Shortcuts to adiabatic rotation of a two-ion chain

We inverse engineer fast rotations of a linear trap with two ions for a predetermined rotation angle and time, avoiding final excitation. Different approaches are analyzed and compared when the ions are of the same species or of different species. The separability into dynamical normal modes for equal ions in a common harmonic trap, or for different ions in non-harmonic traps with up to quartic terms allows for simpler computations of the rotation protocols. For non-separable scenarios, in particular for different ions in a harmonic trap, rotation protocols are also found using more costly numerical optimisations.Comment: 15 pages, 6 figure

Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators

Two-dimensional (2D) systems with time-dependent controls admit a quadratic Hamiltonian modeling 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 wave guides and (ii) we design the state transfer from one coupled oscillator to another.This work was supported by the Basque Country Government (Grant No. IT986-16), and by PGC2018-101355-B-I00 (MCIU/AEI/FEDER,UE). E.T. acknowledges support from PGC2018-094792-B-I00 (MCIU/AEI/FEDER,UE), CSIC Research Platform PTI-001, and CAM/FEDER No. S2018/TCS-4342 (QUITEMAD-CM)

Fast Driving of a Particle in Two Dimensions without Final Excitation

Controlling the motional state of a particle in a multidimensional space is key for fundamental science and quantum technologies. Applying a recently found two-dimensional invariant combined with linear invariants, we propose protocols to drive a particle in two dimensions so that the final harmonic trap is translated and rotated with respect to the initial one. These protocols realize a one-to-one mapping between initial and final eigenstates at some predetermined time and avoid any final excitations.This work was supported by the National Natural Science Foundation of China (Grant No. 12104390), the Natural Science Foundation of Henan Province (Grant No. 212300410238), by Grant PID2021-126273NB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, by the Basque Government through Grant No. IT1470-22, and by the Scientific Research Innovation Team of Xuchang University (Grant No. 2022CXTD005)

Claude Cohen-Tannoudji profesorea Zientzia eta Teknologia Fakultatean

1936. urtean sortu eta handik hilabete gutxira Gerra Zibilagatik itxi zen lehenbiziko euskal unibertsitate publikoa: Euzko Irakastola Nagusia zuen izena, eta unibertsitate hartako medikuntzako euskara (sendakintz-euzkera) irakasten zuen Jose Zinkunegi medikuaz, haren obraz eta haren euskaraz dihardu lan honek. Gaur egungo Euskal Herriko Unibertsitatea eta Euskara Teknikoa irakasgaia 1936ko unibertsitate haren eta irakasgai haren oinordeko dira, hurrenez hurren, eta haiei eta Iñaki Ugarteburu Gastañares zenari egin nahi diegun omenaldi gisa ulertu behar da hitzaldi hau

Invariant-Based Inverse Engineering of Crane Control Parameters

By applying invariant-based inverse engineering in the small-oscillation regime, we design the time dependence of the control parameters of an overhead crane (trolley displacement and rope length) to transport a load between two positions at different heights with minimal final-energy excitation for a microcanonical ensemble of initial conditions. The analogy between ion transport in multisegmented traps or neutral-atom transport in moving optical lattices and load manipulation by cranes opens a route for a useful transfer of techniques among very different fields.We acknowledge our discussions with S. Martínez-Garaot and M. Palmero. This work was supported by Eusko Jaurlaritza (Grant No. IT986-16); MINECO/ FEDER,UE (Grants No. FIS2015-67161-P and No. FIS2015-70856-P); QUITEMAD+CM S2013- ICE2801; and by Programme Investissements d'Avenir under the program ANR-11-IDEX 0002-02, reference ANR-10-LABX-0037-NEXT

Claude Cohen-Tannoudji profesorea Zientzia eta Teknologia Fakultatean

1936. urtean sortu eta handik hilabete gutxira Gerra Zibilagatik itxi zen lehenbiziko euskal unibertsitate publikoa: Euzko Irakastola Nagusia zuen izena, eta unibertsitate hartako medikuntzako euskara (sendakintz-euzkera) irakasten zuen Jose Zinkunegi medikuaz, haren obraz eta haren euskaraz dihardu lan honek. Gaur egungo Euskal Herriko Unibertsitatea eta Euskara Teknikoa irakasgaia 1936ko unibertsitate haren eta irakasgai haren oinordeko dira, hurrenez hurren, eta haiei eta Iñaki Ugarteburu Gastañares zenari egin nahi diegun omenaldi gisa ulertu behar da hitzaldi hau

Invariant-Based Inverse Engineering for Fast and Robust Load Transport in a Double Pendulum Bridge Crane

We set a shortcut-to-adiabaticity strategy to design the trolley motion in a double-pendulum bridge crane. The trajectories found guarantee payload transport without residual excitation regardless of the initial conditions within the small oscillations regime. The results are compared with exact dynamics to set the working domain of the approach. The method is free from instabilities due to boundary effects or to resonances with the two natural frequencies.This research was funded by the Basque Country Government (Grant No. IT986-16) and PGC2018-101355-B-I00 (MCIU/AEI/FEDER, UE