Research ArticlePHYSICS

Interference of clocks: A quantum twin paradox

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Science Advances  04 Oct 2019:
Vol. 5, no. 10, eaax8966
DOI: 10.1126/sciadv.aax8966

Figures

  • Fig. 1 Twin paradox and its quantum version.

    (A) As a consequence of relativity, two initially co-located twins experience time dilation when traveling along different world lines. Upon reunion, they find that they aged differently due to the relative motion between them. (B) In a quantum version of this gedankenexperiment, a single individual is traveling along two paths in superposition, serving as his own twin and aging at two different rates simultaneously.

  • Fig. 2 Time dilation in different interferometer geometries.

    Spacetime diagrams for the light-pulse and gravitationally induced trajectories zk and zg, as well as the accelerations z¨k caused by the light pulses, together with the proper-time difference Δτ, the gravito-kick action ΔSgk, the electromagnetic contribution ΔSem/ℏ, and the total phase difference Δφ of an MZI (left), a symmetric RBI (center), and an asymmetric RBI (right). The first two geometries display a symmetric momentum transfer between the two branches, leading to vanishing proper-time differences. However, the asymmetric RBI features a proper-time difference that has the form of a recoil term. The spacetime diagrams also illustrate the connection to the twin paradox by displaying ticking rates (the dashes) of the two twins traveling along the two branches. Both quantum twins in the MZI and symmetric RBI experience the same time dilation, whereas in the asymmetric RBI, one twin stays at rest and the other one leaves and returns so that their proper times are different. The arrows in the plot of z¨k denote the amplitude of the delta functions that scale with ±ℏk/m. Because of the instantaneous nature of z¨k, the integration over time in Eqs. 4 and 6 reduces to a sampling of the positions zk and zg at the time of the pulses such that the respective phase contributions can be inferred directly from the figure.

  • Fig. 3 Interference of quantum clocks.

    (A) Spacetime diagram of a double-loop RBI in superposition of two different internal states (red and blue) and detection at the zero-momentum output port. We indicate the effect of different recoil velocities due to different rest masses of the internal states by slightly diverging trajectories. The different ticking rates of co-moving clocks on the trajectories are indicated by the frequency of the dashing. The dotted gray lines correspond to the light pulses used to redirect the atoms. (B) The output signal P (solid orange) shows a visibility modulation (dashed black), which can be interpreted as the beating of the individual signals Pa/b of the two internal states (solid and dashed gray). To highlight the effect, we have chosen Δm/m = 0.2 in Eq. 11. The visibility of the signal vanishes at ηΩΔτ = π. (C) Interaction of a light pulse with the excited and ground states (blue and red). Because the states follow slightly different world lines and the speed of light is finite, the light pulse will not interact simultaneously with both. Our assumption of instantaneous interaction is shown by the red and blue lines. In the case of finite pulse propagation speed, indicated by the slightly tilted dotted green lines, the interaction is not simultaneous and the red line for the ground state becomes the outermost purple line.

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