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arXiv:1509.03457 · New Journal of Physics

Shortcuts to adiabaticity for an ion in a rotating radially-tight trap

Mikel Palmero, Shuo Wang, David Guéry-Odelin, Jr-Shin Li, Juan Gonzalo Muga

Published Apr 12, 2016• 19 citations
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Abstract

We engineer the fast rotation of an effectively one-dimensional ion trap for a predetermined rotation angle and time, avoiding the final excitation of the trapped ion. 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.

DOI
10.1088/1367-2630/18/4/043014

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We engineer the fast rotation of an effectively one-dimensional ion trap for a predetermined rotation angle and time, avoiding the final excitation of the trapped ion. 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.
Abstract We inverse engineer fast rotations of a transversally tight, 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 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 harmonic traps, rotation protocols are also found using more costly numerical optimisations.
Abstract Shortcuts to adiabaticity (STA) provides the possibility of high accuracy manipulation of phonon states in ion traps. We propose a scheme realized experimentally for manipulating phonon states using STA and confirmed its effectiveness through generating Fock states. Our results show that the duration of the STA manipulation of phonon states is 16 times faster than that of the adiabatic evolution, and the non-resonant excitation can be suppressed by laser bias frequency, which are confirmed by experimental results. Moreover, we also carried out an experimental research on the robustness of STA, showing good robustness respect to the pulse shape deformation, bias noises and stochastic noise. This might lead to a useful step toward realizing fast and noise-resistant quantum manipulation within current experimental capacity.
We investigate theoretically the possibility for robust and fast cooling of a trapped atomic ion by transient interaction with a pre-cooled ion. The transient coupling is achieved through dynamical control of the ions' equilibrium positions. To achieve short cooling times we make use of shortcuts to adiabaticity by applying invariant-based engineering. We design these to take account of imperfections such as stray fields, and trap frequency offsets. For settings appropriate to a currently operational trap in our laboratory, we find that robust performance could be achieved down to 6.3 motional cycles, comprising 14.2 μs for ions with a 0.44 MHz trap frequency. This is considerably faster than can be achieved using laser cooling in the weak coupling regime, which makes this an attractive scheme in the context of quantum computing.
Abstract We investigate theoretically the possibility for robust and fast cooling of a trapped atomic ion by transient interaction with a pre-cooled ion. The transient coupling is achieved through dynamical control of the ions’ equilibrium positions. To achieve short cooling times we make use of shortcuts to adiabaticity by applying invariant-based engineering. We design these to take account of imperfections such as stray fields, and trap frequency offsets. For settings appropriate to a currently operational trap in our laboratory, we find that robust performance could be achieved down to 6.3 motional cycles, comprising 14.2 μs for ions with a 0.44 MHz trap frequency. This is considerably faster than can be achieved using laser cooling in the weak coupling regime, which makes this an attractive scheme in the context of quantum computing.
Control protocols known as shortcuts to adiabaticity allow to drive a quantum system from an initial to a final state arbitrarily fast. These techniques have recently been proposed for open quantum systems, thus extending their application to allow for fast thermalization. Here, we engineer dynamical schemes for the fast preparation of squeezed thermal states at controlled temperature. We derive the equations of motion of squeezed thermal states in harmonic oscillators under unitary and open dynamics, allowing for temperature and entropy variations between the initial and final states. The counter-diabatic Hamiltonians and associated dissipators are provided, and whenever possible, given in a form relevant to experimental application.The technique is detailed in the setting of trapped-ion experiments with two-photon Raman interaction, where the desired open dynamics is obtained from stochastically shaking the trapping potential, or driving the system with a laser of stochastic amplitude. In this context, we find solutions for the control parameters---namely laser amplitude, phase, and dephasing strength---that allow creating a squeezed thermal state at controlled temperature in arbitrary time.