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arXiv:2005.05726 · Physical Review Letters

Long-Range Multibody Interactions and Three-Body Antiblockade in a Trapped Rydberg Ion Chain

Filippo Maria Gambetta, Chi Zhang, Markus Hennrich, Igor Lesanovsky, Weibin Li

Published Sep 22, 2020• 47 citations
arXivHTMLPDF

Abstract

Trapped Rydberg ions represent a flexible platform for quantum simulation and information processing that combines a high degree of control over electronic and vibrational degrees of freedom. The possibility to individually excite ions to high-lying Rydberg levels provides a system where strong interactions between pairs of excited ions can be engineered and tuned via external laser fields. We show that the coupling between Rydberg pair interactions and collective motional modes gives rise to effective long-range and multibody interactions consisting of two, three, and four-body terms. Their shape, strength, and range can be controlled via the ion trap parameters and strongly depends on both the equilibrium configuration and vibrational modes of the ion crystal. By focusing on an experimentally feasible quasi one-dimensional setup of ^{88}Sr^{+} Rydberg ions, we demonstrate that multibody interactions are enhanced by the emergence of soft modes associated with, e.g., a structural phase transition. This has a striking impact on many-body electronic states and results-for example-in a three-body antiblockade effect that can be employed as a sensitive probe to detect structural phase transitions in Rydberg ion chains. Our study unveils the possibilities offered by trapped Rydberg ions for studying exotic phases of matter and quantum dynamics driven by enhanced multibody interactions.

DOI
10.1103/physrevlett.125.133602

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Trapped Rydberg ions represent a flexible platform for quantum simulation and information processing that combines a high degree of control over electronic and vibrational degrees of freedom. The possibility to individually excite ions to high-lying Rydberg levels provides a system where strong interactions between pairs of excited ions can be engineered and tuned via external laser fields. We show that the coupling between Rydberg pair interactions and collective motional modes gives rise to effective long-range and multibody interactions consisting of two, three, and four-body terms. Their shape, strength, and range can be controlled via the ion trap parameters and strongly depends on both the equilibrium configuration and vibrational modes of the ion crystal. By focusing on an experimentally feasible quasi one-dimensional setup of ^{88}Sr^{+} Rydberg ions, we demonstrate that multibody interactions are enhanced by the emergence of soft modes associated with, e.g., a structural phase transition. This has a striking impact on many-body electronic states and results-for example-in a three-body antiblockade effect that can be employed as a sensitive probe to detect structural phase transitions in Rydberg ion chains. Our study unveils the possibilities offered by trapped Rydberg ions for studying exotic phases of matter and quantum dynamics driven by enhanced multibody interactions.
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State-dependent conformational changes play a central role in molecular dynamics, yet they are often difficult to observe or simulate due to their complexity and ultrafast nature. One alternative approach is to emulate such phenomena using quantum simulations with cold, trapped ions. In their electronic ground state, these ions form long-lived Wigner crystals. When excited to high-lying electronic Rydberg states, the ions experience a modified trapping potential, resulting in a strong coupling between their electronic and vibrational degrees of freedom. In an ion crystal, this vibronic coupling creates electronic state-dependent potential energy surfaces that can support distinct crystal structures-closely resembling the conformational changes of molecules driven by electronic excitations. Here, we present the first experimental observation of this effect, by laser coupling a single ion at the center of a three-ion crystal to a Rydberg state. By tuning the system close to a structural phase transition, the excitation induces a state-dependent conformational change, transforming the Wigner crystal from a linear to a zigzag configuration. This structural change leads to a strong hybridization between vibrational and electronic states, producing a clear spectroscopic signature in the Rydberg excitation. Our findings mark the first experimental step toward using Rydberg ions to create and study artificial molecular systems.
Atoms and ions confined with electric and optical fields form the basis of many current quantum simulation and computing platforms. When excited to high-lying Rydberg states, long-ranged dipole interactions emerge which strongly couple the electronic and vibrational degrees of freedom through state-dependent forces. This vibronic coupling and the ensuing hybridization of internal and external degrees of freedom manifest through clear signatures in the many-body spectrum. We illustrate this by considering the case of two trapped Rydberg ions, for which the interaction between the relative vibrations and Rydberg states realizes a quantum Rabi model. We proceed to demonstrate that the aforementioned hybridization can be probed by radio frequency spectroscopy and discuss observable spectral signatures at finite temperatures and for larger ion crystals.
Trapped ions excited to high-lying electronic states combine strongly coupled collective vibrational and electronic degrees of freedom with long-ranged interparticle interactions. These ingredients enable the quantum simulation of biochemical processes, associated with the dynamics of excitons in non-perturbative parameter regimes. The key feature of such a quantum simulator are electronic-state-dependent molecular potential surfaces which can be strongly coupled. This allows to shed light on a variety of mechanisms underlying exciton transport. We illustrate this in a system of three trapped ions, which is amenable to an ab initio treatment. Given that ion traps can be routinely prepared with hundreds of ions, these quantum simulators can immediately realise scenarios which are inaccessible by current numerical methods.
Trapped ions are one of the leading platforms for quantum technologies due to their excellent control over their internal electronic and external motional degrees of freedom. Many techniques and interesting effects rely on the coupling of the ions to their motion, which makes precise control of them paramount. In this work, two novel techniques for motional state detection are presented. They allow the probing of certain motional states with a single measurement, without affecting the motion of the measured ion. These techniques are employed to generate and detect a highly entangled state between two motional modes in a novel manner. Furthermore, we harness the rich and intricate dynamics arising from the coupling of the ion's motion to its electronic degrees of freedom to study the emergence of interference. Theoretical predictions, describing interference both in the quantum and the classical regimes, are verified, offering a new and more intuitive description of interference, not just for trapped ions, but for a variety of systems that can be described in a similar way. On the other hand, Rydberg excitation with trapped ions enables new interaction mechanisms and makes them extremely sensitive to their surroundings. This thesis presents advances towards Rydberg experiments with longer ion strings and concludes with a first demonstration of coherent population transfer between Rydberg states in trapped ions. The methods developed significantly increase the toolbox for trapped Rydberg ions, enabling more sophisticated experiments, especially when multiple different Rydberg states are involved, and allow more flexibility when using longer ion strings.
Quantum simulation of interacting many-body spin systems is routinely performed with cold trapped ions, and systems with hundreds of spins have been studied in one and two dimensions. In the most common realizations of these platforms, spin degrees of freedom are encoded in low-lying electronic levels, and interactions among the spins are mediated through crystal vibrations. Here we propose a new approach which enables the quantum simulation of two-dimensional spin systems with interaction strengths that are increased by orders of magnitude. This, together with the unprecedented longevity of trapped ions, opens an avenue for the exploration of phenomena that take place on long timescales, e.g., slow and collective relaxation in frustrated and kinetically constrained systems. Our platform makes use of the strong dipolar interactions among electronic Rydberg states and planar confinement provided by a Penning trap. We investigate how the strong electric and magnetic fields that form this trap affect the properties of the Rydberg states and show that spin-spin interaction strengths on the order of MHz are achievable under experimentally realistic conditions. As a brief illustration of the capabilities of this quantum simulator, we study the entanglement in a frustrated spin system realized by three ions.