Introduction to quantum optics

Light as wave and quantum

Classical optics treats light as an electromagnetic wave. This explains interference, diffraction, polarization, and many imaging effects. But some phenomena require light to be quantized. Quantum optics studies light as photons and examines how quantum states of light interact with matter.

A photon has energy

$E=hf=hbaromega$

and momentum

p=rac{h}{lambda}

These equations connect wave properties to particle-like energy and momentum.

Photoelectric clue

The photoelectric effect showed that light transfers energy in discrete packets. Electrons are emitted from a material only if light frequency exceeds a threshold, regardless of intensity. Increasing intensity increases the number of emitted electrons, but frequency controls their maximum kinetic energy.

Einstein explained this using photons. The basic energy relation is

$K_{max}=hf-phi$

where $phi$ is the work function.

Single-photon interference

In a double-slit experiment with extremely weak light, photons can be sent one at a time. Each photon is detected as a localized event, but after many detections an interference pattern appears.

This suggests that quantum probability amplitudes pass through the alternatives and interfere. It is not simply that photons are tiny classical balls going through one slit with ordinary waves guiding them.

Measurement and which-path information

If an experiment determines which slit a photon passes through, the interference pattern disappears. Interference requires indistinguishable alternatives. This is a central idea in quantum mechanics.

The issue is not merely mechanical disturbance. The availability of which-path information changes the quantum description.

Photon statistics

Classical light intensity can vary continuously, but quantum optics studies photon counting statistics. Coherent laser light has photon number fluctuations described approximately by Poisson statistics. Thermal light has different statistics and stronger bunching.

Photon correlation measurements can reveal whether light is classical-like or nonclassical.

Spontaneous and stimulated emission

Quantum optics also explains emission. In spontaneous emission, an excited atom emits a photon into an available mode. In stimulated emission, an incoming photon enhances emission into the same mode. Lasers rely on stimulated emission, but a quantum treatment explains noise, linewidth, and photon statistics more deeply.

Entanglement

Photons can be produced in entangled states, where measurements on one photon are correlated with measurements on another in ways that cannot be explained by classical hidden properties. Entangled photons are used in tests of quantum foundations, quantum communication, and quantum information.

Polarization is a common photon degree of freedom for entanglement experiments.

Quantum technologies

Quantum optics supports technologies such as single-photon detectors, quantum key distribution, optical quantum computing, squeezed light, precision interferometry, and gravitational wave detector enhancement.

Squeezed light redistributes quantum uncertainty between field variables, allowing improved measurement sensitivity in one quantity at the cost of increased uncertainty in another.

The big idea

Quantum optics extends optics to the photon level. Light has wave properties such as interference and polarization, but energy and detection occur in quanta. Single-photon interference, which-path information, photon statistics, and entanglement reveal that light is neither a classical wave nor a classical particle, but a quantum field excitation.