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Science China Physics Mechanics and Astronomy

Quantum simulation of ‘zitterbewegung’ in a single trapped ion under conditions of parity-keeping and parity-breaking

Tao Liu, Mang Feng, WanLi Yang, Liang Chen, Fei Zhou, K. Wang

Published Apr 17, 2014• 4 citations
Publisher
DOI
10.1007/s11433-014-5458-5

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The motional trembling(‘zitterbewegung’)of a relativistic electron governed by Dirac equation was originally predicted by Schr¨odinger in the early days of quantum mechanics and simulated in a recent experiment with a single trapped ultracold ion.We investigate stable and instable confinements of a single trapped ion in a Paul trap under different conditions relevant to parity.Since our treatment involves neither restriction of Lamb-Dicke limit nor rotating-wave approximation,we may demonstrate different quantum dynamics of the single trapped ion in a wide range of the trapping parameters.We discuss the origin of the zitterbewegung which is relevant to the stability of the ion trapping.

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The motional trembling(‘zitterbewegung’)of a relativistic electron governed by Dirac equation was originally predicted by Schr¨odinger in the early days of quantum mechanics and simulated in a recent experiment with a single trapped ultracold ion.We investigate stable and instable confinements of a single trapped ion in a Paul trap under different conditions relevant to parity.Since our treatment involves neither restriction of Lamb-Dicke limit nor rotating-wave approximation,we may demonstrate different quantum dynamics of the single trapped ion in a wide range of the trapping parameters.We discuss the origin of the zitterbewegung which is relevant to the stability of the ion trapping.
Zitterbewegung (ZB), the trembling of free relativistic electrons in a vacuum, could be simulated by a single trapped ion. We focus on the variations of ZB under different parity conditions and find no ZB in the case of odd or even parity. ZB occurs only for the admixture of the odd- and even-parity states. We also show that a similar role is played by the parity operator for the trapped ion in Fock-state representation and the space-inversion operator for a realistic relativistic electron. Although the ZB effect is invisible in a relativistic electron, preparation of the trapped ion in different parity states is a sophisticated job, which makes it possible to observe the parity-relevant ZB effects with currently available techniques.
Abstract A recent trapped-ion experiment realised a lattice gauge theory with the gauge field in the internal states of the ions and bosonic matter in their vibrations. We showed earlier that its noise damage can be predicted. Here, we show that most of it can be undone. The conservation law of the theory is a parity of each vibrational mode, which heating flips, so a heating event leaves a mark that can be read without disturbing the physics. We keep only the runs in which this mark never changed. With equal heating rates and continuous monitoring, the kept runs reproduce the heating-free dynamics exactly, with a closed-form yield. Reading the mark at finite intervals introduces a small bias linear in the interval, which we derive and bound. At the reported rates, a single final check removes most of the heating and preparation damage while accepting eight runs out of ten.