Inverse engineering of fast state transfer among coupled oscillators

Xiao-Jing Lu1,2, Ion Lizuain3,4, and J. G. Muga2,4

1School of Science, Xuchang University, Xuchang 461000, China
2Departamento de Química Física, University of the Basque Country UPV/EHU, Apdo. 644, 48080 Bilbao, Spain
3Department of Applied Mathematics, University of the Basque Country UPV/EHU, Donostia-San Sebastián, Spain
4EHU Quantum Center, University of the Basque Country UPV/EHU

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


We design faster-than-adiabatic state transfers (switching of quantum numbers) in time-dependent coupled-oscillator Hamiltonians. The manipulation to drive the process is found using a two-dimensional invariant recently proposed in S. Simsek and F. Mintert, Quantum 5 (2021) 409, and involves both rotation and transient scaling of the principal axes of the potential in a Cartesian representation. Importantly, this invariant is degenerate except for the subspace spanned by its ground state. Such degeneracy, in general, allows for infidelities of the final states with respect to ideal target eigenstates. However, the value of a single control parameter can be chosen so that the state switching is perfect for arbitrary (not necessarily known) initial eigenstates. Additional 2D linear invariants are used to find easily the parameter values needed and to provide generic expressions for the final states and final energies. In particular we find time-dependent transformations of a two-dimensional harmonic trap for a particle (such as an ion or neutral atom) so that the final trap is rotated with respect to the initial one, and eigenstates of the initial trap are converted into rotated replicas at final time, in some chosen time and rotation angle.

► BibTeX data

► References

[1] A. Tobalina, E. Torrontegui, I. Lizuain, M. Palmero, and J. G. Muga. ``Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators''. Phys. Rev. A 102, 063112 (2020).

[2] Shumpei Masuda and Stuart A. Rice. ``Rotation of the Orientation of the Wave Function Distribution of a Charged Particle and its Utilization''. The Journal of Physical Chemistry B 119, 11079–11088 (2015).

[3] Shumpei Masuda and Katsuhiro Nakamura. ``Acceleration of adiabatic quantum dynamics in electromagnetic fields''. Phys. Rev. A 84, 043434 (2011).

[4] M. Palmero, Shuo Wang, D. Guéry-Odelin, Jr-Shin Li, and J. G. Muga. ``Shortcuts to adiabaticity for an ion in a rotating radially-tight trap''. New J. Phys. 18, 043014 (2016).

[5] I. Lizuain, A. Tobalina, A. Rodríguez-Prieto, and J. G. Muga. ``Fast state and trap rotation of a particle in an anisotropic potential''. Journal of Physics A: Mathematical and Theoretical 52, 465301 (2019).

[6] I. Lizuain, M. Palmero, and J. G. Muga. ``Dynamical normal modes for time-dependent hamiltonians in two dimensions''. Phys. Rev. A 95, 022130 (2017).

[7] M. Palmero, E. Torrontegui, D. Guéry-Odelin, and J. G. Muga. ``Fast transport of two ions in an anharmonic trap''. Phys. Rev. A 88, 053423 (2013).

[8] M. Palmero, R. Bowler, J. P. Gaebler, D. Leibfried, and J. G. Muga. ``Fast transport of mixed-species ion chains within a Paul trap''. Phys. Rev. A 90, 053408 (2014).

[9] Xiao-Jing Lu, A. Ruschhaupt, and J. G. Muga. ``Fast shuttling of a particle under weak spring-constant noise of the moving trap''. Phys. Rev. A 97, 053402 (2018).

[10] Xiao-Jing Lu, J. G. Muga, Xi Chen, U. G. Poschinger, F. Schmidt-Kaler, and A. Ruschhaupt. ``Fast shuttling of a trapped ion in the presence of noise''. Phys. Rev. A 89, 063414 (2014).

[11] Xi Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga. ``Fast Optimal Frictionless Atom Cooling in Harmonic Traps: Shortcut to Adiabaticity''. Phys. Rev. Lett. 104, 063002 (2010).

[12] M. Palmero, S. Martínez-Garaot, U. G. Poschinger, A. Ruschhaupt, and J. G. Muga. ``Fast separation of two trapped ions''. New J. Phys. 17, 093031 (2015).

[13] S. Martínez-Garaot, A. Rodríguez-Prieto, and J. G. Muga. ``Interferometer with a driven trapped ion''. Phys. Rev. A 98, 043622 (2018).

[14] A. Rodríguez-Prieto, S. Martínez-Garaot, I. Lizuain, and J. G. Muga. ``Interferometer for force measurement via a shortcut to adiabatic arm guiding''. Phys. Rev. Research 2, 023328 (2020).

[15] D. Kielpinski, C. Monroe, and D. J. Wineland. ``Architecture for a large-scale ion-trap quantum computer.''. Nature 417, 709–11 (2002).

[16] F. Splatt, M. Harlander, M. Brownnutt, F. Zähringer, R. Blatt, and W. Hänsel. ``Deterministic reordering of $^{40}$Ca$^+$ ions in a linear segmented Paul trap''. New J. Phys. 11, 103008 (2009).

[17] H. Kaufmann, T. Ruster, C. T. Schmiegelow, M. A. Luda, V. Kaushal, J. Schulz, D. von Lindenfels, F. Schmidt-Kaler, and U. G. Poschinger. ``Fast ion swapping for quantum-information processing''. Phys. Rev. A 95, 052319 (2017).

[18] E. Urban, N. Glikin, S. Mouradian, K. Krimmel, B. Hemmerling, and H. Haeffner. ``Coherent control of the rotational degree of freedom of a two-ion coulomb crystal''. Phys. Rev. Lett. 123, 133202 (2019).

[19] Martin W. van Mourik, Esteban A. Martinez, Lukas Gerster, Pavel Hrmo, Thomas Monz, Philipp Schindler, and Rainer Blatt. ``Coherent rotations of qubits within a surface ion-trap quantum computer''. Phys. Rev. A 102, 022611 (2020).

[20] A. Tobalina, J. G. Muga, I. Lizuain, and M. Palmero. ``Shortcuts to adiabatic rotation of a two-ion chain''. Quantum Science and Technology 6, 045023 (2021).

[21] D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga. ``Shortcuts to adiabaticity: Concepts, methods, and applications''. Rev. Mod. Phys. 91, 045001 (2019).

[22] Selwyn Simsek and Florian Mintert. ``Quantum control with a multi-dimensional Gaussian quantum invariant''. Quantum 5, 409 (2021).

[23] H. R. Lewis and W. B. Riesenfeld. ``An Exact Quantum Theory of the Time-Dependent Harmonic Oscillator and of a Charged Particle in a Time-Dependent Electromagnetic Field''. J. Math. Phys. 10, 1458 (1969).

[24] H. Espinós, J. Echanobe, Xiao-Jing Lu, and J. G. Muga. ``Fast ion shuttling which is robust versus oscillatory perturbations'' (2022). arXiv:2201.07555.

[25] O Castaños, R López-Peña, and V I Man'ko. ``Noether's theorem and time-dependent quantum invariants''. Journal of Physics A: Mathematical and General 27, 1751–1770 (1994).

[26] Alejandro R. Urzúa, Irán Ramos-Prieto, Manuel Fernández-Guasti, and Héctor M. Moya-Cessa. ``Solution to the time-dependent coupled harmonic oscillators hamiltonian with arbitrary interactions''. Quantum Reports 1, 82–90 (2019).

[27] S. Simsek and F. Mintert. ``Quantum invariant-based control of interacting trapped ions'' (2021).

[28] T. Villazon, A. Polkovnikov, and A. Chandran. ``Swift heat transfer by fast-forward driving in open quantum systems''. Phys. Rev. A 100, 012126 (2019).

[29] S. Ibáñez, Xi Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt. ``Multiple Schrödinger Pictures and Dynamics in Shortcuts to Adiabaticity''. Phys. Rev. Lett. 109, 100403 (2012).

[30] Shi-fan Qi and Jun Jing. ``Accelerated adiabatic passage in cavity magnomechanics''. Phys. Rev. A 105, 053710 (2022).

[31] E. Urban. ``Implementation of a rotationally symmetric ring ion trap and coherent control of rotational states''. PhD thesis. University of California, Berkeley. (2019).

[32] T. Sägesser, R. Matt, R. Oswald, and J. P. Home. ``Robust dynamical exchange cooling with trapped ions''. New J. Phys. 22, 073069 (2020).

Cited by

[1] Kazutaka Takahashi, "Dynamical invariant formalism of shortcuts to adiabaticity", Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380 2239, 20220301 (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2022-12-08 09:05:02). The list may be incomplete as not all publishers provide suitable and complete citation data.

On SAO/NASA ADS no data on citing works was found (last attempt 2022-12-08 09:05:02).