Recurrence due to periodic multisoliton fission in the defocusing nonlinear Schrödinger equation

Abstract

We address the degree of universality of the Fermi-Pasta-Ulam recurrence induced by multisoliton fission from a harmonic excitation by analyzing the case of the semiclassical defocusing nonlinear Schrödinger equation, which models nonlinear wave propagation in a variety of physical settings. Using a suitable Wentzel-Kramers-Brillouin approach to the solution of the associated scattering problem we accurately predict, in a fully analytical way, the number and the features (amplitude and velocity) of solitonlike excitations emerging post-breaking, as a function of the dispersion smallness parameter. This also permits us to predict and analyze the near-recurrences, thereby inferring the universal character of the mechanism originally discovered for the Korteweg-deVries equation. We show, however, that important differences exist between the two models, arising from the different scaling rules obeyed by the soliton velocities.

Implementation of a generalized controlled-NOT gate between fixed-frequency transmons

“…In this experiment, we demonstrated a generalized CNOT operation between two fixed-frequency transmon qubits using the SWIPHT technique [1,27]. Four slightly different implementations of SWIPHT yielded gate fidelities F g 83 − 84%, similar to initial demonstrations of other all-microwave gates [19,21,43].…”

“…As proposed by Deng et al [27], the gate time could be significantly reduced by using qubits with frequencies that are closer together, leading to significant improvements in fidelity. As we noted above, our measured fidelities include errors associated with state preparation and measurement.…”

“…Here we describe the implementation of a recently proposed all-microwave two-qubit entangling gate known as "Speeding up Waveforms by Inducing Phases to Harmful Transitions" or SWIPHT [1,27]. SWIPHT is a generalized CNOT gate that yields a π-rotation (bit-flip) on the desired transition and a 2π-rotation (no bit-flip) on an undesired transition.…”

Solitary wave fission of a large disturbance in a viscous fluid conduit

“…These experiments exhibit excellent agreement with WKB theory applied to the inverse scattering transform . The WKB approach has also been applied to the defocusing nonlinear Schrödinger equation, yielding the number and amplitudes of emergent solitons (Deng et al 2017). However, none of these quantitative methods are applicable to non-integrable equations.…”

Fibre multi-wave mixing combs reveal the broken symmetry of Fermi–Pasta–Ulam recurrence

“…Our results establish optical fibres to be a viable platform for investigating all as-pects of mode interactions including the role of the mu-tual phases, at the same time highlighting for the first time the role of spontaneous symmetry breaking and the existence of a complex homoclinic structure in FPU dy-namics ruled by MI. This opens the doors to further experimental investigations that range from the mech-anisms of thermalization and their universality [8,9], the observation of higher-order separatrices, their associated phase plane dynamics and their role in rogue wave formation [22] and supercontinuum generation, the link with new mechanisms of soliton-mediated recurrences in fibres [33], as well as the transition to chaos induced around the homoclinic structure (homoclinic chaos) in strongly perturbed structures such as fibre passive cavities and microresonators for frequency comb generation [10], where MI remains a key driving mechanism.…”