Waves, Light

1
Waves, Light Quanta
Tim Freegarde
Web Gallery of Art National Gallery, London
2
Quantum mechanics

1. particles behave like waves, and vice-versa

1. energies and momenta can be quantized, ie
   measurements yield particular results

1. all information about a particle is contained
   within a complex wavefunction, which determines
   the probabilities of experimental outcomes

1. deterministic evolution of the wavefunction is
   determined by a differential (e.g. Schrödinger)
   wave equation

1. 80 years of experiments have found no
   inconsistency with quantum theory

1. explanation of the quantum measurement problem
   the collapse of the wavefunction upon
   measurement remains an unsolved problem

• non-deterministic process

• Heisenbergs uncertainty principle

2
3
Quantum measurement
THE HYDROGEN ATOM
n ?
QUANTUM MEASUREMENT

1. measured energy must be one of allowed values

1. but until measurement, any energy possible

1. after measurement, subsequent measurements will
   give same value

3
4
The experiment with the two holes

• smallest visible feature size ??

4
5
Single slit diffraction
amplitude
x
intensity
5
6
Uncertainty
HEISENBERGS UNCERTAINTY PRINCIPLE

• certain pairs of parameters may not
  simultaneously be exactly determined

• position, momentum

• position, wavelength

• time, energy

• time, frequency

• orientation, angular momentum

• linear, circular polarization

• intensity, phase

• x, y, x, z, y, z components of angular
  momentum

• conjugate parameters cannot be simultaneously
  definite

6
7
Uncertainty
BEATING OF TWO DIFFERENT FREQUENCIES
7
8
Bandwidth theorem
8
9
Bandwidth theorem
9
10
Bandwidth theorem
10
11
Terminology
UNCERTAINTY IN MEASUREMENT

• repeated experiment yields range of results

• before measurement, system was in a superposition

11
12
Uncertainty
QUANTUM MEASUREMENT

• measurement changes observed system so that
  parameter measured is subsequently definite

• conjugate parameters cannot be simultaneously
  definite

• process measure A, measure B not the same as
  measure B, measure A

• measure A, measure B are not commutative / do not
  commute

• commutator measure A, measure B ? 0

12
13
The LASER
LIGHT AMPLIFICATION
by Stimulated Emission of Radiation

• Theodore Maiman, 16 May 1960

beam splitter
mirror
693.4 nm
flash tube
ruby
light amplifier
optical resonator
13
14
Absorption and emission of photons
ABSORPTION
n ?
ABSORPTION
absorption
emission
14
15
Absorption and emission of photons
ABSORPTION
EINSTEIN EQUATIONS

• Einstein A and B coefficients

ABSORPTION

• spontaneous emission stimulated by vacuum field

15
16
The ruby LASER
beam splitter
mirror
693.4 nm
flash tube
ruby
metastable
light amplifier
optical resonator

• Cr3 ions in sapphire (Al2O3) absorb blue and
  green from flash light

absorption
emission

• internal transitions to metastable state

Cr3

• spontaneous emission is amplified by passage
  through ruby

• repeatedly reflected/amplified near-axial light
  builds up to form coherent laser beam

16
17
Laser beam characteristics
693.4 nm

• as initial source recedes down unfolded cavity,
  emission approaches that from distant point source

• divergence determined by diffraction by limiting
  aperture

• focusable

• constructive interference between reflections for
  certain wavelengths

• long pulse ? continuous wave (c.w.)

• monochromatic

• noise from spontaneous emission gives lower limit
  to linewidth

• nonlinear processes have various effects in detail

• Hecht section 13.1

17
18
The ruby LASER
beam splitter
mirror
693.4 nm
flash tube
ruby
light amplifier

• ray optics

• colour

optical resonator

• diffraction

• interference

• quantum physics

• refraction, polarization,

18