← Wave-particle duality and quantum states

Superposition connects to duality

Jocasta dims the laser in a two-slit experiment until photons leave one at a time. Each photon lands on the screen as a single dot. Surely the fringe pattern must vanish now. Overnight, dot by dot, the fringes appear anyway.

Interference fringes were filed as wave-only evidence, and a quantum object can be in a superposition of states. This lesson joins the two: the wave side of wave-particle duality is superposition at work.

Photons pass the slits one at a time. At any moment there is at most one photon between the source and the screen, so no second photon is there to overlap with.

Each photon lands as one dot. Where any single photon lands is random: nobody can predict any single dot's place.

photons leave one at a time
One photon at a time heads for the two slits. The combination of the two paths sets where dots tend to land.
Early in the run: a few scattered dots. Each dot is one detection.

As the dots accumulate, they are not spread evenly. Dots crowd the places where bright fringes belong and avoid the places where dark fringes belong. The full fringe pattern builds up dot by dot.

More detections: the crowding begins where bright fringes belong.
After many detections: the fringe pattern, built dot by dot.

Why do single photons build a two-path pattern? Because each photon is in a superposition of both slit paths, and the combination of the two paths sets where dots tend to land.

That is the bridge: interference appears when a quantum object's superposition of paths combines. The wave side of wave-particle duality is superposition at work.

The dots are the particle side: each detection is one whole photon at one place. The pattern across many dots is the wave side. One experiment shows both.

Matter runs the same experiment. Electrons sent one at a time through two slits also build up fringes, because each electron is in a superposition of both paths.

Describe what the screen shows early in a one-photon-at-a-time two-slit run, and after a long run.

Early, the screen shows a few scattered dots with no visible order: each dot is one photon's detection, and single landings are random.

As detections accumulate, dots crowd where bright fringes belong and avoid where dark fringes belong.

After a long run, the dots have built the full bright-and-dark fringe pattern.

Early: scattered dots. Late: the full fringe pattern, built one detection at a time.

Soraya covers one slit during a one-photon-at-a-time run. What happens to the pattern?

With one slit covered, each photon has only one path state on offer: there is no superposition of two paths.

With no two-path superposition, nothing combines, so no bright-and-dark fringe pattern builds.

The dots pile into one spread band behind the open slit instead.

The fringe pattern does not build: with one slit covered there is no superposition of both paths to combine.

In a two-slit run where photons pass one at a time, what does the screen show after many detections?

Electrons sent one at a time through two slits also build up a fringe pattern. Why can a lone electron still build a two-path pattern?

Soraya says: 'Each dot on the screen is one whole detection, and where any single photon lands cannot be predicted.' Is Soraya correct?

Your turn

Which statement joins wave-particle duality to superposition?

A one-photon-at-a-time two-slit run has only just started, with a few dozen detections so far. What does the screen show?

Kenji's apparatus sends neutrons one at a time through two slits, and a fringe pattern builds up on the detector. Which statement explains the pattern?