Page 194 - Principles and Applications of NanoMEMS Physics

182 Chapter 4

↑↓
↑↓
↑↑
Energy Levels Energy Levels ↑↑ 4J 2 µ + ↓↑+ B B ↓↑
2 µ B B
4J
↓↓
10
J= 0 A >A 2 2 10 + 01+ 01 ↓↓ − ↓↑− ↓↑
J= 0 A >A
↑↓
↑↓
1 1
11 10 − 0110 − 01
11
10
10 01
01
00
00 0 0 J J
(a)
A- G a t e
A- G a t e s s
J- G at e s s
J- G at e
-- - - + + + +
--
+ +
B a rri e
B a rri e r r
Si
Si
e e - -
P P P P
(b)
Figure 4-20. (a) Energy levels for electrons (solid lines) and lowest energy-coupled electron-
nuclear (dashed lines) systems as a function of exchange energy, J. When J < µ B/2 , it is
B
possible to perform two-qubit computations by exercising control over the level splitting
10 − 01 − 10 + 01 with the J-gate. Above J = µ B/2 , the states of the coupled
B
system evolve into states with differing electron spin polarization. When J = 0 the state of
the nucleus with the larger energy splitting, which is controllable by the A-gate, determines
the final electron spin state after an adiabatic increase in J. (b) Only electrons in state
↑↓ − ↓↑ can make transitions into states in which electrons are bound to the same donor
-
(D states). These transitions elicit an electron current that is measurable by capacitive means,
thus enabling the underlying spin states of the electrons and nuclei to be determined. [202].
This implies a change in wavefunction symmetry, i.e., from that of ↓↓ to
that of ↑↓ − ↓↑ .

Two electrons with the latter symmetry, however, are capable of
−
occupying the same donor. In the Si:P the donor takes the form of a D
state, which is always a singlet state with a second electron binding energy
of 1.7meV. Under these circumstances, it will be possible, with the
appropriate bias between the A-gates, to induce electrons from one donor to
−
move the adjacent, already occupied one in order to establish the D state in
it. This charge motion, in turn, is detectable utilizing single-electron