Modern Optics

Question 1

Clock Uncertainty

Answer 1

delta T / T

delta w / w

Question 2

Definition of a second

Answer 2

9,192,631,770 periods of the radiation of the ground state hyperfine transition in Cs

Question 3

Broadening Mechanisms

Answer 3

Collisional
Doppler
Natural - spontaneous (collisions increase spontaneous rate)
Transit time

Question 4

Principle of atomic clock

Answer 4

Atom provides reference freq. +vs Unperturbed atomic transition identical in all atoms of same element, atoms do not wear out.

Question 5

Steps of atomic clock

Answer 5

Atom provides frequency
Oscillator produces EM wave with freq. w
Detector counts atoms in excited state
Servo adjusts w until detector signal maximised
Count no. of oscillations in time you wnt to measure
Seconds = N oscillations/ 9billion ..

Question 6

Minimise broadening mechanisms

Answer 6

Min possible delta w
Maximum time to syncronise EM source with resonance - TT
Conduct under ultra high vaccuum conditions - collisional
Spont. emiss, TT - understand atom/EM field interactions

Question 7

Electrip dipole interaction & moment, magnetic dipole interaction

Answer 7

H’ = -d.E
d = -er
= = -e

H’ = - mu . B

Question 8

Transition

Answer 8

During transition, the atom is in a superposition of the ground and excited states.
is absorption or emission of a photon

Question 9

Spontaneous emission

Answer 9

Atom in excited state may spontaneously decay to lower E level - releases photon in random direction with random phase. Induced by vacuum fluctuations.
Rate of decay by spont emission ~ einstein A coeff.

Question 10

A & Linewidth

Answer 10

A21 = w21^ 3 d^2 g1
3pi hbar epsilon0 c^3 g2

A21 = 1/tau = Gamma - linewidth (total decay rate)
delta w = Gamma (FWHM) - natural linewidth as a result of natural broadening

Can have smaller w or smaller d for smaller A - want to reduce A

Question 11

Is 2p

Answer 11

No - order 10^-8 - best clocks are 10^-19

Question 12

Hyperfine & Fine Structure splitting

Answer 12

Hyperfine - F, fine structure J
J = L + S
F = I + J

Question 13

How do we reduce A

Answer 13

Use magnetic dipole transitions - A different and smaller

Question 14

Fine structure selection rules

Answer 14

delta l = +-1 delta L = 0, +-1
delta J = 0, +-1
delta S = 0
delta mJ = 0, +-1

Question 15

Why do energy levels split? MM

Answer 15

Spin - electron and proton have spin and therefore magnetic moments - can be spin up or down. GS thus has degeneracy 4 and this is lifted by the hyperfine interaction. Nuclear spin interacts with B-field produced by electronic spin and orbital motion.

Question 16

Should HF interaction in an atom not average to 0?

Answer 16

Hyperfine splitting occurs because electron penetrates nucleus

Question 17

HFS Hamiltonian

Answer 17

Hhfs = - mu.Be = A I.J

Question 18

Doppler effect

Answer 18

If an atom absorbs a photon from the direction in which it is travelling it will be decelerated but one must consider Doppler effect. Atom moving relative to photon of freq w will observe:
w’ = w +- kv

+ when moving towards.
To slow atom travelling towards laser beam, laser must be tuned to some lower freq.

Question 19

Optical molasses set up

Answer 19

Three pairs of counter-propagating red-detuned laser beams on each orthogonal axis.

Question 20

Stationary atom OM

Answer 20

Stationary atom will experience no force - scattering is same for each laser beam

Question 21

Moving atom OM

Answer 21

Atom moving with +ve v\ will scatter more photons from beam propagating in direction opposite to atom’s motion because atom is Doppler shifted into resonance with that beam.
Each atom moving in random directions will feel a force pushing it towards the centre of the beams - temperature is lowered.

Question 22

Cooling rate

Answer 22

Rate of change of KE
- alpha 2Ekin/M
=-Ekin/tau damp

Question 23

Caesium Fountain Clock

Answer 23

Atoms trapped in MOT launched up using moving molasses technique
In referenace fram moving upwards all beams appear to atoms to have same freq.
Each atom passes through microwave cavity twice - up and down.
Measured by Ramsay interferometry.

Question 24

Prob of being in upper state in FC

Answer 24

sinc^2 func with width delta w = 2pi/t

Question 25

TDPT

Answer 25

Wrong - assumes very small pertubation - unsatisfactory as gets transition probability wrong

Question 26

Cesium fountain clock summary

Answer 26

For factor of 10 improvement need fountain 100 times higher, two orders of magnitude better than atomic clock beam. Future - clock in zero g.

Question 27

Clock Frequency Instability

Answer 27

signma = (1/Q)(1/(S/N))root(1/tau avg)
Q = w/delta w

Question 28

Optical frequency standards

Answer 28

Ultra-stable local oscillator
Frequency counter
Stable atomic reference to feed back to local oscillator.