'Squeezed' Motion in a Massive Object

Everyone expects objects at the atomic scale to follow the weird rules of quantum mechanics. But in the past few years, scientists at NIST and elsewhere have shown that comparatively large mechanical objects can be coaxed into exhibiting a surprising variety of quantum properties.

Earlier this year, NIST researchers reported that they could accurately measure the "zero-point" motion of a tiny metal membrane cooled near absolute zero, the point at which an object would have no motion at all were it not for Heisenberg's uncertainty principle.* Now the same team has demonstrated that the state of such a membrane's motion can be "squeezed" – another uniquely quantum, non-classical, phenomenon – and that the squeezing can be independently and continuously measured.**

"A big part of our research is trying to engineer these mechanical systems and show that you can get truly quantum properties out of them," says John Teufel of NIST's Physical Measurement Laboratory, who directed the experiment. "This is important for developing new technology that could be useful in quantum networks and quantum information-processing. But it's also important for pushing the limits of the physics to see how big a system you can make behave quantum mechanically, find out what are the fundamental limits, and then see if we can bend or break those rules and go beyond the quantum limit."

The uncertainty principle dictates that for any quantum entity, the simultaneous values of two complementary variables (such as position and momentum) cannot be known with complete accuracy. There will always be a degree of uncertainty, typically manifested as measurement noise. Squeezing shifts all of uncertainty to a single variable, such that the other variable can now be measured with arbitrary accuracy.

"You can get more precise information about one variable if you're willing to throw away some information about the other," says Florent Lecocq, first author on the team's new paper in Physical Review X. "If you're very careful to acquire information about only one variable," he says, "then there is no limit to the accuracy of your measurement"

Squeezed light (in which either one of two complementary wave properties – amplitude or phase – is squeezed) has been used for decades in precision measurements such as spectroscopy and interferometry. Likewise, squeezed motion could open the door for improved force and displacement sensing.

"But up until a few months ago, no one had ever made a squeezed state in an engineered mechanical system," Teufel says. That system (see illustration above) couples two separate microwave circuits to a capacitor with an upper plate made of an aluminum membrane flexible enough to vibrate like a drum head. The microwaves drive the drum-head and determine its vibration state; the drum-head motion, in turn, affects the microwave activity in the circuits. In this case, one circuit serves to control the drum-head motion, and the other measures the response. The goal is to prepare and measure one of the two complementary variables of the drum-head motion – equivalent to its amplitude and phase – near absolute zero.

First, the device is cooled to about 30 millikelvin. Then one of the microwave circuits is driven at two different frequencies, applying forces either in phase or out of phase with the motion. "One drive acts like a viscous medium," Teufel says. "It makes the mechanical membrane feel like it's moving through molasses, stealing energy, damping and cooling the motion to its ground state.*** The other drive tends to amplify the motion instead of damp it. If you tune their strength and frequency just right, you can get something that looks like cooling to the ground state, but has an extra level of interference that makes it cool to a squeezed state instead."

Preparing the squeezed state, however, is only half of the problem. One must also measure without destroying the delicate quantum state of the system. Avoiding that kind of "back-action" results in what is called a "quantum non-demolition measurement."

The team implements this special kind of measurement by illuminating the system only at time intervals that correspond to the period of the mechanical motion (much like adjusting a strobe light until it shows a swinging metronome arm at exactly the same place every flash).

"The squeezed state is a brutally honest indication of whether your measurement is perfect," Teufel says, "and the measurement is a brutally honest indication of whether your state preparation is perfect. In mechanical systems, it's the first time anyone has ever used that technique to measure a non-classical state. For us, it's equally important that we developed a state of the art measurement, and a state of the art squeezing preparation, and then also showed that they're compatible with each other."

Independently measuring a squeezed state, however, is by no means the end of this line of research. The team hopes eventually to engineer the mechanical equivalent of a quantum superposition state, in which an object has properties with two or more values at the same time until it is measured, at which point it takes on a specific value.

"One of the things we're really after is a Schrodinger cat state,"**** Teufel says, "in which we put the drum in two places at once, up and down as the same time, and then verify it. Squeezed states are the first stepping stone toward that."

* The uncertainty principle states that there is an absolute limit to the precision with which two complementary variables of a quantum object or system can be known at the same time. The most familiar variable pair is position and momentum. But the principle also applies to the phase and amplitude of light and other wave phenomena. Each complementary property is termed a "quadrature."

**  "Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object," F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel Phys. Rev. X5, 041037 – Published 7 December 2015.

*** The "ground state" is the lowest-energy condition an object or system can reach. In some contexts, it is referred to as the "zero point."

**** Physicist Erwin Schrödinger illustrated the paradoxical nature of quantum superposition by imagining that a cat was inside a box containing a poison that was either released or not depending on a quantum event that was in a superposition of two values and would not take on specific value until observed. Thus, until the box was opened, the cat would be in a superposition of dead and alive.