Page 193 - Principles and Applications of NanoMEMS Physics

4. NANOMEMS APPLICATIONS: CIRCUITS AND SYSTEMS 181

where () BH represents the magnetic field interaction terms between spins,
the respective hyperfine interaction energies of the nucleus-electron systems
is given by A and A , respectively, and 4J is the exchange energy, which
1 2
is a function of the electronic wavefunction overlap and, for donors in a host
semiconductor of dielectric constant İ , and Bohr radius a , and separated
B
by a distance r of about 100-200 Å, is given by [203],
5
e 2 § r · 2 § − 2r ·
4J () ≅ 1.6r ¨ ¨ ¸ exp ¨ ¨ ¸ . (40 )
¸
¸
İa a a
B © B ¹ © B ¹
The wavefunction overlap, to which J is proportional, is captured by this
exchange energy. Thus, varying the voltage applied via the J-gate one can
modulate coupling between separated qubits.
Once qubits have been manipulated to effect a quantum computation, the
result of the computation must be read off. In the silicon-based nuclear spin
QC, this is accomplished by measuring the current that results from the
conversion of nuclear spins into electron polarization, in response to a bias
voltage, see Fig. 4-20 below. In particular, this conversion of the nuclear
spin into an electron polarization is prompted by the coupling of the states
↓↓ and ↑↓ − ↓↑ , which is produced by the hyperfine interaction

between the nuclei and the electronic states as the exchange energy J is
increased adiabatically from J < µ B/2 to J > µ B/2 , see Fig. 4-20(a)
B B
[199].