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PT Symmetry in Coupled Active-passive Microcavities and Optically-induced Atomic Lattices

By Min Xiao, University of Arkansas

A coupled gain-loss waveguide pair with balanced gain and loss can mimic the parity-time (PT) symmetric Hamiltonian constructed in quantum mechanics [1], which has started an active research field of PT-symmetric optics in the past ten years. Many interesting new phenomena related to such PT-symmetry systems have been theoretically predicted and, some of them, experimentally demonstrated recently.

In this talk, two experimental systems will be discussed that show interesting PT-symmetry properties. The first one is consisted of a pair of coupled active-passive high-Q microtoroid cavities. With carefully balanced gain and loss in the active and passive microcavities, an exceptional (phase transition) point emerges in the transmitted spectral plot (the two spectral peaks merge into one) as the coupling strength between the two microtoroids decreases beyond a certain point (i.e. when the loss equals to gain in the two microtoroids, and becomes larger than the coupling strength between the microtoroids), indicating a PT symmetry breaking to occur in the system [2]. By exploring the gain-saturation nonlinearity in the active microtoroid, nonreciprocal light transmission can be realized in this coupled active-passive microcavity [2]. Such nonreciprocal light transmission can work for balanced & unbalanced gain/loss conditions and under PT-symmetry & broken PT-symmetry cases [2], indicating that the nonreciprocal light transmission is mainly due to the gain-saturation nonlinearity in the system. Actually, nonreciprocal light propagation and optical circulation can be realized in a single active high-Q microtoroid cavity [3,4], which is a much easier system to implement for practical applications.

The second system showing PT-symmetric behavior is done in optically-induced atomic lattices [5,6]. By setting up two sets of coupling and pump standing-wave laser beams in a four-level N-type atomic medium (inside a heated vapor cell) to form optical lattices with controllable gain/loss ratio in the adjacent channels, symmetric refractive index and anti-symmetric gain/loss profiles can be achieved for the injected signal beam [5-7]. Due to the large available parametric spaces, the refractive index and gain/loss (via Raman gain and modified absorption due to the electromagnetically induced transparency) profiles induced by the two sets of the atomic lattices can be easily tuned/controlled and reconfigured in this four-level atomic configuration. The presence of a well-defined exceptional point (or breaking-phase threshold) under balanced gain/loss condition was experimentally verified by observing an abrupt change of relative phase difference between the gain and loss channels [7]. Results from numerical simulations can be used to qualitatively explain the observed phenomenon.

1. R. El-Ganainy, K.G. Makris, D.N. Christodoulides, and Z.H. Musslimani, Opt. Lett. 32, 2632 (2007).

2. L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, Nature Photonics 8, 524 (2014).

3. J. Wen, X.S. Jiang, M. Zhang, L. Jiang, S. Hua, H. Wu, C. Yang, and M. Xiao, Photonics 2, 498 (2015).

4. X. S. Jiang, C. Yang, H. Wu, S. Hua, J. Wen, L. Jiang, L. Chang, Y. Ding, M. Zhang, Q. Hua, and M. Xiao, “On-chip optical nonreciprocity using an active microcavity”, submitted, 2015.

5. J. Sheng, M-A. Miri, D. N. Christodoulides, and Min Xiao, Phys. Rev. A 88, 041803(R) (2013).

6. J. Sheng, J. Wang, M-A. Miri, D. N. Christodoulides, and M. Xiao, Optics Express 23, 19777 (2015).

7.  Z.Y. Zhang, Y.Q. Zhang, J. Sheng, L. Yang, M.A. Miri, D. N. Christodoulides, B. He, Y.P. Zhang and M. Xiao, “Observation of parity–time symmetry in optically induced atomic lattices”, submitted, 2016.