Quantum Optics Fundamentals

Light exhibits both wave-like and particle-like properties depending on how it is measured. In Young's double-slit experiment, a single photon passes through both slits simultaneously (wave behavior) and creates an interference pattern. Yet when detected, it always arrives at a single, discrete location (particle behavior).

This duality is not a limitation of measurement — it is a fundamental property of nature. The de Broglie relation λ = h/p connects wavelength and momentum for all quantum particles, including photons where p = ℏk.

The electromagnetic field is quantized into discrete excitations called photons. The quantum state of a light field is described by Fock states |n⟩ — eigenstates of the photon number operator n̂ = â†â — where n is the exact number of photons present.

Fock states are the "pure" photon number states. Coherent states (laser light) are superpositions with indefinite photon number following a Poisson distribution.

Two photons are entangled when their quantum states cannot be described independently — measuring one instantly defines the state of the other, regardless of the distance between them. This is the EPR paradox, proven real by Bell inequality violations.

Entanglement powers quantum teleportation, dense coding, E91 cryptography, and distributed quantum computing. SPDC in nonlinear crystals is the standard method for generating entangled photon pairs.

A quantum system can exist in a superposition of multiple states simultaneously: |ψ⟩ = α|0⟩ + β|1⟩, where |α|² + |β|² = 1. Only upon measurement does it collapse to one definite state.

The Mach-Zehnder interferometer splits a photon into superposition along two paths, then recombines them — interference determines which detector clicks with certainty. This is the engine of quantum speedup.

The Heisenberg uncertainty principle states: ΔxΔp ≥ ℏ/2 — the product of uncertainties in position and momentum can never be zero. For photons, this manifests as the complementarity between photon number and phase: ΔnΔφ ≥ ½.

Squeezed states exploit this by reducing uncertainty in one variable below the standard quantum limit at the expense of increased uncertainty in the conjugate variable — enabling sub-shot-noise sensing in LIGO.

Quantum superpositions are fragile — interaction with the environment causes decoherence, collapsing the quantum state into a classical mixture. Maintaining quantum coherence is the central engineering challenge of quantum technology.

The surface code is the leading approach, requiring ~1,000 physical qubits per logical qubit at current error rates. Photonic systems are naturally resilient because photons rarely interact with room-temperature environments.

Lasers produce coherent light — photons in the same quantum state with identical frequency, phase, and direction. Coherent states |α⟩ are eigenstates of the annihilation operator: â|α⟩ = α|α⟩, with a Poisson photon number distribution.

Modern quantum optics experiments require single-photon emitters and photon-number-resolving detectors that go far beyond laser physics — probing the deepest nonclassical states of light.

QKD uses quantum mechanics to distribute encryption keys with information-theoretic security — any eavesdropping attempt disturbs the quantum states, revealing the interceptor. The most widely implemented protocol is BB84.

Modern CV-QKD uses coherent states and homodyne detection instead of single photons, making it compatible with standard telecom infrastructure at speeds exceeding 1 Gbit/s.