Quantum Superposition
One Photon, Two Ways
One Photon, Two Ways
A half mirror lets half the light through and turns the other half aside. Send it light one photon at a time, with a detector on each side, and each photon is found whole in one of them, by chance, half and half.
Now let two ordinary mirrors bring the two ways together again at a second half mirror, with a detector past it on each side. This is an interferometer. If each photon really took one way, the second half mirror would toss it again, and the two detectors would share the photons half and half. They do not. With the two ways the same length, every photon arrives at the same detector, and the other never clicks; a well-made real setup lets only a tiny share stray.
Block one of the ways, and the silent detector comes to life. Half the photons now stop in the block, and the rest are shared evenly between the two detectors. Opening a second way made a detector go dark, which no photon taking one way could do. The scene sends a dimmed laser’s photons one at a time, but a careful test needs more: a dimmed laser still sometimes sends two together. Physicists have made that test with a source that gives out single photons, each announced by a partner. They checked that the two detectors behind a half mirror almost never click together, far less often than they would if the light’s energy were split there, as an ordinary wave’s is. Then they saw the photons interfere as they lengthened one way little by little. Something of each photon goes both ways, and what comes along the two ways meets again at the second half mirror.
A Wave That Meets Itself
What goes both ways is the photon’s wave. Quantum physics gives each possible way a number called an amplitude: the height of that way’s wave, and where it is in its swing. Where two ways meet, their amplitudes add, crest to crest or crest to trough, as ripples do on water. A photon whose wave runs both ways is in a superposition of the two: one state that combines them.
The chance that a detector finds the photon is the square of the size of its wave’s swing there. This is called the Born rule. So a wave that carries half the chance is not half as high: its height squared is a half, so it is about seven tenths as high. At the second half mirror each way’s wave splits again, and two waves half as high as the whole reach each detector. At one they arrive crest to crest and add up to the whole wave: a certainty. At the other they arrive crest to trough and cancel: never.
Why should the two exits differ, when the two ways are the same length? In the kind of half mirror drawn here, a wave turned aside falls a quarter swing behind the wave that goes straight through. Other half mirrors share the lag differently, but none can do without it: otherwise both exits could brighten at once, and more light would leave than came in. On the way to the detector straight ahead, each half is turned aside once and goes straight once, so the two arrive in step. On the way to the other, one half is turned aside twice and the other not at all, so they arrive half a swing apart.
Lengthen one way by half a wavelength, about a quarter of a thousandth of a millimeter for green light, and the halves fall out of step. Now the first detector never clicks and the second gets every photon. Each way on its own still gives an even chance at each detector. Only the timing between the two waves has changed, what physicists call the phase. No single click shows the phase; the share of clicks over many photons does.
A Superposition of What?
Being in a superposition is not something a photon is on its own. It depends on the question asked. A polarizing filter asks each photon one question: does it swing along the filter’s line, or across it? A photon swinging along the line always passes, and one swinging across never does. One swinging at an angle passes by chance, half the time at 45 degrees. For this filter, that photon is in a superposition of along and across. For a filter turned to its own angle it is simply along, with nothing superposed about it.
Two crossed filters pass nothing. Slip a third filter between them, turned halfway, and light gets through the last one again. Every photon the middle filter lets through now swings at 45 degrees, whatever it did before. To the last filter that is an even superposition of along and across, so half of those pass: a quarter of the light that got through the first filter. Adding a filter lets light through. With bright light this is a wave’s swing split into parts. Sent one photon at a time, each photon passes a filter whole or not at all, and the same quarter arrive.
A detector, or a filter that absorbs what fails it, asks one question, with a set of possible answers. A half mirror only splits the wave; detectors behind it ask which way. A state is a superposition only with respect to such a set. Ask a different question, and the same state is a different superposition, or no superposition at all.
Not a Hidden Choice
The detector that never clicks rules out a photon that takes one way with nothing at all going the other way, nature only hiding which. A stubborn reader can hold out for something subtler. Perhaps a particle carries a ready answer to every question it could be asked, and only shows them in an odd way.
For a question with only two answers, ready answers can be faked. For anything with three or more possible answers, such as a photon that can take one of three ways, it has been proved that ready answers cannot work if each is fixed regardless of what else is asked. No such set of answers fits all the questions quantum physics allows. One early proof needed 117 directions in space. Experiments with light, trapped ions and neutrons have found nature behaving as quantum physics says. One way out remains. Some questions can be asked together without clashing, and the answer to one may depend on which others are asked with it. The pilot-wave theory takes that way. What cannot survive is a world in which every value sits ready in advance, whatever else you choose to ask.
A Record of Which Way
If anything keeps a full record of which way the photon took, the meeting is spoiled; a partial record spoils it in part. The block is the bluntest record. A gentler one turns the light on one of the ways to swing across instead of along, so that every photon from that way carries a mark. Two waves swinging at right angles cannot cancel crest against trough, so the two detectors share the photons half and half again, though no photon was stopped and no one looked. What matters is the record, not a watcher.
The same holds for the stripes that light builds dot by dot behind two slits: mark which slit each photon came through, and the stripes fade into a smooth, unstriped glow. Air molecules and stray light that bump into a thing keep records of it too, without anyone reading them. That is why superpositions are easy to keep with single photons and very hard to keep with anything large and warm.
How Big Can It Get?
Superposition is not only for light. Electrons, atoms and molecules interfere just as photons do, and physicists push the size up in two different ways. Molecules of 2,000 atoms have been sent through an interferometer and met themselves again. Now clusters of more than 7,000 sodium atoms have done it too, each about 8 nanometers across, its wave spread over a region far wider than itself. In another test, a vibration of sound in a sapphire crystal was put into a superposition of two opposite swings. It moves the mass of some 10¹⁷ atoms, 16 millionths of a gram, but its two swings differ by only a few billionths of a billionth of a meter, far less than the width of an atom’s nucleus.
Erwin Schrödinger imagined a cat shut in a box with an atom that might decay and set off a poison. If the rules held without limit, the cat would be in a superposition of alive and dead. The equations set no limit: if each of two histories is possible, so is their sum, so a superposition passes from the atom to the counter, the poison and the cat. He meant it as an objection, to show how strange it would be. Cats never show it because a large, warm thing is recorded by its surroundings all the time, which washes out the meeting of its two possibilities almost at once. Why one result is then seen, and not the other, is still argued over.
What It Makes Possible
A quantum computer’s bits, called qubits, are built on superposition. Each added qubit doubles the number of amplitudes the machine carries at once, because an amplitude goes to every combination of the qubits’ answers, not to each qubit alone: fifty qubits carry more than a quadrillion. But a measurement gives one answer, picked by chance, so the machine cannot simply try every answer and read off the right one.
Its steps must be arranged so that the waves for wrong answers meet crest to trough and cancel, while those for the right answer add, as they do at the second half mirror. Ways to do that are known for only some problems, such as factoring large numbers, which needs machines far larger than any built so far, or simulating molecules. This is why a quantum computer will not be faster at everything.
