^z 10th January 2024 at 8:23am

Look closely enough at anything and it starts to get fuzzy — not simply from imperfections in the eye, or resolution limitations due to the wave nature of light, but rather because of quantum mechanics. Objects are described by wavefunctions. It's impossible to measure both position and velocity with absolute precision. The more accurately you try to sense one, the greater the disturbance you induce in the other. The limit applies to any pair of "conjugate variables".

In ordinary circumstances the quantum limit is too tiny to matter. But if you want to detect something really subtle (like a gravitational wave from an exploding star halfway across the universe) then problems arise. Ordinary sensors, that couple to bodies in the usual way, won't work — they add noise that drowns out any signal.

You need quantum non-demolition (QND). The trick is simple: measure one variable while (carefully now!) making sure that you learn nothing about its conjugate. Do it right and you can detect arbitrarily small perturbations. Vladimir Braginsky and colleagues at Moscow State University recognized the QND challenge in the mid-1970s; Kip Thorne and colleagues at Caltech worked out the solution. (See Caves, Drever, Thorne, Zimmermann, and Sandberg, Rev. Mod. Phys., 1980, and associated papers.)

A simple example (my little contribution to this work, a minor and obvious insight) will make it clear: consider a (quantum!) child on a swing in a totally dark room. She promises that she will refrain from "pumping", dragging her feet, or otherwise disturbing her free oscillation. Your goal is to keep her honest. But the only way you have to observe her is to flash a bright light at her — a strobe that causes her to flinch unpredictably. So whenever you look at her position, you inevitably cause a huge and unknowable change in her velocity. How can you tell if she cheats between flashes? There is a way; if you want to come up with it for yourself, stop reading now...

The girl on the swing in the dark room is precisely the same as the quantum gravitational wave antenna. How can one couple a sensor to an antenna without demolishing its quantum state and inducing an intolerable level of noise? Answer: look once per cycle of the swing, and space the measurements exactly one cycle apart. The magic of the (ideal) swing is that its period is a constant, independent of the amplitude of its oscillation: perfect simple harmonic motion.

When you trigger the strobe you make a precise position measurement. That causes a big kick to the swing's velocity — but no matter what the unknown kick may have been, after one cycle the swing comes right back to where it was. That's when you take the next flash picture. If the swing is any place other than the previously-observed location, then (aha!) something must have happened during the time between flashes.

That's the QND stroboscopic technique, a straightforward way to beat the quantum limit. (You can actually measure twice per cycle, but you have to flip the sign of the position measurement on the odd observations; looking once every cycle is easier to explain.) Strobing makes use of the fact that momentum and position uncertainty slosh back and forth in a quantum harmonic oscillator — they trade places every quarter cycle. Extensions of the same principle let one couple to a quantum system more often (even continuously) though at the cost of greater complexity.

The key idea of QND remains: look carefully at one parameter of a system, and make sure not to learn anything about the conjugate parameter. Heisenberg's Uncertainty Principle still holds; QND skates around it and averts its eyes at the critical moment.

Saturday, February 05, 2000 at 12:42:29 (EST) = 2000-02-05

TopicScience - TopicPersonalHistory

(correlates: SeeingStars0, MandatoryInversion, DeptOfRedundancyDept, ...)