Exploring the decay processes of a quantum state weakly coupled to a finite-size reservoir

Ingrid Fadelli is a writer for the website Phys.org.

The golden rule of time- dependent theory is a formula that can be used to calculate the rate at which an initial quantum state transitions into a final state. It's important to consider how systems respond to imposed perturbations and settle into stationary states over time if you want to solve many physics problems.

There are instances in which an initial quantum state is weakly coupled to a continuum of other final states. In order to investigate what happens when a quantum state is coupled to a set of final states with a non zero mean level spacing, researchers have recently set out.

The decay of a quantum state into some continuum of final states is associated with incoherent decay processes. An excited atom emits a photon into an infinite vacuum. Current date experimentations often realize systems with quantum states coupled to finite size reservoirs that are composed of separate sets of final states.

Understanding the conditions under which quantum states are coupled to finite size can be difficult. Micklitz and his colleagues wanted to understand the process through which a quantum state decays when coupled to a finite size.

Micklitz said that the first thing they wanted to do was consider generic finite size reservoirs. Powerful analytical tools are available for such systems, which show quantum chaotic behavior.

Micklitz and his colleagues used a combination of effective matrix integral techniques to carry out their analyses. They used exact diagonalization to benchmark the results of their analyses.

Micklitz said they hadn't expected the decay to be described in such a way. The probability to reside in the weakly coupled level shows a non-motonous time-dependence with initial decay and a raise. Thespectral form factor, a well-studied object in the quantum chaos community, is followed by the temporal profile. In retrospective, this makes sense.

A recent study by a team of researchers has been published in the journal Physical Review Letters. There is a connection between the problem of how a quantum state decays into a set of final states to the statistics associated with energy levels and wave functions.

The ratio of the probability's minimum and saturation values to the statistics of reservoir-eigen functions is related to the temporal profile of the probability of residence. The work focuses on an example of relaxation into a finite size reservoir. We are trying to address more complex systems. Progress can be made using the same methods that were used in the paper.

More information: Tobias Micklitz et al, Emergence of Fermi's Golden Rule, Physical Review Letters (2022). DOI: 10.1103/PhysRevLett.129.140402 Journal information: Physical Review Letters

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