Chemistry Reference
In-Depth Information
and correspond to the fast relaxation within the wells. These fast processes are, of
course, not captured by Eq. (237).
Note that the ground-state tunnel splitting
is typically very small, so that
it is very difficult to experimentally realize
to see coherent oscillations
of the spin between the two states. To increase
,
one has to apply a strong
transverse field. In the case
W
|
W
|
(
W>
0), the levels becomes dehybridized,
ρ
eq
ρ
eq
−
++
=
S
,
and one obtains
S,
−
S
1
e
−
t
ρ
eq
−
e
−
t
ρ
S
(
t
)
=
+
−
(238)
−
S,
−
S,
−
5. Relaxation Rate Between two Tunnel-Split States
The relaxation rate
for the ground-state doublet can be found analytically
[13]. In particular, for the uniaxial model in the presence of a transverse field
along the
x
axis, with the help of the high-order perturbation theory in
H
x
, one
obtains
−+
m
−
√
W
2
m
ψ
−
|
S
z
|
ψ
+
=−
2
+
2
m
−
gμ
B
H
x
W
√
W
2
m
ψ
−
|
S
x
|
ψ
+
=
2
+
2
S
y
ψ
m
−
ψ
=−
gμ
B
H
x
m
i
(239)
−
+
2
Then, from Eq. (155) in components,
ω
0
−
|
S
x
|
+
=−
i
ψ
ψ
−+
,x
−
ψ
S
y
ψ
gμ
B
H
z
+
ψ
−
|
S
z
|
ψ
+
gμ
B
H
y
−
+
ω
0
ψ
S
y
ψ
=−
i
−+
,y
−
+
−
ψ
−
|
S
z
|
ψ
+
gμ
B
H
x
+
ψ
−
|
S
x
|
ψ
+
gμ
B
H
z
=−
i
ω
0
ψ
−
|
S
z
|
ψ
+
−+
,z
gμ
B
H
y
+
ψ
S
y
ψ
gμ
B
H
x
−
ψ
−
|
S
x
|
ψ
+
(240)
−
+
with
H
y
=
0 one obtains
=
0
−+
,z
m
−
gμ
B
H
x
m
=−
i
(
W
−
gμ
B
H
z
)
−+
,x
2
m
−
√
W
2
m
=
gμ
B
H
x
−+
,y
2
+
2
1
2
(
gμ
B
H
x
)
2
−
W
(
W
gμ
B
H
z
)
(
gμ
B
H
x
)
2
−
×
−
(241)
