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Rydberg State Engineering and Motional Interference with Trapped Ions

Robin Thomm

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

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.

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Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.

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Rydberg ions in coherent motional states: A new method for determining the polarizability of Rydberg ions

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We present a method for measuring the polarizability of Rydberg ions confined in the harmonic potential of a Paul trap. For a highly excited electronic state, the coupling between the electronic wave function and the trapping field modifies the excitation probability depending on the motional state of the ion. This interaction strongly depends on the polarizability of the excited state and manifests itself in the state-dependent secular frequencies of the ion. We initialize a single trapped $^{40}$Ca$^+$ ion from the motional ground state into coherent states with $|α|$ up to 12 using electric voltages on the trap segments. The internal state, firstly initialised in the long-lived 3D$_{5/2}$ state, is excited to a Rydberg S$_{1/2}$-state via the 5P$_{3/2}$ state in a two-photon process. We probe the depletion of the 3D$_{5/2}$ state owing to the Rydberg excitation followed by a decay into the internal ground 4S$_{1/2}$ state. By analysing the obtained spectra we extract the polarizability of Rydberg states which agree with numerical calculations. The method is easy-to-implement and applicable to different Rydberg states regardless of their principal or angular quantum numbers. An accurate value of the state polarizability is needed for quantum gate operations with Rydberg ion crystals.

arXiv:2208.11117•Aug 23, 2022•0 citations
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.
Trapped ion systems are at the forefront of the development of various forms of quantum technology. Continuing to improve and establish new devices and techniques for the control of trapped ions is a vital element of ongoing research. In this thesis, a range of experiments which aim to expand the quantum toolkit of trapped ion systems are presented. These results primarily focus on the control and detection of bound motional states of a single trapped 88Sr+ ion for the purposes of quantum simulation and computation. We demonstrate how the interference between motional modes can reveal an interesting new interpretation of the mechanism behind light-matter interaction and introduce two separate techniques for the detection of motional states, based on the Autler-Townes effect and the use of composite pulses respectively. Additionally, we introduce a novel method to perform micromotion compensation and build upon previous works studying the effects of trapping electric fields on a single trapped Rydberg ion, observing the second-order quadrupolar response of the ion with a highly precise sensitivity.
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.
Trapped Rydberg ions are a novel approach to quantum information processing [1], [2]. Qubit rotations in the ion's lower lying electronic states are combined with entanglement operations that take advantage of strong Rydberg interactions [3]. In our experimental setup we excite trapped strontium ions from the metastable 4D state to the Rydberg manifold using a two photon excitation process. Certain properties of the ion become more prominent for highly excited states. One example is the polarizabilty which reacts to the surrounding electric field of the trapping electrodes. While effects due to the polarizability are negligible for lower lying states, they become more prominent for highly-excited states. This change leads to an altered trapping potential for the high lying Rydberg states, as shown in Fig. 1 [4]. For previous experiments those shifts have always been compensated for to perform, for example, sub-microsecond entangling gates between trapped ions [5]. However, this trapping field displacement can also be used to coherently control the ions' motion.
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
Abstract We present a method for measuring the polarizability of Rydberg ions confined in the harmonic potential of a Paul trap. For a highly excited electronic state, the coupling between the electronic wave function and the trapping field modifies the excitation spectra depending on the motional state of the ion. This interaction strongly depends on the polarizability of the excited state and manifests itself in the state-dependent secular frequencies of the ion. We initialize a single trapped 40 Ca + ion from the motional ground state into coherent states with | α | up to 12 using electric voltages on the trap segments. The internal state, firstly initialised in the long-lived 3D 5 / 2 state, is excited to a Rydberg S 1 / 2 -state via the 5P 3 / 2 state in a two-photon process. We probe the depletion of the 3D 5 / 2 state owing to the Rydberg excitation followed by a decay into the internal ground 4S 1 / 2 state. By analysing the obtained spectra we extract the polarizability of Rydberg states which agree with numerical calculations. The method is applicable to different Rydberg states regardless of their principal or angular quantum numbers. An accurate value of the state polarizability is needed for quantum gate operations with Rydberg ion crystals.
We present a method for measuring the polarizability of Rydberg ions confined in the harmonic potential of a Paul trap. For a highly excited electronic state, the coupling between the electronic wave function and the trapping field modifies the excitation probability depending on the motional state of the ion. This interaction strongly depends on the polarizability of the excited state and manifests itself in the state-dependent secular frequencies of the ion. We initialize a single trapped 40^{40}40Ca+^++ ion from the motional ground state into coherent states with ∣α∣|α|∣α∣ up to 12 using electric voltages on the trap segments. The internal state, firstly initialised in the long-lived 3D5/2_{5/2}5/2​ state, is excited to a Rydberg S1/2_{1/2}1/2​-state via the 5P3/2_{3/2}3/2​ state in a two-photon process. We probe the depletion of the 3D5/2_{5/2}5/2​ state owing to the Rydberg excitation followed by a decay into the internal ground 4S1/2_{1/2}1/2​ state. By analysing the obtained spectra we extract the polarizability of Rydberg states which agree with numerical calculations. The method is easy-to-implement and applicable to different Rydberg states regardless of their principal or angular quantum numbers. An accurate value of the state polarizability is needed for quantum gate operations with Rydberg ion crystals.