Abstract
Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some systems are not separable into independent modes by a point transformation. For these "coupled systems" 2D invariants may still guide the Hamiltonian design. The theory to perform the inversion and two application examples are provided: (i) We control the deflection of wave packets in transversally harmonic waveguides; and (ii) we design the state transfer from one coupled oscillator to another.
Highlights
Controlling the motional dynamics of quantum systems is of paramount importance for fundamental science and quantum-based technologies [1]
The paper is organized as follows: First we introduce the model and its dynamical normal modes in Sec
In some multidimensional systems with time-dependent control there are no point transformations that lead to uncoupled normal modes
Summary
Controlling the motional dynamics of quantum systems is of paramount importance for fundamental science and quantum-based technologies [1]. A distinction can be made between STA methods that keep the structure of some Hamiltonian form and design the time dependence of the controls, e.g., using invariants [5] and those techniques that add new terms, e.g., counterdiabatic driving [6]. The two oscillators have to be driven simultaneously with common controls but, among the plethora of parameter trajectories, it is possible to find the ones that satisfy simultaneously the boundary conditions imposed on both oscillators This strategy has been successfully applied to design the driving of different operations on two trapped ions such as transport or expansions [9,10], separation of two equal ions in double wells [11], phase gates [12], or dynamical exchange cooling [13].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
