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      Analyzing the Quantum Zeno and anti-Zeno effects using optimal projective measurements

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      Scientific Reports
      Nature Publishing Group UK

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          Abstract

          Measurements in quantum mechanics can not only effectively freeze the quantum system (the quantum Zeno effect) but also accelerate the time evolution of the system (the quantum anti-Zeno effect). In studies of these effects, a quantum state is prepared repeatedly by projecting the quantum state onto the initial state. In this paper, we repeatedly prepare the initial quantum state in a different manner. Instead of only performing projective measurements, we allow unitary operations to be performed, on a very short time-scale, after each measurement. We can then repeatedly prepare the initial state by performing some projective measurement and then, after each measurement, we perform a suitable unitary operation to end up with the same initial state as before. Our objective is to find the projective measurements that minimize the effective decay rate of the quantum state. We find such optimal measurements and the corresponding decay rates for a variety of system-environment models such as the pure dephasing model and the spin-boson model. We find that there can be considerable differences between this optimized effective decay rate and the usual decay rate obtained by repeatedly projecting onto the initial state. In particular, the Zeno and anti-Zeno regimes can be considerably modified.

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          The Zeno’s paradox in quantum theory

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            Nonlinear atom interferometer surpasses classical precision limit

            Interference is fundamental to wave dynamics and quantum mechanics. The quantum wave properties of particles are exploited in metrology using atom interferometers, allowing for high-precision inertia measurements [1, 2]. Furthermore, the state-of-the-art time standard is based on an interferometric technique known as Ramsey spectroscopy. However, the precision of an interferometer is limited by classical statistics owing to the finite number of atoms used to deduce the quantity of interest [3]. Here we show experimentally that the classical precision limit can be surpassed using nonlinear atom interferometry with a Bose-Einstein condensate. Controlled interactions between the atoms lead to non-classical entangled states within the interferometer; this represents an alternative approach to the use of non-classical input states [4-8]. Extending quantum interferometry [9] to the regime of large atom number, we find that phase sensitivity is enhanced by 15 per cent relative to that in an ideal classical measurement. Our nonlinear atomic beam splitter follows the "one-axis-twisting" scheme [10] and implements interaction control using a narrow Feshbach resonance. We perform noise tomography of the quantum state within the interferometer and detect coherent spin squeezing with a squeezing factor of -8.2dB [11-15]. The results provide information on the many-particle quantum state, and imply the entanglement of 170 atoms [16].
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              Picosecond coherent optical manipulation of a single electron spin in a quantum dot.

              Most schemes for quantum information processing require fast single-qubit operations. For spin-based qubits, this involves performing arbitrary coherent rotations of the spin state on time scales much faster than the spin coherence time. By applying off-resonant, picosecond-scale optical pulses, we demonstrated the coherent rotation of a single electron spin through arbitrary angles up to pi radians. We directly observed this spin manipulation using time-resolved Kerr rotation spectroscopy and found that the results are well described by a model that includes the electronnuclear spin interaction. Measurements of the spin rotation as a function of laser detuning and intensity confirmed that the optical Stark effect is the operative mechanism.
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                Author and article information

                Contributors
                adam.zaman@lums.edu.pk
                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group UK (London )
                2045-2322
                18 September 2017
                18 September 2017
                2017
                : 7
                : 11766
                Affiliations
                GRID grid.440540.1, School of Science & Engineering, Lahore University of Management Sciences (LUMS), ; Opposite Sector U, D.H.A, Lahore, 54792 Pakistan
                Article
                11787
                10.1038/s41598-017-11787-9
                5603598
                28924194
                fc22815d-0dad-4511-b5e8-e1e959e48c91
                © The Author(s) 2017

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 10 April 2017
                : 30 August 2017
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