{"id":9148,"date":"2023-06-29T08:43:18","date_gmt":"2023-06-29T06:43:18","guid":{"rendered":"https:\/\/fermi.univ-tlse3.fr\/?post_type=tribe_events&p=9148"},"modified":"2023-06-29T08:43:18","modified_gmt":"2023-06-29T06:43:18","slug":"optimal-control-of-quantum-systems-applications-to-the-robust-control-of-bose-einstein-condensates-and-to-quantum-speed-limit-with-piecewise-constant-control-etienne-dionis-lcar-seminar-2","status":"publish","type":"tribe_events","link":"https:\/\/fermi.univ-tlse3.fr\/fr\/home\/event\/optimal-control-of-quantum-systems-applications-to-the-robust-control-of-bose-einstein-condensates-and-to-quantum-speed-limit-with-piecewise-constant-control-etienne-dionis-lcar-seminar-2\/","title":{"rendered":"Optimal control of quantum systems: Applications to the robust control of Bose-Einstein Condensates and to quantum speed limit with piecewise constant control. – (Etienne Dionis \/ LCAR \/ Seminar). – 29\/06\/2023, 9H"},"content":{"rendered":"

Etienne Dionis<\/span> <\/strong>(Laboratoire Interdisciplinaire Carnot de Bourgogne, Universit\u00e9 de Bourgogne-Franche Comt\u00e9)<\/p>\n

S\u00e9minaire LCAR Jeudi 29 juin, 9H00. – Nouvelle Salle de conf\u00e9rence, 3R4<\/span><\/p>\n

R\u00e9sum\u00e9<\/strong> :
\nThis presentation will focus on two recent applications of optimal control techniques to quantum
\nsystems.<\/p>\n

In the first part, the goal is to manipulate the motional states of an atomic Bose-Einstein
\ncondensate (BEC) in a one-dimensional optical lattice. This study is a joint work wit the experi-
\nmental group of Pr. D. Gu\u00e9ry-Odelin in Toulouse University (France). The protocols operate on
\nthe momentum comb associated with the lattice through its amplitude and phase [3]. A precise and
\nversatile control for a wide variety of targets has been demonstrated. However, in order to improve
\nthe agreement between theory and experiment, it is important to design control processes that are
\nrobust with respect to experimental uncertainties (Figure 1). One limitation of the experimental
\nsetup under study is the value of the quasi-momentum which is not exactly zero as assumed in
\n[3]<\/strong>. Due to the large dimension of the Hilbert space, numerical algorithms such as GRAPE [1]<\/strong>
\nhave to be used. In the case of the simultaneous control of an ensemble of systems, we propose
\na new formulation of GRAPE with a sequential-update of the control. We show numerically the
\nsuperiority of this sequential approach with respect to the standard one [2].<\/strong>
\nIn the second part, we apply a recent extension of the Pontryagin Maximum Principle (PMP) [4]<\/strong>
\nto piecewise constant control. PMP, on which optimal control theory is based, was originally for-
\nmulated for continuous functions. In practice, experimental implementations resort to piecewise
\nconstant signals. In [5]<\/strong>, the authors have mathematically proved that for general non-linear dy-
\nnamics, the PMP should be modified in a non-trivial way. We have transposed this result to
\nquantum systems and applied it to the time-optimal control of simple quantum systems with two
\nlevels (Figure 2). In these systems, we derive exact quantum speed limits accounting for this key
\nexperimental constraint [6]<\/strong>. This should be an important step toward understanding the role of
\ntechnological limitations in the manipulation of quantum systems, a key issue in quantum control.<\/p>\n

References<\/strong>
\n[1] <\/strong>Glaser S. J., Boscain U., Calarco T., Koch C., Kockenberger W., Kosloff R., Kuprov I., Luy
\nB., Schirmer S., Schulte-Herbr\u00fcggen T., Sugny D. and Wilhelm F. 2015 Eur. Phys. J. D 69,
\n279
\n[2]<\/strong> Dionis E. and Sugny D. 2022 J. Phys. B: At. Mol. Opt. Phys. 55, 184006
\n[3]<\/strong> Dupont N., Chatelain G., Gabardos L., Arnal M., Billy J., Peaudecerf B., Sugny D. and
\nGu\u00e9ry-Odelin D. 2021 PRX Quantum 2, 040303
\n[4]<\/strong> Boscain U., Sigalotti M. and Sugny D. 2021 PRX Quantum 2, 030203
\n[5]<\/strong> Bourdin L. and Tr\u00e9lat E. 2017 Automatica 79, 273
\n[6]<\/strong> Dionis E. and Sugny D. 2023 Physical Review A 107, 032613<\/p>\n

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