Andreas Ruschhaupt

We propose a scheme for piston control in a two-ion quantum device with motion confined to orthogonal axes. In this system, one ion plays the role of a ''classical'' piston driven by the Coulomb interaction with the other ion, whose quantum motion is controlled through modulation of its trapping potential. The stationary state is determined self-consistently, taking quantum effects into account. We identify a narrow quantum regime of the ground state connecting two broad classical regimes. We further design inverse-engineering protocols to control the motion of the ''classical'' ion. The proposed control scheme provides a useful route toward controlled piston dynamics in microscopic quantum devices.

Fast and robust quantum control protocols are often based on an idealised approximate description of the relevant quantum system. While this may provide a performance which is close to optimal, improvements can be made by incorporating elements of the full system representation. We propose a new technique for such scenarios, called enhanced shortcuts to adiabaticity (eSTA). The eSTA method works for previously intractable Hamiltonians by providing an analytical correction to existing STA protocols. This correction can be easily calculated and the resulting protocols are outside the class of STA schemes. We demonstrate the effectiveness of the method for three distinct cases: manipulation of an internal atomic state beyond the rotating wave approximation, transport of a neutral atom in an optical Gaussian trap and transport of two trapped ions in an anharmonic trap.

We investigate the effect of slow spring-constant drifts of the trap used to shuttle two ions of different mass. We design transport protocols to suppress or mitigate the final excitation energy by applying invariant-based inverse engineering, perturbation theory, and a harmonic dynamical normal-mode approximation. A simple, explicit trigonometric protocol for the trap trajectory is found to be robust with respect to the spring-constant drifts.

We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particle's arrival at the counter is identified with the loss of normalization for an initial wave packet. Under the sole assumption that the absorbing term vanishes on the initial wave function, we show that $ΔT ΔE \geq \sqrt p \hbar/2$ and $<T> ΔE\geq 1.37\sqrt p\hbar$, where $<T>e$ denotes the mean arrival time, and $p$ is the probability for the particle to be eventually absorbed. Nearly minimal uncertainty can be achieved in a two-level system, and we propose a trapped ion experiment to realize this situation.