Strength Distributions and Symmetry Breaking in Coupled Microwave Billiards

Flat microwave cavities can be used to experimentally simulate quantum mechanical systems. By coupling two such cavities, we study the equivalent to symmetry breaking in quantum mechanics. As the coupling is tunable, we can measure resonance strength distributions as a function of the symmetry breaking. We analyze the data by employing a qualitative model based on random matrix theory and show that the results derived from the strength distribution are consistent with those previously obtained from spectral statistics.

Figure 1

Size of the tunable coupling $\lambda$ between the two cavities sketched in the inset. The function $\eta (\lambda )$ enters Eq. (6).

Figure 2

Monte Carlo simulation of resonance strength distributions (solid lines) compared to the calculated strength distribution (dashed lines) for the couplings (a) $\lambda =0.03$, (b) $\lambda =0.10$, (c) $\lambda =0.17$, (d) $\lambda =0.24$.

Figure 3

The experimental resonance strength distributions (histograms) for the couplings (a) $(8,0)$, (b) $(5,3)$, (c) $(4,4)$, and (d) $(5,8)$ fitted to the calculated strength distribution. The symmetry breaking parameter $\lambda$ equals $\lambda =0$ in (a), $\lambda =0.110$ in (b), $\lambda =0.125$ in (c), and $\lambda =0.185$ in (d). The insets in (b), (c), and (d) show experimental strength distributions together with RMT model fits for a $z$ interval $[-3,1.5]$ in which the probability of missing strength is small.