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arXiv:2609.06600 · Physical Review A

Shortcuts to adiabaticity for rapid soliton compression in nonlocal media

Yingjia Li, Qian Kong, Xihua Yang, Xi Chen

Published Aug 10, 2026• 1 citation
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Abstract

We investigate shortcut-to-adiabaticity protocols for the rapid compression of optical solitons in nonlocal media. Using a variational approximation, we derive an effective Ermakov-like equation for the soliton width and employ inverse engineering to design propagation-dependent control parameters. Three control strategies are compared, based respectively on modulation of the characteristic nonlocal length, the Kerr nonlinearity, and the external parabolic confinement. We show that all three protocols enable high-fidelity compression over strongly reduced propagation distances. By comparing control smoothness and final fidelity, we find that the relative performance of the protocols in the very short-distance regime depends on the chosen criterion, revealing a trade-off between implementation smoothness and target-profile accuracy. These results establish a practical and general route to fast soliton manipulation in nonlocal media.

DOI
10.1103/k911-q7k5

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The challenge to fully grasp and to harness the bizarre phenomena which take place in the quantum realm is crucially linked to the ability to engineer and manipulate quantum systems with high precision. The scientific progress in this direction is opening new routes for the investigation of fundamental quantum physics, and it is at the same time paving the way to the development of the first quantum technologies. \n\nThis thesis is dedicated to the search of strategies for high-fidelity and noise-tolerant quantum control.\nA versatile theoretical framework is set up for the design of optimized control protocols based on accelerated adiabatic processes. The benefits of the adiabatic dynamics, rooted in its intrinsic stability versus control imperfections, are released from the requirement of slow evolution: this is achieved thanks to the theoretical construction of accelerating control Hamiltonians which dynamically counteract deviations from the target dynamics. Our framework provides a methodical way to engineer these Hamiltonians by introducing fast modulations of the initially-available control parameters, and it results from the interplay between the theory of counterdiabatic fields and Floquet-Magnus average Hamiltonian theory. As compared to other shortcut-to-adiabaticity strategies, our control method keeps the system always close to the exact adiabatic path while not requiring the implementation of new Hamiltonian couplings. Moreover, the flexibility in the construction of the accelerating Hamiltonians offers a fertile ground for the hybridization with optimal control techniques.\n\nThe general setup is applied to exemplary control problems of relevance in quantum optics and quantum information processing. First, a protocol is designed for the generation of entanglement between effective two-level systems coupled through a transmission line, in the experimental context of circuit quantum electrodynamics. Second, an accelerated version of the widespread technique of stimulated Raman adiabatic passage is presented, which dramatically enlarges its range of applicability for implementations both in the optical and in the microwave regime.\n\nThe results strongly support the potential of the quantum control framework developed in this thesis. In particular, our methodology offers the opportunity to flank high fidelities and small error sensitivity with on-demand adaptability to experimental constraints and the flexibility for integrations with other control techniques. This makes it a valuable resource for applications in many branches of quantum science, with a natural outlet in quantum computation and simulation.
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We discuss differences between the variational approach to solitons and the accessible soliton approximaion in a highly nonlocal, nonlinear medium. We compare results of both approximations by considering the same system of equations in the same spatial region, under the same boundary conditions. We also compare these approximations with the numerical solution of the equations. We find that the variational highly nonlocal approximation provides more accurate results and, as such, is a more appropriate solution than the accessible soliton approximation. The accessible soliton model offers a radical simplification in the treatment of highly nonlocal, nonlinear media, with easy comprehension and convenient parallels to a quantum harmonic oscillator, however, with a hefty price tag: a systematic numerical discrepancy of up to 100% with the numerical results.