Hello all,
I recently gave a seminar for WG2 on our recent preprint “Quantum signatures of proper time in optical ion clocks,” written in collaboration with Gabriel Sorci, Dietrich Leibfried, Christian Sanner, and Igor Pikovski [1]. Dennis suggested I start a discussion on this work; feel free to contribute in the replies, I will be glad to discuss further.
In our paper, we show that optical ion clocks can be used to probe quantum signatures of proper time that cannot be explained by a semiclassical description (e.g. one in which the clock’s evolution occurs with respect to a fixed external parameter). We derive observable signatures in optical ion clocks that require a “quantisation” of proper time through dependence on the momentum operator, tau = tau(p-hat^2). We show that by preparing initial squeezed motional states of the clock, the interferometric visibility of the internal states (i.e. “the clock”) observably reduces, an effect that results from entanglement between the internal and external degrees of freedom of the clock. We also show that this quantum treatment of proper time leads to anomalous excitation of the clock’s motion when initially prepared in its ground state, leading to a new frequency shift dubbed “quantum second-order Doppler shift”.
Albert raised some good questions following the seminar, and the discussion can be viewed on the recording of the seminar on the RQI-Cost YouTube page. One question was whether state-engineering the ground and excited states of the clock to follow the same trajectory can “mitigate” the visibility loss effect.
[1] https://arxiv.org/abs/2509.09573
Thank you, Josh, for starting this discussion on the interesting work that you presented in your talk.
Just for clarification: rather than "engineering" the state, I was talking about a choice of trapping potentials that leads to the same frequencies at the trap minima for both internal states. This property guarantees that both the motion of the atoms near the trap minima and the ground-state energy of the potentials are the same for the two internal states.
More specifically, I was saying that for some applications the kind of effect that you considered can be regarded as a problem, but it can be circumvented by "engineering" the trapping potential. This is possible in cases where the trapping potential for the two internal states can be separately adjusted. A particularly relevant example is the optical potential in optical atomic clocks based on neutral atoms trapped in optical lattices, as I briefly explain next.
Indeed, if one uses a "magic" wavelength for the optical lattice, the optical potential is the same for both internal states. However, the frequency of the approximately harmonic function at the minima of the potential will be slightly different due to the mass difference \Delta m = \Delta E / c^2 between atoms in the two different internal states, i.e. \Omega_1 \neq \Omega_2. This in turn implies a different ground-state energy for the atom's center-of-mass degree of freedom in each lattice site, \hbar \Omega_1 / 2 \neq \hbar \Omega_2 / 2, which can be a problem.
Nevertheless, for blue-detuned optical lattices, one can choose a suitable laser wavelength, differing only slightly from the "magic" wavelength, that leads to different optical potentials but with the same frequencies \Omega_1 = \Omega_2 at the minima. In fact, this wavelength would be automatically selected in the usual calibration process performed in such experiments. A more detailed discussion can be found in sec. IV.C (page 8) of this reference: https://doi.org/10.1103/PhysRevX.10.021014
There it is also explained that the effects due to \Omega_1 \neq \Omega_2 for the "magic" wavelength typically lie beyond the sensitivity of the state-of-the-art atomic clocks based on neutral atoms trapped in optical lattices. For clocks using charged ions, where the electrostatic trapping potential is the same for atoms in both internal states, one also has \Omega_1 \neq \Omega_2. Compared to optical lattices, the effect can be a bit larger because the frequencies at the minimum of the trapping potential are typically larger in this case.
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The other discussion point that I brought up at the end of the seminar had to do with the conceptual interpretation of the results presented and their (partial) relation to time dilation. I can elaborate on that in a separate post.