Observation of a Chiral State in a Microwave Cavity

Abstract

A microwave experiment has been realized to measure the phase difference of the oscillating electric field at two points inside the cavity. The technique has been applied to a dissipative resonator which exhibits a singularity -called exceptional point -in its eigenvalue and eigenvector spectrum. At the singularity, two modes coalesce with a phase difference of π/2 . We conclude that the state excited at the singularity has a definitiv chirality.PACS numbers: 05.45. Mt, 41.20.Jb, 03.65.Vf, Recently a surprising phenomenon occurring in systems described by non-hermitian Hamiltonians has received considerable attention: the coalescence of two eigenmodes. If the system depends on some interaction parameter λ , the value λ EP at which the coalescence occurs is called an exceptional point (EP) [1]. At an EP, the eigenvalues and eigenvectors show branch point singularities [1,2,3,4,5] [3,13]. So far EPs have been observed in decaying systems described by a complex symmetric effective Hamiltonian [14]. While the theoretical and experimental articles cited above discuss the properties of systems in the vicinity of an EP, a recent theoretical work [15] investigates the complex symmetric Hamiltonian of a two-level system at the EP. The eigenfunction at the EP turns out to be( 1) for any choice of the basis states |1 and |2 . This is a chiral state: in quantum, acoustical and electromagnetic systems the two orthogonal basis states oscillate in time; if they are superimposed according to Eq. (1) -where they follow each other with a time lag of a quarter period -the result is rotating either clockwise or counter-clockwise. This is in analogy with the

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

“…A that the eigenstates |Ψ + and |Ψ − are mapped into one another upon topological encirclement of one or the other (but not both) exceptional points, except that one or the other eigenstate will pick up an additional 180 • phase change. This property of EP2s has already been demonstrated over a decade ago in a series of quasi-static microwave cavity experiments [54,[78][79][80][81] (see also Ref. [82]), although a true dynamical encirclement is a more complex problem [83,84] that has only been achieved in experiment very recently for the EP2B [85][86][87].…”

Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities

“…[44,45]. The solutions (ψ 1 (t), ψ 2 (t)) of the Schrödinger-type equation (7) can be found analytically.…”

Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation

“…General formulae describing coupling and decoupling of eigenvalues, crossing and avoided crossing of eigenvalue surfaces were derived. Both the DP and EP cases are interesting in applications and were observed in experiments, see [Ramachandran and Ramaseshan (1961)], [Dembowsky et al (2001)], [Dembowsky et al (2003)], [Stehmann et al (2004)]. …”