Ninety years after theorists first wrestled with how a fading vibration might be written in the language of quantum mechanics, two physicists at the University of Vermont have produced an exact answer. The question was an old one: the ordinary world shows us a plucked string whose motion dies away through friction, yet nobody had cleanly shown how such damping could coexist with Heisenberg's principle, which forbids us from knowing a particle's position and momentum perfectly at once. Their solution returns to a model Horace Lamb sketched in 1900, long before the quantum revolution, and shows
UVM Physicists Crack 90-Year-Old Puzzle by Building a Quantum Damped Harmonic Oscillator
A guitar-string type of motion at the scale of atoms
Mark
Why does a 1900 model matter to quantum physics now?
Mimi
Lamb described a vibrating particle in a solid losing energy to the solid through elastic waves. Clougherty and Dinh asked whether that picture could be rebuilt quantum mechanically, which theorists had tried for about 90 years.
Mark
What made it so hard?
Mimi
Keeping Heisenberg's uncertainty principle intact. Clougherty says that requires including the atom's interaction with all the other atoms in the solid, a many-body problem.
Luke
And the solution is exact, correct? Not an approximation?
Mimi
The paper describes it as an exact solution to the model, using a multimode Bogoliubov transformation.
Luke
Fine, but it's a solution to Lamb's model, not to a measured real material. That's worth keeping straight.
Mark
What's the payoff they point to?
Mimi
The model predicts how an atom's position uncertainty changes with its interactions, so position might be measured below the standard quantum limit, using a squeezed vacuum state.
Luke
That's a prediction and a possibility. The source describes a tiny tape measure as potential, and no device or experiment is reported.
Mark
And the gravitational wave comparison?
Mimi
It shows the same kind of squeezing trick has already worked in practice, in detectors recognized with the 2017 Nobel Prize.
Luke
It's an analogy for the technique, not evidence this work will get there.
O Pulso
- For nearly a century, a stubborn mismatch between classical energy loss and quantum uncertainty left a central problem of physics unresolved.
- The Vermont team had to hold Heisenberg's principle intact while letting an atom bleed energy into the solid around it, a tension that refused easy compromise.
- By treating every atom in the solid as part of one many-body system, they used a multimode Bogoliubov transformation to tame the equations into an exact solution.
- The resulting squeezed vacuum state points toward measurements of position below the standard quantum limit, opening a path toward ultra-precision sensors that is still largely theoretical.
Ninety years after theorists first wrestled with how a fading vibration might be written in the language of quantum mechanics, two physicists at the University of Vermont have produced an exact answer. The question was an old one: the ordinary world shows us a plucked string whose motion dies away through friction, yet nobody had cleanly shown how such damping could coexist with Heisenberg's principle, which forbids us from knowing a particle's position and momentum perfectly at once. Their solution returns to a model Horace Lamb sketched in 1900, long before the quantum revolution, and shows that the atom's energy loss can only be understood by accounting for the whole crowded society of atoms around it. What it promises is a finer way of locating the smallest things, though whether that promise becomes instruments remains for the future to decide.
In a study published July 7, 2025, in Physical Review Research, two physicists at the University of Vermont reported an exact solution to a problem that had resisted theorists for roughly ninety years: how to describe a damped harmonic oscillator in quantum terms. Everyday experience offers the image of a plucked guitar string fading as friction drains its energy. The authors asked whether something similar happens among atoms, and if so, whether a quantum theory could capture it.
Dennis Clougherty, a UVM physics professor since 1992, led the work with his student Nam Dinh, who has moved from a 2024 bachelor's degree to a 2025 master's and now a PhD in mathematics. The research was supported by the National Science Foundation and NASA. The central difficulty was keeping Heisenberg's uncertainty principle intact while describing energy loss. Clougherty explained that earlier attempts had struggled exactly here.
Their starting point was a model Horace Lamb built in 1900, before Heisenberg was born. Lamb showed, using Newton's laws, that a vibrating particle inside a solid sends elastic waves back onto itself, damping its motion. Dinh observes that this is intuitive in classical physics but far less obvious in the quantum regime. The reformulation required including the atom's interaction with every other atom in the solid, turning the problem into a many-body one. Using a multimode Bogoliubov transformation, the authors arrived at a multimode squeezed vacuum state that describes the oscillation precisely.
The payoff lies in measurement. The model predicts how position uncertainty shifts as atoms interact, and Clougherty suggests that reducing it could allow position to be measured beyond the standard quantum limit, a kind of tiny tape measure for quantum distances. The same mathematical family underlies the gravitational wave detectors that won the 2017 Nobel Prize. Whether the Vermont result will yield comparable devices is unknown; for now, the achievement is the exact solution and its clear prediction.
In a study published July 7, 2025, in Physical Review Research, two physicists at the University of Vermont reported an exact solution to a problem that theorists had worked on, with limited success, for roughly 90 years: how to describe a damped harmonic oscillator in quantum terms. In the everyday world, the image is a plucked guitar string whose vibration fades as friction and air resistance drain its energy. The authors wanted to know whether something like that exists among atoms.
The researchers are Dennis Clougherty, a UVM physics professor since 1992, and his student Nam Dinh. Dinh graduated from UVM in 2024 with a bachelor's degree in physics, earned a master's in 2025, and is now pursuing a PhD in mathematics there. Their work was supported by the National Science Foundation and NASA. Clougherty put the guiding question this way: if such systems exist, can a quantum theory of the damped harmonic oscillator be constructed?
The obstacle was Heisenberg's uncertainty principle. It sets a fundamental limit on how precisely a particle's position and momentum can be known at once; at the scale of an atom, measuring one more accurately means knowing the other less accurately. Clougherty says the difficulty in earlier attempts lay in preserving that principle while describing energy loss.
The model they used predates quantum physics. British physicist Horace Lamb built it in 1900, before Werner Heisenberg was born. Lamb wanted to describe how a vibrating particle inside a solid loses energy to the solid. Using Newton's laws, he showed that elastic waves produced by the particle's motion feed back on the particle and damp it, so that it vibrates with less and less energy over time. Dinh notes that while energy loss from friction is familiar in classical physics, it is not so obvious in the quantum regime.
Clougherty and Dinh reformulated Lamb's model for the quantum world and solved it. Clougherty explains that to keep the uncertainty principle intact, the atom's interaction with all the other atoms in the solid has to be included in detail, which makes it a many-body problem. The authors write that they did this through a multimode Bogoliubov transformation, which diagonalizes the system's Hamiltonian and lets its properties be determined. The result is a state called a multimode squeezed vacuum. In plain terms, they reformulated Lamb's system mathematically so that an atom's oscillation could be described precisely.
The practical interest is in measurement. The model predicts how the uncertainty in an atom's position changes with its interactions with the other atoms in the solid. Clougherty says that by reducing this uncertainty, position can be measured with an accuracy below the standard quantum limit. The squeezed vacuum does this by lowering quantum noise in one variable, position, while raising it in another, momentum. The source describes possible applications as a kind of tiny tape measure for quantum distances, along with other ultra-precision sensors.
The same sort of mathematical maneuver underlies the first successful gravitational wave detectors, which can detect changes in distance a thousand times smaller than an atomic nucleus and which earned a Nobel Prize in 2017. Whether the Vermont solution leads to comparable devices is not yet known; for now, what exists is the exact solution and its prediction for how position uncertainty behaves.
Citações Notáveis
By reducing this uncertainty, one can measure position to an accuracy below the standard quantum limit.— Dennis Clougherty, UVM physics professor
To preserve the uncertainty principle, the atom's interaction with all the other atoms in the solid must be included in detail, making it a many-body problem.— Dennis Clougherty (paraphrased)
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