Large parity violating effects in atomic dysprosium with nearly degenerate Floquet eigenvalues

TL;DR

This paper investigates parity nonconservation effects in atomic dysprosium using Floquet theory, revealing potential large asymmetries and beat frequencies proportional to the square root of the parity-violating interaction, with implications for experimental detection.

Contribution

It introduces a Floquet matrix approach to analyze P-violation in nearly degenerate atomic levels, highlighting the possibility of observing large asymmetries and beat frequencies in atomic dysprosium.

Findings

Floquet eigenvalues can have contributions proportional to √Hw.

Large parity-violating asymmetries can be achieved within a few Floquet cycles.

Detecting beat frequencies proportional to √Hw is challenging due to rapid decay.

Abstract

In this article we study effects of parity nonconservation in atomic dysprosium, where one has a pair of nearly degenerate levels of opposite parity. We consider the time evolution of this two-level system within oscillatory electric and magnetic fields. These are chosen to have a periodical structure with the same period, such that a Floquet matrix describes the time evolution of the quantum states. We show that, if the states are unstable, the eigenvalues of the Floquet matrix may have contributions proportional to the square root of the parity violating interaction matrix element $H_w$ while they are almost degenerate in their parity even part. This leads to beat frequencies proportional to $\sqrt{H_w}$ which are expected to be larger by several orders of magnitude compared to ordinary P-violating contributions which are of order $H_w$. However, for the simple field configurations we considered, it still seems to be difficult to observe these P-violating beat effects, since the states decay too fast. On the other hand, we found that, within only a few Floquet cycles, very large parity violating asymmetries with respect to experimental setups of opposite chirality may be obtained. The electric and magnetic fields as well as the time intervals necessary for this are in an experimentally accessible range. For statistically significant effects beyond one standard deviation a number of about $10^7$ atoms is required. Our ideas may be applied directly to other 2-level atomic systems and different field configurations. We hope that these ideas will stimulate experimental work in this direction.