L3 - 2 level atom

Question 1

delta E =

Answer 1

hbar omega

Question 2

Why can we assume E field constant in an atom
(the EM wave - incident excitation light)

Answer 2

Lambda&raquo_space; |r|
lambda = 400-700nm visible
r = dist between nucleas and e-
Dipole approximation

Question 3

In SE for 2 level atom why is V11 = V22 = 0

Answer 3

Parity considerations
V_ab proportional to r_ab and r_aa = 0 since even bounds odd function integral1

Question 4

What is r12 or r21

Answer 4

The transition dipole moment
- electric dipole moment assosiatied with transition betwen lvl 1 and 2

Matrix element of vec{r}
complex vector quantity since Phi could be complex

Question 5

X - Chi

Answer 5

The Rabi frequency
Mediates interation between light and matter
X proportional to E field strength and transition dipole moement direction alighnment with e fireld

Question 6

2 level atom:
X = 0 case

Answer 6

X =0 => E_0 = 0
no light
a1(t) = a1(0)
a2(t) = a2(0) exp decay factor

Question 7

2 level atom:
w = w21 case

Answer 7

in RWA approx:
Oscillations at generalised rabi freq

Question 8

RWA approx

Answer 8

Rotating wave approx
2w is very fast compared to other time chages so overlonger time oscillating terms with 2w are ignored = 0

Question 9

detuning

Answer 9

Capital delta
w21-w
At resonance when detuning = 0 –> w21 =w
Units (inverse time)

Question 10

When can the rabi freq be taken as real

Answer 10

Constant E0 vector ( Efield polarisation)
appropriate phases for orbital wave functions

Question 11

Generalised rabi freq

Answer 11

Omega = sqrt(X^2 + Delta^2)
if on resonance then D = 0 and Omega = X

Question 12

Prob (ground state)

Answer 12

a1a1* = c1c1*

Question 13

2 lvl atom with w approx = w21 what happens to P2(t)

Answer 13

Upper state prob
larger detuning => higher freq Rabi oscillations with Lower amplitude
Found state never gets fully depleted, P2(t) != 1 ever