A single-ion trap with minimized ion–environment interactions

The Dirac equation successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation-relativistic quantum mechanics-is considered to be the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects, such as Klein's paradox and 'Zitterbewegung', an unexpected quivering motion of a free relativistic quantum particle. These and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. In recent years, there has been increased interest in simulations of relativistic quantum effects using different physical set-ups, in which parameter tunability allows access to different physical regimes. Here we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, as well as the crossover from relativistic to non-relativistic dynamics. The high level of control of trapped-ion experimental parameters makes it possible to simulate textbook examples of relativistic quantum physics.

Singly ionized ytterbium, with ultranarrow optical clock transitions at 467 and 436 nm, is a convenient system for the realization of optical atomic clocks and tests of present-day variation of fundamental constants. We present the first direct measurement of the frequency ratio of these two clock transitions, without reference to a cesium primary standard, and using the same single ion of 171Yb+. The absolute frequencies of both transitions are also presented, each with a relative standard uncertainty of 6×10(-16). Combining our results with those from other experiments, we report a threefold improvement in the constraint on the time variation of the proton-to-electron mass ratio, μ/μ=0.2(1.1)×10(-16)  yr(-1), along with an improved constraint on time variation of the fine structure constant, α/α=-0.7(2.1)×10(-17)  yr(-1).

Accurate measurements of different transition frequencies between atomic levels of the electronic and hyperfine structure over time are used to investigate temporal variations of the fine structure constant α and the proton-to-electron mass ratio μ. We measure the frequency of the (2)S1/2→(2)F7/2 electric octupole (E3) transition in (171)Yb(+) against two caesium fountain clocks as f(E3)=642,121,496,772,645.36  Hz with an improved fractional uncertainty of 3.9×10(-16). This transition frequency shows a strong sensitivity to changes of α. Together with a number of previous and recent measurements of the (2)S1/2→(2)D3/2 electric quadrupole transition in (171)Yb(+) and with data from other elements, a least-squares analysis yields (1/α)(dα/dt)=-0.20(20)×10(-16)/yr and (1/μ)(dμ/dt)=-0.5(1.6)×10(-16)/yr, confirming a previous limit on dα/dt and providing the most stringent limit on dμ/dt from laboratory experiments.