M. Palmero

We propose protocols to prepare highly excited energy eigenstates of a trapped ion in a harmonic trap which do not require laser pulses to induce transitions among internal levels. Instead the protocols rely on smoothly deforming the trapping potential between single and double well configurations. The speed of the changes is set to minimize non-adiabatic transitions by keeping the adiabaticity parameter constant. High fidelities are found for times more than two orders of magnitude smaller than with linear ramps of the control parameter. Deformation protocols are also devised to prepare superpositions to optimize interferometric sensitivity, combining the ground state and a highly excited state.

We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent modes can indeed be defined is identified, and a geometrical analogy is put forward. The results explain and unify recent work to design fast operations on trapped ions, needed to implement a scalable quantum-information architecture: transport, expansions, and the separation of two ions, two-ion phase gates, as well as the rotation of an anisotropic trap for an ion are treated and shown to be analogous to a mechanical system of two masses connected by springs with time dependent stiffness.

We implement faster-than-adiabatic two-qubit phase gates using smooth state-dependent forces. The forces are designed to leave no final motional excitation, independently of the initial motional state in the harmonic, small-oscillations limit. They are simple, explicit functions of time and the desired logical phase of the gate, and are based on quadratic invariants of motion and Lewis-Riesenfeld phases of the normal modes.

We engineer the fast rotation of a quantum particle confined in an effectively one-dimensional, harmonic trap, for a predetermined rotation angle and time, avoiding final excitation. Different schemes are proposed with different speed limits that depend on the control capabilities. We also make use of trap rotations to create squeezed states without manipulating the trap frequencies.

We design fast protocols to separate or recombine two ions in a segmented Paul trap. By inverse engineering the time evolution of the trapping potential composed of a harmonic and a quartic term, it is possible to perform these processes in a few microseconds without final excitation. These times are much shorter than the ones reported so far experimentally. The design is based on dynamical invariants and dynamical normal modes. Anharmonicities beyond the harmonic approximation at potential minima are taken into account perturbatively. The stability versus an unknown potential bias is also studied.

We investigate the dynamics under diabatic expansions/compressions of linear ion chains.Combining a dynamical normal-mode harmonic approximation with the invariant-based inverse-engineering technique, we design protocols that minimize the final motional excitation of the ions. This can substantially reduce the transition time between high and low trap-frequency operations, potentially contributing to the development of scalable quantum information processing.

We investigate the dynamics of mixed-species ion crystals during transport between spatially distinct locations in a linear Paul trap in the diabatic regime. In a general mixed-species crystal, all degrees of freedom along the direction of transport are excited by an accelerating well, so unlike the case of same-species ions, where only the center-of-mass-mode is excited, several degrees of freedom have to be simultaneously controlled by the transport protocol. We design protocols that lead to low final excitations in the diabatic regime using invariant-based inverse-engineering for two different-species ions and also show how to extend this approach to longer mixed-species ion strings. Fast transport of mixed-species ion strings can significantly reduce the time overhead in certain architectures for scalable quantum information processing with trapped ions.

We design fast trajectories of a trap to transport two ions using a shortcut-to-adiabaticity technique based on invariants. The effects of anharmonicity are analyzed first perturbatively, with an approximate, single relative-motion mode, description. Then we use classical calculations and full quantum calculations. This allows to identify discrete transport times that minimize excitation in the presence of anharmonicity. An even better strategy to suppress the effects of anharmonicity in a continuous range of transport times is to modify the trajectory using an effective trap frequency shifted with respect to the actual frequency by the coupling between relative and center of mass motions.