metric amplification (OPA) in a PT-symmetric coupler. We derive Schrodinger-type equations for the biphotons gen- erated in spontaneous regime and formulate ...
Quantum and classical parametric processes in PT-symmetric quadratic nonlinear couplers with loss Diana A. Antonosyan, Alexander S. Solntsev, and Andrey A. Sukhorukov 1
Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 0200 Australia
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Photonic structures composed of coupled waveguides with lossy regions offer new possibilities for shaping optical beams and pulses compared to conservative structures. A directional coupler made of parallel waveguides with different absorption characteristics can represent an optical analogue of complex parity-time (or PT)-symmetric potentials, where the beam dynamics can demonstrate unique features due to phase transition effects [1, 2], and unusual switching regimes can be obtained in nonlinear structures. We consider the waveguides made of material with quadratic nonlinear response, and study the effect of absorption in one of the waveguides, which can be introduced, for instance, in hybrid metal-dielectric structures. The studies of stability of nonlinear modes generated in the PT-symmetric media depending on interplay of quadratic nonlinearity and the PT-symmetric potentials are presented in [3]. We study the photon-pair generation through spontaneous parametric down-conversion (SPDC) and generation of signal and idler modes through optical parametric amplification (OPA) in a PT-symmetric coupler. We derive Schrodinger-type equations for the biphotons generated in spontaneous regime and formulate analytical solutions for the photon correlations [4] as well as present solutions for photon numbers from Schrodinger equations for the signal and idler photon amplitudes generated in stimulated regime and compare the results. Scheme of PT-symmetric coupler is pre-
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signal and idler modes generated in OPA can be measured by two-powermeters. Here we present characteristic results for the case of the pump coupled only to the second waveguide with losses. When the loss coefficient is below the PT-symmetry breaking threshold, the photons generated both in the processes SPDC and OPA can couple between the waveguides similar to quantum walks in conservative nonlinear couplers [5]. Oscillations of SPDC photon correlations are visualised in Fig. 1(b). The losses above the symmetry breaking threshold appear to destroy the quantum walks in both systems. Fig. 1(c) illustrates the behavior of the largest eigenmode of the OPA depending on the loss coefficient and the phasematching condition. The detailed depiction of the symmetry breaking threshold and the mode distribution is presented in Fig. 1(d). The system is PT-symmetric when the modal intensity is equally divided between the two sites, even though we have loss only in one waveguide and the input pump is not symmetrically distributed. The dark part on Fig. 1(d) corresponds to the case with PT-symmetry in the system and the light part is for the case without the symmetry in it. It is remarkable to mention that we can control the symmetry of the system varying various parameters like phase-matching. For instance, we can clearly see that only one mode remains for the zero phase mismatch with loss coefficient above 1 which corresponds to symmetry breaking in the system. We noticed that there is a strong correlation between the shape of the biggest eigenmode (Fig. 1(c)) and the distribution of PT-symmetry regions (Fig. 1(d)). We have found differences in the behavior of biphotons (SPDC) and signal/idler (OPA) amplitudes at long distances. Namely, for the losses above the symmetry breaking threshold biphotons tend to non zero constant values while the signal/idler amplitudes drop to zero. Moreover, the analysis of the behavior of the signal and idler mode intensities in the OPA shows that we can control the PT-symmetry breaking threshold varying the input pump and induced nonlinearity. These results indicate new possibilities for photon generation and control in structures with loss, such as hybrid plasmonic waveguides.
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Figure 1: (a) Scheme of a PT-coupler with loss only in one waveguide and (b) behavior of photon-pair correlation generated through the SPDC depending on the propagation direction. Loss coefficient is below the PT-symmetry breaking threshold, phase-mismatch equal to 2. (c) The behavior of the largest eigenmode for the OPA depending on loss coefficient and the phase-mismatch (d) picture of PT-symmetry breaking for the largest eigenmode in the process of OPA. The input pump is coupled to the waveguide with losses. All coefficients are normalized to the coupling between the waveguides. sented in Fig. 1(a). The SPDC photon-pair coincidences can be measured by two single photon detectors while the powers of
References [1] A. Guo, G. J. Salamo, D. Duchesne, R.Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides,Phys. Rev. Lett. 103, 093902 (2009). [2] C. E. Ruter, K. G. Makris, R. El-Ganainy,D.N. Christodoulides, M. Segev, and D. Kip, Nature Physics 6, 192 (2010). [3] K. Li, D. A. Zezyulin, P. G. Kevrekidis, V. V. Konotop, and F. Kh. Abdullaev, Phys. Rev. A 88, 053820 (2013). [4] D.A. Antonosyan, A. S. Solntsev, and A. A. Sukhorukov, arXiv:1401.7070 (2014). [5] A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 023601 (2012).
