PT-Symmetry in two Synthetic Dimensions

Abstract

Using standard telecommunication equipment, we present an experimental platform for investigating Parity-Time (PT) symmetry in a two-dimensional synthetic lattice with tunable gain, loss and phase structure. By exploiting the fibre nonlinearity, dissipative TT solitons and wave collapse are realized, for which the later one gives rise to an amplified, self-accelerating nonlinear wave packet. Following a concept developed in [1], we present a novel protocol for realizing TT-symmetry in a 2D synthetic lattices based on mixed short and long-range coupling. Our set-up (see Fig. 1a) consists of two pairs of slightly dissimilar coupled fibre loops, where each fibre patch is approximately 30 km long. As shown in Fig. 1a, a 20ns long optical pulse at 1550 nm wavelength is injected into the outer left loop and splits at the first 50/50 coupler at the entrance of the two inner loops. The lengths of the inner two loops differ by ΔLinner ≈ 600m (ΔTinner ≈ 3μs), while that of the outer loops by ΔLouter ≈ 6m (ΔTouter = 30ns). After passing through the second 50/50 coupler, the pulses split again and propagate through the outer loops back to the first 50/50 coupler. After a mean round trip time Τ ≈ 300 μs, an ordered sequence of four pulses arrives at the first coupler and starts its journey again. In each roundtrip m pulse delay increases / decreases by ΔTinner, if the pulse passes the long / short inner loop which is equivalent to a step to the right / left on an effective 2D synthetic lattice denoted by x. Afterwards, by propagating through the outer long / short loop, the pulse delay increases / decreases by ΔTouter, respectively, and thus the pulse makes a step up / down on the lattice denoted by y. In this way, any path through the 2D lattice can be interpreted as a combination of roundtrips through the four different loops. The arrival times of the pulses at the photodetector are measured, sampled electronically and mapped onto a 2D discrete lattice spanned by the χ and y coordinates (see Fig. 1b). This synthetic lattice is, for instance, equivalent to a 2D waveguide array and both 50/50 couplers resemble the effect of wave coupling to neighbouring waveguides in horizontal or vertical direction. TT-symmetry can be realized by applying a balanced gain/loss space-dependent protocol on the synthetic lattice (red and blue arrows in Fig. 1b). Unbroken TT-symmetry is only realized if in addition phase modulation scheme is applied (orange diagonal regions in Fig. 1b).