At a Glance
- University of Vermont researchers developed an exact quantum theory for a damped harmonic oscillator, a longstanding challenge in physics that describes how vibrating atoms lose their energy.
- They successfully reformulated a classical 1900 model from physicist Horace Lamb for the quantum world, solving it with a mathematical method called a Bogoliubov transformation.
- Their solution shows that the system’s ground state is a multimode squeezed vacuum, a special quantum state that preserves the fundamental Heisenberg uncertainty principle during the interaction.
- This squeezed state enables a reduction in the uncertainty of a particle’s position, potentially allowing for measurement accuracy that surpasses the standard quantum limit for sensors.
- The complete findings from physicists Dennis Clougherty and Nam Dinh, which align with previous predictions, were published in the scientific journal Physical Review Research.
Physicists at the University of Vermont have solved a 90-year-old quantum puzzle, developing an exact theory for a “damped harmonic oscillator”—a motion similar to a plucked guitar string falling silent, but at the atomic scale. The research, led by Professor Dennis Clougherty and his student Nam Dinh, provides a complete quantum description of how a vibrating particle embedded in a medium loses energy over time. Their findings were published on July 7, 2025, in the journal Physical Review Research.
For decades, scientists struggled to create such a model because of a fundamental rule of the subatomic world: Heisenberg’s uncertainty principle. This principle states that it is impossible to know a particle’s position and momentum simultaneously with perfect accuracy. Previous attempts to describe a damped quantum system failed because they could not properly incorporate this rule. “The difficulty involves preserving Heisenberg’s uncertainty principle,” Clougherty said in a university press release, explaining that a full solution required accounting for the complex interactions between the main particle and all the other atoms in its surrounding environment.
To overcome this hurdle, the researchers revived a model first proposed by British physicist Horace Lamb in 1900, long before the development of quantum theory. By reformulating Lamb’s classical equations for the quantum world, Clougherty and Dinh employed a powerful mathematical technique known as a multimode Bogoliubov transformation. This method allowed them to find an exact solution, revealing that the system’s lowest energy state is a “multimode squeezed vacuum,” a special quantum state that carefully balances the trade-offs required by the uncertainty principle.
The discovery has implications far beyond theoretical physics. A squeezed vacuum state allows for the uncertainty in one property, like a particle’s position, to be reduced below normal quantum limits by increasing the uncertainty in another, like its momentum. This “quantum trick” could pave the way for new ultra-precise sensor technologies capable of measuring distances smaller than an atom’s nucleus. “By reducing this uncertainty, one can measure position to an accuracy below the standard quantum limit,” Clougherty said, referencing a technique that was crucial in the development of gravitational wave detectors.
References
- Brown, J. & University of Vermont. (2025, August 15). Physicists solve 90-year-old puzzle of quantum damped harmonic oscillators. Phys.Org; University of Vermont. https://phys.org/news/2025-08-physicists-year-puzzle-quantum-damped.html
- Clougherty, D. P., & Dinh, N. H. (2025). Quantum Lamb model. Physical Review Research, 7(3), L032004. https://doi.org/10.1103/9fxx-2x6n
