The development of fully controlled quantum systems in the laboratory has seen tremendous progress in recent years. One experimental platform which has shown to allow for an excellent level of control are trapped atomic ions, stored in linear radio-frequency traps. Here, one-dimensional chains of up to several tens of ions have already been employed successfully to carry out quantum simulation tasks [1,2]. In our work we aim to scale up the number of individually controllable trapped ions for quantum simulations beyond the state of the art of ~50 particles, by using the platform of planar ion crystals stored in a linear Paul trap. In this way some scalability-related problems of long ion chains, such as high heating rates of the axial motional modes and difficulties in laser-addressing outer ions, can be circumvented.
On this poster we present our new apparatus, the centerpiece of which is a novel monolithic linear Paul trap, enabling us to trap stable 2-dimensional crystals of up to 100 40Ca+ ions. Moreover, we demonstrate our recent results on correlation spectroscopy, implemented in a planar crystal consisting of 91 ions . Correlation spectroscopy is a powerful tool, initially developed in the context of precision metrology, and allows phase differences between qubits to be measured precisely even in the presence of strong correlated phase noise [4,5]. The key idea here is that due to their spatial proximity to each other in the trap the qubits, encoded in each of the 91 ions, will be affected in a collective way by noise processes such as ambient magnetic field fluctuations. Correlations in the outcomes of collective Ramsey measurements provide information about the phase differences between the qubits, even for probe times significantly longer than the coherence time of the individual particles. We apply correlation spectroscopy to characterize a magnetic field gradient, which gives rise to transition frequency differences across the planar ion crystal. In the context of measurement uncertainties, we are able to show that considering N-qubit correlations reduces the phase uncertainty with respect to 2-qubit correlations, and the advantage of using entangled states becomes negligible for N→∞.
 C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C.F. Roos and P. Zoller, Self-verifying variational quantum simulation of lattice models, Nature 569, 355–360 (2019)
 J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, Nature 551, 601–604 (2017)
 H. Hainzer, D. Kiesenhofer, T. Ollikainen, M. Bock, F. Kranzl, M.K. Joshi, G. Yoeli, R. Blatt, T. Gefen and C.F. Roos, Correlation spectroscopy with multi-qubit-enhanced phase estimation, Preprint 2022
 M. Chwalla, K. Kim, T. Monz, P. Schindler, M. Riebe, C. F. Roos and R. Blatt, Precision spectroscopy with two correlated atoms. Appl. Phys. B 89, 483 (2007)
 C. W. Chou, D. B. Hume, M. J. Thorpe, D. J. Wineland and T. Rosenband, Quantum Coherence between Two Atoms beyond Q=1015. Phys. Rev. Lett. 106, 160801 (2011)
|Presenter name||Helene Hainzer|
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