the energy difference between the two spin states. More generally, if
the spin qubit is in a superposition state, e.g., Į ↓ + ȕ ↑ then, consistent
with conservation of energy, the energy exchange produces the transition
(Į ↓ + ȕ ↑ )0 → ↓ ( 0Į + ȕ 1 ). As depicted in Fig. 4-1 ,
1

. . .
. . .

Confining
Confining Laser Beam Phononic
Phononic
Laser Beam
Electrode Motion
Motion
Electrode
(a)
e e 1 1 e e 0 0
i) i) iii)
iii)
ii) ii)

g g
(b)
Figure 4-1 . (a) Cirac-Zoller ion-trap qubit. (b) Qubit states g and e , are separated by
2
0
=
an energy ω .
0