# Dynamical trapping through harmonic breathing

## TL;DR

This paper introduces a novel quantum and optical trapping method using high-frequency harmonic breathing of the system, effectively creating a potential well without nonlinear effects, supported by analytical and numerical results.

## Contribution

It presents a new trapping strategy based on harmonic breathing, applicable to quantum particles and optical beams, with analytical and numerical validation.

## Key findings

- Effective trapping achieved through harmonic breathing at high frequencies.
- Analytical solutions for arbitrary potentials demonstrate the method's generality.
- Optical waveguide lattices can trap beams without nonlinear effects.

## Abstract

A new strategy for trapping quantum particles is presented, which behaves like an effective harmonic oscillator potential trap wherever is desired. The approach is based on harmonic contraction and expansion of the system around a fixed point (trapping point) at high frequencies. Analytical results are presented for an arbitrary potential and contrasted with numerical calculations for a quantum particle between two impenetrable walls. Similarly, making use of the analogy between quantum mechanics and optics, it is shown that an harmonically breathing waveguide lattice can be used to trap optical beams using frequencies of the order of the coupling constant without needing to resort to nonlinear dielectric terms.