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Abstract:
We calculate analytically the geometric phases that
the eigenvectors of a parametric dissipative two-state system described by a
complex symmetric Hamiltonian pick up
when an exceptional point (EP) is encircled. An EP is a parameter
setting where the two eigenvalues and the corresponding eigenvectors of
the Hamiltonian coalesce. We show that it can be
encircled on a path along which the eigenvectors remain approximately
real and discuss a microwave cavity experiment, where such an encircling of
an EP was realized. Since the wavefunctions remain
approximately real, they could be reconstructed
from the nodal lines of the recorded spatial intensity distributions
of the electric fields inside the resonator. We measured the geometric
phases that occur when an EP is encircled four times and thus confirmed
that for our system an EP is a branch point of fourth order.
