Contours dénergie constante. 2 Drude Oscillations de Bloch.
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Transcript of Contours dénergie constante. 2 Drude Oscillations de Bloch.
²~k =¹h2k2
x
2m
²~k =¹h2
2m(k2
x + k2y)
Contours d’énergie constante
D(²) /1
p²
D(²) / Cted = 2
d = 1
D(²)d² = nombre d'¶etats dans une tranche d'¶energie [²;² + d²]
kx
kxky
²~k
kx
kx
ky
2
²~k =¹h2k2
x
2m
²~k =¹h2
2m(k2
x + k2y)
Contours d’énergie constante
D(²) /1
p²
D(²) / Cted = 2
d = 1
D(²)d² = nombre d'¶etats dans une tranche d'¶energie [²;² + d²]
kx
kxky
²~k
kx
kx
ky
2( ) [ ( )]x
kx x
ej v f
Vk k k
2( ) [ ( )]
kxx x k
ej v k k f
V
2( ) [ ( )] 0x x
k
ej v f
Vk k
Fk
F
k
F
k
F
k
F
F
0xx
Ek e
2( ) [ ( )] [ ( )] 0x x x
k
ej v k f k k i f k
V
xE
2Fk
a
BT BT Drude
B
hT
Fa
F
k
F
k
F
k
Fk
2Fk
a
F t
k
BT BT Drude
B
hT
Fa
Oscillations de Bloch
F
k
F
k
F
k
k
B
hT
Fa
710BT s1210 s
Pour des électrons dans les solides
Pas d’oscillations de Bloch
F tk
BT Oscillations de Bloch
F
k
k
Atoms re-arrange and form optical lattice
Bloch Oscillations of Atoms in an Optical Potential, M. Dahan et al.
Phys. Rev. Lett. 76, 4508 (1996)
F tk
BT Oscillations de Bloch
F
k
Atomes dans un réseau optique
k
Periodicity of lattice leads to band structure of energy spectrum of the particle
Band structure for a particle in the periodic potential
and mean velocity : a) Free particle , b)
U(z) U0 sin2( z /d)
v0 q
( U0 0 )
U0 E0 2 2 /2md2
(a) (b)
Mean atomic velocity v as a function of t a for values
of the potential depth : (a)U0 =1.4ER, (b)U0 = 2.3ER, (c)U0 = 4.4ER
k
k
v
Mean atomic velocity v as a function of t a for values
of the potential depth : (a)U0 =1.4ER, (b)U0 = 2.3ER, (c)U0 = 4.4ER
k
k
v