L5 - rate eqns

Question 1

whata approx when soft collisions dominate

Answer 1

adiabatic or wuasi static approx

Question 2

For large beta what happenes

Answer 2

Any oscillations of the atomic probabilitya re well damped

Question 3

population rate eqns

Answer 3

drho11/dt and same for 22

Question 4

R12 meaning

Answer 4

R12 = R21
avsorption and stimulated emission rate

Question 5

info on R12 params and shape

Answer 5

Lorentzian profile proportinal to |E0|^2 so proportioanl to I of light
If Detuning less the R21 More

Question 6

R12 definition

Answer 6

Sigma Phi
Sigma depend on v ( freq of incident excitation light)

Question 7

Sigma

Answer 7

Absorption cross section
Sig dep on detuning

Question 8

Phi

Answer 8

Photon flux
Associatied with the light field E0
units: Photons per (area time)
Proportional to light intensity (I is macroscopic measuremnet)

Question 9

Energy of a photon

Answer 9

E = h v(n)

Question 10

Density of atoms in a state

Answer 10

N1 = N rho11
N2 = N rho22
these are the density of atoms ina given level

Question 11

Gamma meaning

Answer 11

Inelastic collision energy transition probability

Question 12

Compare inelastic collisions vs spontatnoues emission

Answer 12

Gamma_12, Gamma_21 &laquo_space;A21
inelatic have little influence comapred to spont emission
so N1 + N2 = NT tends to remain constnat

Question 13

Steady state we cna assume

Answer 13

Constant photon flux Phi

Question 14

N2 population
case: NO flux

Answer 14

Phi = 0
N2 = N2(0) exp(-A21 t)
All atoms end up in GS
spont emission dominates ( inelastic collision Gamma not really large enough)
No stimulated processes (due to sigma Phi) i.e. R12,R21

Question 15

N2 population:
Case: Low flux
Weak excitiation

Answer 15

R21 = sigma Phi != 0 but R21 &laquo_space;A21
So more e- lost from N2 due to spont emission than is brought up by the stimulated absorption

if N2(0) then
N2(t) = constant [1 - exp(-A21t)]
same decaying exp reaches max 1 (t = 0)= > N2 = 0 initially
when t large exp -> and N2 is at a max => SATURATION

Question 16

N2 population:
Case: Low flux behavrious in graph

Answer 16

Initally asymptotic approach (concave down)

Question 17

N2 population:
Case: High flux
Strong excitiation

Answer 17

R21 = sigma Phi&raquo_space;A21
stimulated rate&raquo_space; spont emission rate
N2 (t) -> N/2 —– SATURATION

Question 18

Why high flux not good enough

Answer 18

N - > N/2 saturation
Require population inversion for gain not population equalisation

Question 19

N2 population:
Case: High flux - Power broadening
Strong excitiation

Answer 19

Assume statead state and exp factor&raquo_space;1
N2(t=infty)/N = lorentzian profile
profile widens with larger X ( larger E0)

So N2(infty)/N becomes broader and taller as E0 flux increases