This is an experimental work [1] on mimicking the motion of a particle that is subject to Dirac-type model. It managed to detect a quivering motion, the so-called Zitterbewegung, which is understood to arise from the interference between positive energy components and negative energy components. Such quivering occurs at very high frequency (ten powered to 21 Hz) and with very tiny amplitude (of the order of Compton wavelength) for electrons in vacuum, and very difficult to observe. In this work, the authors considered the Dirac equation in 1+1 dimensions, which was realized with a single trapped ion. For such a 'relativistic' ion, the oscillation period is couple of microseconds.
Experimental recipes:
(1)trap a single 40Ca1 ion in a linear Paul trap22 with axial trapping frequency vax52p31.36MHz and radial trapping frequency vrad52p33 MHz;
(2)prepare the ion in the axial motional ground
state and in the internal state jS1/2,mJ51/2æ (mJ, magnetic quantum
number).
(3)identify spinor states.
How to measure the average position of the trapped ion without a full reconstruction of the state:
To measure the position for a motional state rm, we have to
(1) prepare the ion’s internal state in an eigenstate of sy,
(2) apply a unitary transformation, U(t), that maps information about rm onto the internal states;
(3) record the changing excitation as a function of the probe time t, by measuring
fluorescence22.
Results are displayed on the figures.
[1]Vol 463|7 January 2010| doi:10.1038/nature08688
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