Quantum polarization properties of two-mode energy eigenstates

Abstract

We show that any pure, two-mode, $N$-photon state with $N$ odd or equal to two can be transformed into an orthogonal state using only linear optics. According to a recently suggested definition of polarization degree, this implies that all such states are fully polarized. This is also found to be true for any pure, two-mode, energy eigenstate belonging to a two-dimensional SU(2) orbit. Complete two- and three-photon bases whose basis states are related by only phase shifts or geometrical rotations are also derived.Comment: 6 pages, no figure, references and an extended proof of unit polarization for all odd N adde

Unpolarized states and hidden polarization

“…The maximum degree P (1) 2 is attained for the pure states (1) 8) and they are the transformed of the state |1,0 under SU(2) rotationsR(α,β,γ ). Incidentally, these states have served as the thread to experimentally verify the existence of hidden polarization [32,33]. They coincide with the anticoherent states introduced in Ref.…”

Multipolar hierarchy of efficient quantum polarization measures

“…Some results along these lines have already been reported, but either they use magnitudes difficult to determine in practice, such as distances [19], generalized visibilities [20][21][22][23], and central moments [24], or they go only up to second order [25,26], and the pertinent extensions are difficult to discern.…”

Distance-based degrees of polarization for a quantum field

“…The first condition is to some extent trivial: it ensures that unpolarized and only unpolarized states have a zero degree of polarization. The second takes into account that the requirement that an unpolarized state is invariant under any SU(2) polarization transformation makes it also invariant under any energy-preserving unitary transformation [45]: these include not only the transformations generated byŜ, but also those generated bŷ S 0 , which, in technical terms, corresponds to the group U(2) [22].…”