Optical Energy-Difference Conservation in a Synthetic Anti-PT-Symmetric System

Anti-parity-time (APT) symmetry is associated with various effects beyond the fundamental limitations implied in the standard Hermitian-Hamiltonian dynamics. Here, we create an optical APT-symmetric system in a synthetic frequency domain using a conventional fiber without intrinsic gain or loss and experimentally reveal photonic APT-symmetric effects, including energy-difference conservation and synchronized power oscillation, which have not yet been confirmed experimentally in the optical domain. The optical fiber-based APT-symmetric system has a long interaction length because of its negligible loss, and the APT-symmetric Hamiltonian is precisely tunable with optical pumping density and phase mismatch. On this basis, we observe the phase transition at exceptional points, energy-difference conservation, and synchronized power oscillation. Our results provide a robust theoretical and experimental framework connecting the emerging non-Hermitian physics with technologically important nonlinear fiber-optic interactions.

Figure 1

Experimental setup of the proposed system. PUMP, pump laser; SEED, seed laser; PC, polarization controller; CF, combining filter; DSF, dispersion-shifted fiber; ILP, in-line polarizer; BS, beam splitter; TF, tunable filter; PM, power meter.

Figure 2

Phase transition between oscillation and amplification in the $\mathrm{\Delta }\nu$ and $P_p$ parameter space. The power of the signal and generated idler beams on a log scale are presented in the $\mathrm{\Delta }\nu$ and $P_p$ parameter space. (a) is the experimental result, and (b) is the theoretical calculations [note Eq. (4)]. The red line is the calculated power of the signal light at the EP pump power. The transparent gray surface is the guided surface of the EP in the parameter space.

Figure 3

Phase transition behaviors versus pump power. (a)–(c) The seeded signal and generated idler powers on a log scale are plotted against the input pump power. The background is shaded gray above the EP pump power. The lines are the calculated signal and idler powers. (d)–(f) The signal and idler powers normalized by their sum in (a)–(c), respectively. (g)–(i) The extracted eigenvalues from the data in (a)–(c) on a linear scale. In (a),(d),(g), (b),(e),(h), and (c),(f),(i), the detuning between the pump and seed lasers is set to 0.27, 0.30, and 0.33 THz, respectively.

Figure 4

Energy-difference conservation and bounded oscillation. The signal (blue dots and lines) and idler (red dots and lines) output powers and the difference between them (green dots and lines) are represented on a linear scale for detunings of (a) 0.10, (b) 0.15, and (c) 0.20 THz at a fixed pump power of 0.47 W, showing EDC above, right at, and below the EP, and for detunings of (d) 0.29, (e) 0.30, and (f) 0.31 THz at a fixed pump power of 1.6 W, showing bounded oscillation and EDC below the EP. The lines represent theoretical predictions.