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We have introduced the concept of rotation-time (RT) symmetry in bosonic systems, in which we have demonstrated coalescence of energy values [2], which is known as an exceptional point [1]. We have demonstrated that the RT symmetry is a generalisation of the parity-time (PT) symmetry, which was first presented by Bender and Boettcher [3]. We also established general principles for constructing non-Hermitian RT-symmetric Hamiltonians. This provides a foundation for studying the physics of spectral singularities in bosonic systems, including nonlinear interactions between modes. We investigated the effect of laser pumping on the spectral singularity.
It has been shown that also systems without gain components, that include only losses, can exhibit EPs. When only losses are included, a system is known to have passive PT symmetry. Eigenenergies for such systems have a common imaginary part and its presence is not an obstacle in observing EPs. The first experimental realisations of passive PT systems were already performed. To reveal the desirable symmetry, the appropriate relation between the lossy components of both coupled modes has to be obtained. The result of that interplay is the increase of transmitted power in one of the modes despite the fact that only lossy mechanisms are included. We have shown that if the whole non-Hermitian Hamiltonian, being not PT-symmetric nor RT-symmetric, can be expressed as a composition of two parts: (i) RT-symmetric term and (ii) a term commuting with (i), then the hidden RT symmetry is present in this non-Hermitian Hamiltonian [4]. We refer to the frame, where the hidden PT or RT symmetry is clearly seen, as to equilibrium frame (EF).
Here, we present non-linear, RT-symmetric passive system with spectral singularities. This system exhibit photon blockade and thus can be considered as single photon source as the nonlinearity is crucial for obtaining such phenomena.
References
[1] Hossein Hodaei, Absar U Hassan, Steffen Wittek, Hipolito Garcia-Gracia, Ramy El-Ganainy, Demetrios N Christodoulides, and Mercedeh Khajavikhan. Enhanced sensitivity at higher-order exceptional points. Nature, 548(7666):187–191, 2017.
[2] Ewelina Lange, Grzegorz Chimczak, Anna Kowalewska-Kudlaszyk, and Karol Bartkiewicz. Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of PT symmetry. Sci. Rep., 10(1):19906, Nov 2020.
[3] Carl M. Bender and Stefan Boettcher. Real spectra in non-hermitian hamiltonians having PT symmetry. Phys. Rev. Lett., 80:5243–5246, Jun 1998.
[4] G Chimczak, A Kowalewska-Kudlaszyk, E Lange, and K Bartkiewicz. Equilibrium frame reveals hidden PT symmetry of passive systems. preprint arXiv:2008.06532, 2020
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