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Quantum simulation of mesoscopic systems with highly excited atoms and ions

Final Report Summary - QUANTSIM (Quantum simulation of mesoscopic systems with highly excited atoms and ions)

The interdisciplinary field of ultracold atomic physics has undergone a breathtakingly rapid development during the past years and its achievements have yielded remarkable insights in many-body, condensed matter physics and quantum optics. This success story is rooted in the unique properties of atoms which allow an unprecedented control over their trapping and interaction behaviours, e.g. by exploiting so-called Feshbach resonance the interatomic interaction can be tuned from strongly repulsive to strongly attractive. Also a gas of noninteracting atoms, i.e. 'ideal gas', which constitutes a prime model system in theoretical physics, can be achieved. This seemingly trivial example already reveals the enormous power of ultra cold atoms to simulate complex physical systems, i.e. to serve as a (quantum) simulator. In the proposed research, we envisioned a quantum simulator in which the many-body dynamics is not simulated by the external degrees of freedoms of atoms, but by electrons which constitute the natural constituents of many physical systems. This research is part of a plethora of worldwide activities which aim at turning quantum physics into useful technology. The objectives include simulating molecules and mesoscopic spin chains with highly excited atoms and ions. The specific subject matter of this proposal is systems composed out of few atoms or ions which are spatially sufficiently far separated that individual laser addressing is possible. Such a scenario is naturally achieved in the above-mentioned case of trapped ions. A different way of realising them is to confine atoms in optical or magnetic microtraps. Due to the possibility to discriminate the traps, individual atoms can be separately excited to high-lying electronic states. Once excited atoms confined in distant sites they will interact state-dependently. Such system offers unprecedented possibilities to model and study complex quantum system as well as in quantum computing as all relevant degrees of freedom can be externally controlled.

Key results and advances in line with the objectives

We have studied the properties of calcium ions in a Paul trap and segmented ion traps in the first stage of the project. The static and dynamic behaviors of a single ion and ion crystals were extensively investigated. During the course of these studies, we have achieved the following results.

(1) Single ion properties in an ion trap
We calculated the bare Rydberg states and Rydberg lifetime of Ca+. Using these data, we studied dynamics of a Rydberg ion in an ion trap. The Stark shift and states mixing dynamics of a Rydberg Ca+ in a linear Paul trap were investigated. Our results show that the ionic vibration is strongly coupled with the trap electric fields mediated by the Rydberg electron. Such a coupling can significantly influence the Rydberg ion excitation in the trap.

(2) Long-range interactions between Rydberg ions
We calculated the long-range interactions between two Ca+ both in Rydberg nP state. Apart from the normal multi-polar interactions, the dipole-charge and quadruple-charge interactions between the Rydberg electron and the neighbor ionic core are extremely important. Using a diagonalisation method, we calculated the dependences of the long-range interaction on the Rydberg states and on the distance between the two Rydberg ions.

(3) Electronically excited cold ion crystals
We demonstrated that even a single localised Rydberg excitation in an ion crystal can exhibit pronounced many-body character. In an exemplary illustration in a three-ion crystal, the laser excitation of the central ion to a Rydberg nP state can change its equilibrium structure from a zigzag configuration to a linear string. In addition, vibrational states with large phonon numbers can be coherently prepared during the Rydberg excitation. This study provides a new handle for the coherent manipulation of cold ion crystals with possible applications in quantum information processing.

(4) Mode shaping and parallel quantum computation
The strong mechanical force induced by Rydberg excitations can be used in shaping the crystal vibrations. The mode shaping was demonstrated in a one-dimensional crystal by exciting a small fraction of ions into Rydberg states. We found interesting modes which are strongly localised on the groundstate ions that are blocked by a pair of Rydberg ions. Currently, we are using this feature to design robust multi-qubit quantum gates operated in parallel at high gate speed. In the second stage of the research, we explored dynamics of strongly interacting Rydberg-dressed neutral atoms trapped in an optical lattice. The Rydberg-dressed atom has relatively long lifetime compared to the bare Rydberg state, which is especially useful for the study of long-time coherent dynamics. On the other hand, the strong and long-range interaction still persists in the dressed-atoms. As a result, dynamics of the dressed atoms is described by an extended Bose-Hubbard model, where exotic phases are expected. When the dressed atoms are released from the optical lattice, the long-range interaction brings new dynamical evolution and new symmetry in the interference pattern. These features were used to probe and characterise the long-range Rydberg-dressed interaction.

Research impacts

The results achieved during the research have attracted a great deal of interest worldwide and have led to new collaborations being formed with a number of world-leading research groups. We have built international collaborations with the group of Peter Zoller (Innsbruck, Austria) and the experimental group of F. Schmidt-Kaler and J. Walz (Mainz, Germany). Together with them, we have successfully applied for further funding, CHIST-ERA (R-ION project). Within this collaboration, the group of F. Schmidt-Kaler and J. Walz in University of Mainz, Germany is setting up a Rydberg Ca+ experiment. In the next two years, some of our results can be tested and experimentally realised in the lab. Moreover, we have initialised collaborations with Dr Markus Hennrich, in the University of Innsbruck, Austria. His group is building a new experiment to study Rydberg states of Sr+. As different elements of Rydberg ions have very different physical properties, these explorations can greatly extend the perspectives of Rydberg ions in the study of quantum simulation and quantum computation. In addition, our work has received considerable interest amongst those groups investigating cold trapped ions, as our study enriches current state of the art quantum simulator experiments thereby open up new ways towards the realisation of complex many-body models. Recently, Prof. Richard Thompson, from the Quantum Optics and Laser Science Research Group in Imperial College London, expressed strong interests in our results of the electronically excited cold ion crystal. In the future, the respective physics, such as structural phase transition in the Rydberg ion crystal, could be explored in his group.

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