In physics, there are some ultimate limits, like the speed of light and Heisenberg’s uncertainty principle that prevents perfect measurement of a particle. But this uncertainty can be reduced by certain quantum tricks such as through calculating a particle’s behavior (say its position) in a special “squeezed state”. “By reducing this uncertainty, one can measure position to an accuracy below the standard quantum limit,” says Dennis Clougherty, a professor at the University of Vermont. In recent work published in Physical Review Research, Clougherty and his graduate student, Nam Dinh employed mathematical tricks to do just that, solving a 90-year puzzle in quantum physics and paving the way for important practical applications.

Here’s the problem. Imagine plucking a guitar string. It vibrates for seconds, then stops and falls silent. Similarly, a playground swing, emptied of its passenger, will gradually come to rest. These are what physicists call, “damped harmonic oscillations”. On normal everyday scales, such oscillation behaviors are understood by Newton’s laws of motion.

Not so at the atomic level where quantum physics rule. Heisenberg’s uncertainty principle shows that there is a fundamental limit to the precision we can predict the position and momentum of a particle simultaneously. The more accurately we measure a particle’s momentum, the less accurate are the measurements of its position. And precisely locating the position of one atom could lead to important application like super-tiny “quantum tapes” – new methods of measuring quantum distances and other ultra-precision sensor technologies.

For 90 years, physicists have tried but failed to reduce position uncertainty below the standard quantum limit. So how did Clougherty and Dinh solve this problem? The short answer: by employing some pretty clever (and deep) mathematical tricks which (hold your breath), involves “multimode Bogoliubov transformation (to) diagonalize the Hamiltonian of the system.” Never mind about the technicalities, the real genius of their approach lies in finding the right mathematical tool to picture an atom in a “squeezed state” where its oscillation properties could be fully described in precisely terms.

This is not the first time mathematics have been used to reduce nature’s fundamental limits. One notable recent example was the use of mathematical tricks to create the world’s first gravitational wave detectors that can measure changes in distance a thousand times smaller than the nucleus of an atom – and for which the Nobel Prize was awarded in 2017. Exciting times lie ahead for physics and engineering in the wake of Clougherty and Dihn’s breakthrough.