Inverse engineering of fast state transfer among coupled oscillators

TL;DR

This paper presents a method for rapid, high-fidelity quantum state transfer in coupled oscillators using a two-dimensional invariant, enabling precise control of state rotation and scaling in a time-efficient manner.

Contribution

It introduces a novel invariant-based approach for designing faster-than-adiabatic state transfers in coupled oscillators, allowing perfect state switching regardless of initial eigenstates.

Findings

Achieved fast state transfer with high fidelity using invariant-based control.

Derived generic expressions for final states and energies in coupled oscillators.

Demonstrated control of trap rotation and eigenstate transformation in harmonic potentials.

Abstract

We design faster-than-adiabatic state transfers (switching of quantum numbers) in time-dependent coupled-oscillator Hamiltonians. The manipulation to drive the process is found using a two-dimensional invariant recently proposed in S. Simsek and F. Mintert, Quantum 5 (2021) 409, and involves both rotation and transient scaling of the principal axes of the potential in a Cartesian representation. Importantly, this invariant is degenerate except for the subspace spanned by its ground state. Such degeneracy, in general, allows for infidelities of the final states with respect to ideal target eigenstates. However, the value of a single control parameter can be chosen so that the state switching is perfect for arbitrary (not necessarily known) initial eigenstates. Additional 2D linear invariants are used to find easily the parameter values needed and to provide generic expressions for the final states and final energies. In particular we find time-dependent transformations of a two-dimensional harmonic trap for a particle (such as an ion or neutral atom) so that the final trap is rotated with respect to the initial one, and eigenstates of the initial trap are converted into rotated replicas at final time, in some chosen time and rotation angle.