Designed quantum states for metrology

Abstract/Short Project description

In this project, we develop methods to extend the excellent accuracy of single ion clocks to multi ion crystals. Increasing the number of particles, improves signal-to-noise ratio of the clock interrogation and therefore shortens the average times for clock interrogation. Entangling of the ions can reduce this further by surpassing the standard quantum limit.

Ion trap and crystals

We investigate 40Ca+-ions trapped in a segmented Paul trap with low excess micromotion [1]. The compact and versatile setup [2] enables us to test methods to improve the statistical uncertainty of ion-based clocks, while maintaining their accuracy.

For suppressing of the motional frequency shifts emerging from residual ion motion, we employ different laser cooling technics. With doppler-cooling on the broad 397nm transition, temperatures in the mK range are reached. Further reduction in temperature is done with electromagnetic induced transparency (EIT) [3] cooling and/or pulsed sideband cooling. The advantages of the first are a fast cooling time, as well as a cooling over a large range of secular motional frequencies, thus several motion modes can get cooled at once. With the latter we archive the lowest motional mode excitation on the order of n≈0.02.

Fig. 1) sCMOS camera pictures of different ion crystals. Depending on the Voltages applied to the Paul trap and the number of ions, different ion crystal shapes from linear (a), to 3D-spherical (c) are possible.
Fig. 2) Photography of the four layer segmented Paul trap. On chip filtering electronics and temperature sensor are visible. The rf-voltage is feed in via copper strips.

Continuous Dynamic Decoupling

The frequency stability of extended ion crystals suffers from several environmental perturbations.

For the 40Ca+ ions, the largest contributions are the Zeeman shift arising from magnet field fluctuations as well as inhomogeneous broadening like quadrupole (QPS) and tensor stark shift (TASS) caused by different electric field gradients along the ion crystal. We use a continuous dynamic decoupling scheme, to suppress these shifts [4]. Designed rf-pulses are used to mix the Zeeman sublevels of the 729nm clock transition. The sensitive to environmental perturbations can be drastically reduced for the dressed states.

With this technic, we could show spectroscopy of the clock transition of a single ion close to the natural lifetime decay limit (see Fig. 3), as well as suppression of the QPS on a linear five ion crystal.

Fig. 3) Continuous dynamic decoupling schematic (a), level-scheme (b), dressed state spectroscopy (c) and pulse-time spectrogram (d). The linewidth (c) and decay (d) of the measured transition is mainly limited by the natural lifetime limit of 40Ca+.

Entanglement gain for metrology

For entangled ions the statistical uncertainty of the clock interrogation is not limited by standard quantum projection noise (QPN). Depending on the degree of entanglement, the scaling of the uncertainty with the number of ions changes [5]. We employ Mølmer-Sørensen gates to entangle two ions with high fidelity. With the help of single ion addressing pulses, we reach a decoherence free subspace (DFS), immune to environmental perturbations. We investigate the prospect of entangled ions for quantum metrology for a realistic scenario.

Fig. 4) Level scheme of an decoherence free sub-space in 40Ca+ clock transition.

References

[1] J. Keller, et. al, Probing Time Dilation in Coulomb Crystals in a High-Precision Ion Trap, Phys. Rev. Applied, 11, 011002 (2019), DOI: 10.1103/PhysRevApplied.11.011002

[2] S. Hannig, et. al, Towards a transportable aluminium ion quantum logic optical clock, Rev. Sci. Instrum., 90 (053204) May (2019), DOI: 10.1063/1.5090583

[3] N. Scharnhorst, et. al, Experimental and theoretical investigation of a multimode cooling scheme using multiple electromagnetically-induced-transparency resonances, Physical Review A (2018) ), DOI: doi.org/10.1103/PhysRevA.98.023424

[4] N. Aharon, et. al, Robust Optical Clock Transitions in Trapped Ions Using Dynamical Decoupling, New J. Phys. 21, 083040 (2019), DOI: doi.org/10.1088/1367-2630/ab3871

[5] Kessler, et. al, Heisenberg-Limited Atom Clocks Based on Entangled Qubits, Phys. Rev. Lett. 112, 190403, DOI : 10.1103/PhysRevLett.112.190403