Quantum invariant-based control of interacting trapped ions

Abstract

Invariant-based inverse engineering is an elegant approach to quantum control with corresponding experimental implementations that perform tasks with applications in quantum information processing such as shuttling trapped ions. We build on recent work to generalise invariant-based inverse engineering to control two coupled harmonic oscillators in any number of spatial dimensions. This may be used to perform experimentally relevant tasks such as separation of trapped ions, which is demonstrated numerically, achieving transfer fidelities of over 96% as well as low motional number excitations.

Inverse engineering of fast state transfer among coupled oscillators

“…Thanks to the relations (36), ( 38), (39), and (40) several important results will depend only on the parameter b ≡ c * x c x , (41) so we use a special notation for it. We shall find shortly that this is exactly the parameter that appears in the expression of the energy increment (27).…”

“…to the process considered in [22]. The methodology presented here may be extended into problems in higher dimensions such as ion separations [27]. A further extension concerns the boundary conditions for the potential.…”

“…Any state |n, k i evolves in time within the invariant subspace n + k, which is spanned by the states that evolve dynamically from the initial eigenstates but, except for the ground state, the final state is in general a linear combination of the eigenstates of H(t f ) that span the subspace, rather than the desired |k, n f . Numerical calculations, see an example in Table I, demonstrate that the energy increment when the state starts at |n, k i takes a remarkably simple form, namely, 3 (27) where…”

Optimal Shortcuts to Adiabatic Control by Lagrange Mechanics

“…At present, STA technology has been successfully applied to atoms, molecules, optical physics, solid state physics, chemistry, engineering, quantum systems, and classical systems [12,[20][21][22][23][24][25]. With the development of STA technology, the STA technique includes many different schemes, such as the quantum invariant-based inverse control method [26][27][28][29], the reverse thermal transfer compensation method [30][31][32], the no-jump quantum drive method [33][34][35], etc. These methods have been validated in a number of experiments.…”

Fast Driving of a Particle in Two Dimensions without Final Excitation

“…The process may be faster than the adiabatic one and it is not state-specific, in other words, the initial quantum numbers need not be known. In more detail, we identified first a “family” of driving processes based on a quadratic invariant found by Simsek and Mintert [ 8 , 9 , 10 ]. This invariant is degenerate except for the ground state, so the processes in this family do not guarantee swapping in general.…”