How did scientists crack a 90-year-old quantum enigma?

The quantum damped harmonic oscillator has been an elusive puzzle for physics researchers for nearly ninety years. While classical physics beautifully explains how systems such as guitar strings or playground swings gradually lose energy and slow down over time, extending this understanding to the quantum realm posed profound challenges.

Quantum particles follow basic rules that make it impossible to measure their position and momentum exactly at the same time, which makes it difficult to create a model for energy loss at the atomic level.

University of Vermont physics professor Dennis Clougherty and his former student Nam Dinh have successfully cracked this problem by extending the classical Lamb model into the quantum domain.

Their research accounts for the complex interaction of a vibrating atom with all surrounding atoms in a solid, transforming the problem into a many-body quantum system that had long resisted exact solutions.

Did you know?
This study represents the first exact quantum solution to the damped harmonic oscillator problem without violating Heisenberg’s uncertainty principle.

What is the quantum damped harmonic oscillator problem?

The central challenge lies in describing a quantum system that gradually loses energy, akin to a fading vibration, while adhering to Heisenberg's uncertainty principle. Previous approaches made simplifying assumptions or broke key quantum rules.

Clougherty and Dinh used an advanced mathematical technique called the multimode Bogoliubov transformation. The results allowed them to diagonalize the Hamiltonian, the central energy operator for the system, revealing a unique quantum ground state known as a multimode squeezed vacuum.

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Why preserving the uncertainty principle was such a challenge

To balance the need to model damping while respecting the uncertainty principle, researchers found it necessary to include the full many-body interactions of atoms in the solid, resulting in a highly complex mathematical problem that they solved exactly for the first time.

Their solution answers a long-standing theoretical question and creates new possibilities for very accurate quantum measurements and technologies like detecting gravitational waves, quantum acoustics, and advanced sensors.

It also enhances our understanding of quantum friction and energy dissipation in nanostructures, potentially improving the design of quantum computers and communication devices.

This breakthrough marks a major milestone in quantum physics and sets the stage for future experimental and technological advances.