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arXiv:1801.06306 · Scientific Reports

Effect of different filling tendencies on the spatial quantum Zeno effect

Xin Zhang, Chang Xu, Zhongzhou Ren, Jie Peng

Published Jul 2, 2018• 2 citations
arXivHTMLPDF

Abstract

The quantum Zeno effect is deeply related to the quantum measurement process and thus studies of it may help shed light on the hitherto mysterious measurement process in quantum mechanics. Recently, the spatial quantum Zeno effect is observed in a Bose-Einstein condensate depleted by an electron beam. We theoretically investigate how different intrinsic tendencies of filling affect the quantum Zeno effect in this system by changing the impinging point of the electron beam along the inhomogeneous condensate. Surprisingly, we find no visible effect on the critical dissipation intensity at which the quantum Zeno effect appear. Our finding shows the recent capability of combining the Bose-Einstein condensate with an electron beam offers a great opportunity for studying the spatial quantum Zeno effect, and more generally the dynamics of a quantum many-body system out of equilibrium.

DOI
10.1038/s41598-018-27605-9

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The quantum Zeno effect is deeply related to the quantum measurement process and thus studies of it may help shed light on the hitherto mysterious measurement process in quantum mechanics. Recently, the spatial quantum Zeno effect is observed in a Bose-Einstein condensate depleted by an electron beam. We theoretically investigate how different intrinsic tendencies of filling affect the quantum Zeno effect in this system by changing the impinging point of the electron beam along the inhomogeneous condensate. Surprisingly, we find no visible effect on the critical dissipation intensity at which the quantum Zeno effect appear. Our finding shows the recent capability of combining the Bose-Einstein condensate with an electron beam offers a great opportunity for studying the spatial quantum Zeno effect, and more generally the dynamics of a quantum many-body system out of equilibrium.
We study the possibility of suppressing three-body losses in atomic Bose-Einstein condensates via the quantum Zeno effect, which means the delay of quantum evolution by frequent measurements. It turns out that this requires very fast measurements with the rate being determined by the spatial structure of the three-body form factor, i.e., the point interaction approximation ${\ensuremath{\delta}}^{3}(\mathbf{r}\ensuremath{-}{\mathbf{r}}^{'})$ is not adequate. Since the molecular binding energy Eb{E}_{b}Eb​ provides a natural limit for the measurement rate, this suppression mechanism can only work if the form factor possesses certain special properties.
The quantum measurement problem, namely how the deterministic quantum evolution leads to probabilistic measurement outcomes, remains a profound question to be answered. In the present work, we propose a spectacular demonstration and test of the subtle and peculiar character of the quantum measurement process. We show that a bright soliton supported by a Bose-Einstein condensate can be reflected as a whole by an electron beam, with neither attraction nor repulsion between the condensate's neutral atoms and the beam's electrons. This macroscopic reflection is purely due to the quantum Zeno dynamics induced by the frequent position measurement of the condensate's atoms by the electron beam. As an example of application, just as a soccer player would stop a coming ball, an electron beam moving backward with half the velocity of the bright soliton can precisely stop the soliton. This offers an entirely new and useful tool for manipulating bright solitons.
It is generally impossible to probe a quantum system without disturbing it. However, it is possible to exploit the back action of quantum measurements and strong couplings to tailor and protect the coherent evolution of a quantum system. This is a profound and counterintuitive phenomenon known as quantum Zeno dynamics. Here we demonstrate quantum Zeno dynamics with a rubidium Bose–Einstein condensate in a five-level Hilbert space. We harness measurements and strong couplings to dynamically disconnect different groups of quantum states and constrain the atoms to coherently evolve inside a two-level subregion. In parallel to the foundational importance due to the realization of a dynamical superselection rule and the theory of quantum measurements, this is an important step forward in protecting and controlling quantum dynamics and, broadly speaking, quantum information processing. While a quantum system is always disturbed by any observation, one can exploit the back action of measurements and strong couplings to tailor the system evolution via quantum Zeno dynamics. Schäfer et al. demonstrate quantum Zeno dynamics in a five-level Hilbert space using a 87Rb Bose–Einstein condensate.
Frequent Measurements on an unstable particle located at observable initial state freeze the particle on this state, known as quantum Zeno effect [1-14]. Measurements on an observable subspace further open the prelude of quantum Zeno dynamics [15-17]. These phenomena affect the results of quantum measurement that has been widely used in quantum information and quantum computation [18-21]. However, this common argument is insufficient when the initial state is coupled with a continuum reservoir. In such an irreversible system, intrinsic decay property destroys the frozen behavior. Although it has been proven that the decay rate of the initial state will be affected by measurements [7], the knowledge of detailed mechanisms for this measurement-dependent decay is still limited. In this work, we found based on three-subsystem perturbation theory that the indirect correlation between a continuum reservoir and a measurement apparatus through the interaction with a quantum system causes a Rabi-like inter-modulation among these subsystems. The indirect correlation effect from this combination drives the system into quantum Zeno and reactivation regions, which are dependent upon the Rabi strength, pulse duty, and its repetition rate. We also found that the dynamical changes of decay rate are quite different in continuous and pulsed measurements, and, thus, significantly affect the dynamics of the system.
Quantum Zeno effect is conventionally interpreted by the assumption of the wave-packet collapse, in which does not involve the duration of measurement. However, we predict duration τmτ_mτm​ of each measurement will appear in quantum Zeno effect by a dynamical approach. Moreover, there exists a model-free critical measurement time, which quantum Zeno effect does not occur when τmτ_mτm​ takes some special values. In order to give these predictions, we first present a description of quantum Zeno effect in the Heisenberg picture, which is based on the expectation value of an observable and its fluctuation. Then we present a general proof for quantum Zeno effect in the Heisenberg picture, which is independent of the concrete systems. Finally, we calculate the average population and relative fluctuation after NNN successive measurements in XX model, which agrees with our prediction about the critical measurement time.