1 Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London

2 2 Quantum mechanics 1.particles behave like waves, and vice-versa 2.energies and momenta can be quantized, ie measurements yield particular results 3.all information about a particle is contained within a complex wavefunction, which determines the probabilities of experimental outcomes 4.deterministic evolution of the wavefunction is determined by a differential (e.g. Schrödinger) wave equation 5.80 years of experiments have found no inconsistency with quantum theory 6.explanation of the ‘quantum measurement problem’ – the collapse of the wavefunction upon measurement – remains an unsolved problem non-deterministic process Heisenberg’s uncertainty principle

3 3 Quantum measurement allowed energies energy 0 n = 1 n = 3 n =  n = 2 1.measured energy must be one of allowed values 2.…but until measurement, any energy possible 3.after measurement, subsequent measurements will give same value THE HYDROGEN ATOM QUANTUM MEASUREMENT

4 4 The experiment with the two holes x y fringe maxima when  fringe spacing smallest visible feature size   illumination wavelength  illumination momentum equivalent to change in illumination angle and hence by

5 5 Single slit diffraction x amplitude intensity

6 6 Uncertainty HEISENBERG’S UNCERTAINTY PRINCIPLE certain pairs of parameters may not simultaneously be exactly determined {position, momentum} {time, energy} {orientation, angular momentum} {intensity, phase} {x, y}, {x, z}, {y, z} components of angular momentum {position, wavelength} {time, frequency} {linear, circular} polarization conjugate parameters cannot be simultaneously definite

7 7 Uncertainty BEATING OF TWO DIFFERENT FREQUENCIES

8 8 Bandwidth theorem

9 9

10 Bandwidth theorem

11 Terminology UNCERTAINTY IN MEASUREMENT repeated experiment yields range of results expectation value = mean uncertainty = standard deviation before measurement, system was in a superposition probability of given result given by

12 Uncertainty conjugate parameters cannot be simultaneously definite QUANTUM MEASUREMENT measurement changes observed system so that parameter measured is subsequently 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 HEISENBERG’S UNCERTAINTY PRINCIPLE certain pairs of parameters may not simultaneously be exactly determined {position, momentum} {time, energy} {orientation, angular momentum} {intensity, phase} {x, y}, {x, z}, {y, z} components of angular momentum {position, wavelength} {time, frequency} {linear, circular} polarization

13 The LASER by Stimulated Emission of Radiation LIGHT AMPLIFICATION Theodore Maiman, 16 May 1960 beam splitter flash tube mirror ruby nm light amplifier optical resonator

14 Absorption and emission of photons ABSORPTION energy 0 n = 1 n = 3 n =  n = 2 absorptionemission EMISSION SPONTANEOUS ABSORPTION EMISSION STIMULATED

15 Absorption and emission of photons ABSORPTION EMISSION SPONTANEOUS ABSORPTION EMISSION STIMULATED EINSTEIN EQUATIONS spontaneous emission stimulated by vacuum field amplification of light if atomic population is inverted i.e. thermal equilibrium  blackbody spectrum Einstein A and B coefficients

16 The ruby LASER beam splitter flash tube mirror ruby nm light amplifier optical resonator energy absorptionemission Cr 3+ Cr 3+ ions in sapphire (Al 2 O 3 ) absorb blue and green from flash light internal transitions to metastable state metastable spontaneous emission is amplified by passage through ruby repeatedly reflected/amplified near-axial light builds up to form coherent laser beam

17 Laser beam characteristics beam splitter flash tube mirror ruby nm as initial source recedes down unfolded cavity, emission approaches that from distant point source long pulse  continuous wave (c.w.) narrow linewidth for long pulses ( ) noise from spontaneous emission gives lower limit to linewidth nonlinear processes have various effects in detail divergence determined by diffraction by limiting aperture Hecht section 13.1 focusable monochromatic constructive interference between reflections for certain wavelengths

18 The ruby LASER beam splitter flash tube mirror ruby nm light amplifier optical resonator ray optics colour diffraction interference quantum physics refraction, polarization, …