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Final Report Summary - OPTIQUOS (Optimal Control of Quantum Optical Systems)

Description of the work carried out to achieve the project’s objectives
In the first 12 months of the project Dr. Antonio Negretti has worked on four different topics: (i) robustness in QOCT; (ii) QIP with Wigner crystals of ions; (iii) microscopic models for studying Bose gases at finite temperature; (iv) optimal control of dissipative quantum systems. As regards (i), in collaboration with Prof. R. Fazio of the Scuola Normale Superiore (Pisa, Italy) and Prof. T. Calarco (Ulm), a novel approach to assess the error in quantum optimal control problems has been introduced. The developed method offers a strategy to define new control pulses that are not necessarily optimal but still able to yield an error not larger than some fixed a priori threshold, and therefore to provide control pulses that might be more amenable for an experimental implementation.
Concerning (ii), a precise study of the modulated-carrier quantum phase gate implemented with Wigner crystals of ions confined in Penning traps has been performed. It has been demonstrated that fast and robust two-qubit gates are achievable within the current experimental limitations. Moreover, a description of the implementation of the state-dependent sign-changing dipole forces needed to realize the investigated quantum computation scheme has been provided. The work is the result of the collaboration with Prof. T. Calarco, Dr. J. Taylor (NIST, US), and the Ph.D. student J. Baltrusch.
In the work (iii), together with PD Dr. C. Henkel (Potsdam, Germany) and the scientists Dr. S. Cockburn and Dr. N. Proukakis (Newcastle, United Kingdom), the equilibrium properties of a weakly interacting, trapped quasi-one-dimensional (1D) Bose gas at finite temperature compared to different theoretical approaches has been investigated. The analysis has been focused in particular on two stochastic theories: a number-conserving Bogoliubov approach and a stochastic Gross-Pitaevskii equation. Although the two stochastic theories are built on different thermodynamic ensembles, it has been shown that they yield the correct condensate statistics in a large condensate.
In work (iv), optimal control of open quantum systems without rotating-wave or Markovian approximations has been investigated. The study was based on an exact description of open quantum systems in terms of a stochastic Liouville-von Neumann (SLN) equation. Within this scheme the Krotov's iterative algorithm has been generalized, preserving its monotonic convergence. This formalism has been applied to the problem of controlling a particle in a harmonic trap whose thermal bath is characterized by an ohmic spectrum. Interestingly, it has been shown that optimal control can modify the quantum dissipative dynamics to the point where its entropy change turns negative. This work has been done in collaboration with Prof. T. Calarco and the group led by Prof. J. Ankerhold at the University of Ulm.
In the last 12 months of the project, that is, the second half of the fellowship, Dr. Antonio Negretti has worked on: (a) optimal transport of matter waves in dipole traps; (b) hybrid Josephson transistor; (c) magnetometry with a single spin; (d) mean field theories for quasi-one dimensional Bose condensates; (e) optimal and ultrafast coherent transfer of a quasi 1D Bose gas from the transverse ground state to the lower excited state of a waveguide potential.
Work (a) concerns the planned subproject (2) of the proposal. Here the applicant numerically investigated the performance of the atomic transport in optical dipole microtraps via the so-called spatial adiabatic passage by means a novel optimization technique: the chopped random basis algorithm. He investigated the ultimate limits of the speed of the transport in a triple well configuration for both a single atomic wave packet and a Bose-Einstein condensate by means of QOCT and within a regime of experimental parameters achievable with current optical technology. This work has been carried out with the collaboration of the Ph.D. student A. Benseny and Prof. J. Mompart of the Universitat Autònoma de Barcelona (Spain), and with Prof. T. Calarco (Ulm).
Instead, work (b) concerns the planned subproject (3), where the applicant investigated, together with the experimentalist Dr. R. Gerritsma (Mainz), the properties of an atomic bosonic Josephson junction in a double well potential coupled to a trapped ion. By deriving a single particle description based on a quantum defect theory, the two-mode approximation for investigating the quantum dynamics of a small condensate has been employed. It has been found that placing a single trapped ion in between the two wells significantly increases the tunneling rate. For strongly confined atoms and ions, the tunneling rate can be tuned depending on the internal state of the ions, making it possible to create mesoscopic entanglement between the two systems and to measure their interaction to high precision. The work has been done also with the collaboration of the Ph.D. student H. Doerk, Dr. Idziaszek (Poland), Prof. T. Calarco, and Prof. F. Schmidt-Kaler.

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UNIVERSITAET ULM
Germany
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