AbstractRecently, there has been growing interest in the utilization of physical systems as heuristic optimizers for classical spin Hamiltonians. A prominent approach employs gain-dissipative optical oscillator networks for this purpose. Unfortunately, these systems inherently suffer from an inexact mapping between the oscillator network loss rate and the spin Hamiltonian due to additional degrees of freedom present in the system such as oscillation amplitude. In this work, we theoretically analyze and experimentally demonstrate a scheme for the alleviation of this difficulty. The scheme involves control over the laser oscillator amplitude through modification of individual laser oscillator loss. We demonstrate this approach in a laser network classical XY model simulator based on a digital degenerate cavity laser. We prove that for each XY model energy minimum there corresponds a unique set of laser loss values that leads to a network state with identical oscillation amplitudes and to phase values that coincide with the XY model minimum. We experimentally demonstrate an eight fold improvement in the deviation from the minimal XY energy by employing our proposed solution scheme.

Non-Hermitian Hamiltonians, and particularly parity-time (PT) and anti-PT symmetric Hamiltonians, play an important role in many branches of physics, from quantum mechanics to optical systems and acoustics. Both the PT and anti-PT symmetries are specific instances of a broader class known as anyonic-PT symmetry, where the Hamiltonian and the PT operator satisfy a generalized commutation relation. Here, we study theoretically these novel symmetries and demonstrate them experimentally in coupled lasers systems. We resort to complex coupling of mixed dispersive and dissipative nature, which allows unprecedented control on the location in parameter space where the symmetry and symmetry breaking occur. Moreover, tuning the coupling in the same physical system allows us to realize the special cases of PT and anti-PT symmetries. In a more general perspective, we present and experimentally validate a new relation between laser synchronization and the symmetry of the underlying non-Hermitian Hamiltonian.

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Phase locking of coupled lasers is severely hindered by the spread in their natural lasing frequencies. We present an intra-cavity adaptive optics method that reduces the frequency spread and thereby improves phase locking. Using an intra-cavity spatial light modulator and an iterative optimization algorithm, we demonstrate a fourfold enhancement of phase locking 450 coupled lasers, as quantified by the peak intensity and the inverse participation ratio of the far-field output distributions. We further show that the improvement is long-lasting, and suitable for phase locking of weakly coupled lasers.

We demonstrate the generation of chiral super-modes in a network of symmetrically-coupled lasers by applying an on-site complex potential, a combination of loss and frequency detuning, and adjusting it to an exceptional point.