Dynamical phase transitions versus cross-over in the atom maser

What is it about?

The atom maser is a well-known model consisting of a microwave cavity coupled to a thermal bath and pumped by excited two-level atoms passing through the cavity at a constant rate; the cavity and the atoms interact in a resonant way and there is a non-null probability that the cavity absorbs energy from the atom, leaving it in the ground state. Numerical simulations and experimental data show that for certain values of the atom-cavity interaction strength, the record of atoms detected in the ground versus the excited state exhibits intermittency and long-time correlations reminiscent of dynamical phase transitions in non-equilibrium statistical mechanics. In tandem, the cavity has distinct low and high energy quasi-stationary regimes with rare but fast switches between the two. Our work addresses the physics literature debate on whether observed dynamical behaviour implies that the atom maser exhibits a type of phase transition. We answer this in the negative, providing a rigorous mathematical proof using the formalism of large deviations theory. Interestingly, both numerical simulations and our theoretical results suggest that the phase transition does happens in the limit of large pumping rate.

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Photo by Tom Wheatley on Unsplash

Photo by Tom Wheatley on Unsplash

Why is it important?

Beyond clarifying important questions relating to the atom maser dynamics, our work offers a first mathematically rigorous large deviation result for quantum trajectories of infinite dimensional quantum systems.

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