Physicists resolve 90-year-old puzzle of quantum damped harmonic oscillators

A plucked guitar string can vibrate for seconds earlier than falling silent. A playground swing, emptied of its passenger, will progressively come to relaxation. These are what physicists name “damped harmonic oscillators” and are effectively understood when it comes to Newton’s legal guidelines of movement.

But within the tiny world of atoms, issues are unusual—and function underneath the weird legal guidelines of quantum physics. University of Vermont professor Dennis Clougherty and his pupil Nam Dinh questioned if there are techniques within the atomic world that behave just like the vibrating movement of a guitar string within the Newtonian world. “If so, can we construct a quantum theory of the damped harmonic oscillator?” Clougherty questioned.

In a examine published July 7, 2025, within the journal Physical Review Research, he and Dinh did simply that: discovered a precise answer to a mannequin that behaves as a “damped quantum harmonic oscillator,” they write—a guitar-string kind of movement on the scale of atoms.

It seems that for roughly 90 years, theorists have tried to explain these damped harmonic techniques utilizing quantum physics—however with restricted success. “The difficulty involves preserving Heisenberg’s uncertainty principle, a foundational tenet of quantum physics,” says Clougherty, a professor of physics at UVM since 1992.

Unlike the human-scale world of, say, bouncing balls or arcing rockets, the famed Heisenberg uncertainty precept exhibits that there’s a elementary restrict to the precision with which the place and momentum of a particle could be identified concurrently. At the size of an atom, the extra precisely one property is measured, the much less precisely the opposite could be identified.

The mannequin studied by the UVM physicists was initially constructed by British physicist Horace Lamb in 1900, earlier than Werner Heisenberg was born, and effectively earlier than the event of quantum physics. Lamb was occupied with describing how a vibrating particle in a strong might lose vitality to the strong. Using Newton’s legal guidelines of movement, Lamb confirmed that elastic waves created by the particle’s movement feed again on the particle itself and trigger it to damp—that’s, to vibrate with much less and fewer vitality over time.

“In classical physics, it is known that when objects vibrate or oscillate, they lose energy due to friction, air resistance, and so on,” says Dinh. “But this is not so obvious in the quantum regime.”

Clougherty and Dinh (who graduated from UVM in 2024 with a BS in physics, in 2025 with a grasp’s diploma, and is now pursuing a Ph.D. in arithmetic at UVM) reformulated Lamb’s mannequin for the quantum world and located its answer.

“To preserve the uncertainty principle, it is necessary to include in detail the interaction of the atom with all the other atoms in the solid,” Clougherty explains. “It’s a so-called many-body problem.”

How did they resolve this downside? Hold onto your seat. “Through a multimode Bogoliubov transformation, which diagonalizes the Hamiltonian of the system and allows for the determination of its properties,” they write, yielding a state known as a “multimode squeezed vacuum.” If you missed a little bit of that, suffice it to say that the UVM researchers had been in a position to mathematically reformulate Lamb’s system in order that an atom’s oscillating conduct might be totally described in exact phrases.

And exactly finding the place of 1 atom might result in one thing just like the world’s tiniest tape measure: new strategies for measuring quantum distances and different ultra-precision sensor applied sciences. These potential functions emerge from an essential consequence of the UVM scientists’ new work: it predicts how the uncertainty within the place of the atom modifications with the interplay to the opposite atoms within the strong. “By reducing this uncertainty, one can measure position to an accuracy below the standard quantum limit,” Clougherty says.

In physics, there are some final limits, just like the pace of sunshine and that Heisenberg’s uncertainty precept prevents excellent measurement of a particle. But this uncertainty could be decreased past regular limits by sure quantum methods—on this case, calculating the particle’s conduct in a particular “squeezed vacuum” state which reduces the noise of quantum randomness in a single variable (location) by growing it in one other (momentum).

This sort of mathematical maneuver was behind the creation of the primary profitable gravitational wave detectors, which may measure modifications in distance one thousand instances smaller than the nucleus of an atom—and for which the Nobel Prize was awarded in 2017. Who is aware of what the Vermont theorists’ discovery of a brand new quantum answer to Lamb’s century-old mannequin may reveal.