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 electric field gradients along the ion crystal. We use a two stage continuous dynamic decoupling scheme, to suppress these shifts [4,5,6]. Designed rf-pulses are used to mix the Zeeman sublevels of the 729nm clock transition. The sensitivity to environmental perturbations can be drastically reduced for the dressed states.

With this technique, we could demonstrate a two orders of magnitude longer coherence time on the optical transition, as well as suppression of the QPS on a linear five ion crystal.

Fig. 3) Continuous dynamic decoupling (CDD) sketch (a), two stage CDD level-scheme (b), five ion quadrupole shift suppression (c) and pulse-time spectrogram (d). The coherence time (d) of the measured transition are two orders of magnitude longer and close to the 40Ca+ lifetime limit.

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 a sequence of motional sideband gates and single ion addressing pulses to reach a decoherence free subspace (DFS) with two entangled ions with high fidelity. The DFS is immune to environmental perturbations especailly magnet field fluctuations. We investigate the prospect of entangled ions for quantum metrology in a realistic scenario by comparing two entangled ions with the correspoding classical correlated DFS state.

Fig. 4) a) Ramsey interferometer on two 40Ca+ ion clock transition in decoherence free sub-space. b) Comparison of Ramsey contrast single ion and decoherence free sub-space


[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:

[4] N. Aharon, et. al, Robust Optical Clock Transitions in Trapped Ions Using Dynamical Decoupling, New J. Phys. 21, 083040 (2019), DOI:

[5] V. J. Martínez-Lahuerta, L. Pelzer, K. Dietze, L. Krinner, P. O. Schmidt, and K. Hammerer, Quadrupole Transitions and Quantum Gates Protected by Continuous Dynamic Decoupling, Quantum Sci. Technol. 9, 015013 (2023). DOI: 10.1088/2058-9565/ad085b

[6] L. Pelzer, K. Dietze, V. J. Martínez-Lahuerta, L. Krinner, J. Kramer, F. Dawel, N. C. H. Spethmann, K. Hammerer, and P. O. Schmidt, Multi-Ion Frequency Reference Using Dynamical Decoupling, arXiv:2311.13736.

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


The Team

Lennart Pelzer, Kai Dietze and Piet O. Schmidt