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arXiv:1904.08099 · Physical Review Letters

Highly Polarizable Rydberg Ion in a Paul Trap

Gerard T. Higgins, Fabian Pokorny, Chi Zhang, Markus Hennrich

Published Oct 11, 2019• 19 citations
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Abstract

Usually the influence of the quadratic Stark effect on an ion's trapping potential is minuscule and only needs to be considered in atomic clock experiments. In this work we excite a trapped ion to a Rydberg state with polarizability ∼8 orders of magnitude higher than a low-lying electronic state; we find that the highly polarizable ion experiences a vastly different trapping potential owing to the Stark effect. We observe changes in trap stiffness, equilibrium position, and minimum potential, which can be tuned using the trapping electric fields. These effects lie at the heart of several proposed studies, including a high-fidelity submicrosecond entangling operation; in addition we demonstrate these effects may be used to minimize ion micromotion. Mitigation of Stark effects is important for coherent control of Rydberg ions; we illustrate this by carrying out the first Rabi oscillations between a low-lying electronic state and a Rydberg state of an ion.

DOI
10.1103/physrevlett.123.153602

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arXiv:2208.11117•Aug 23, 2022•0 citations
Usually the influence of the quadratic Stark effect on an ion's trapping potential is minuscule and only needs to be considered in atomic clock experiments. In this work we excite a trapped ion to a Rydberg state with polarizability ∼8 orders of magnitude higher than a low-lying electronic state; we find that the highly polarizable ion experiences a vastly different trapping potential owing to the Stark effect. We observe changes in trap stiffness, equilibrium position, and minimum potential, which can be tuned using the trapping electric fields. These effects lie at the heart of several proposed studies, including a high-fidelity submicrosecond entangling operation; in addition we demonstrate these effects may be used to minimize ion micromotion. Mitigation of Stark effects is important for coherent control of Rydberg ions; we illustrate this by carrying out the first Rabi oscillations between a low-lying electronic state and a Rydberg state of an ion.
Trapped Rydberg ions are a promising new system for quantum information processing. They have the potential to join the precise quantum operations of trapped ions and the strong, long-range interactions between Rydberg atoms. Combining the two systems is not at all straightforward. Rydberg atoms are severely affected by electric fields which may cause Stark shifts and field ionization, while electric fields are used to trap ions. Thus, a thorough understanding of the physical properties of Rydberg ions due to the trapping electric fields is essential for future applications. Here we report the observation of two fundamental trap effects. First, we investigate the interaction of the Rydberg electron with the trapping electric quadrupole fields which leads to Floquet sidebands in the excitation spectra. Second, we report on the modified trapping potential in the Rydberg state compared to the ground state which results from the strong polarizability of the Rydberg ion. By controlling both effects we observe resonance lines close to their natural linewidth demonstrating an unprecedented level of control of this novel quantum platform.
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.
Trapped Rydberg ions are a promising new system for quantum information processing. They have the potential to join the precise quantum operations of trapped ions and the strong, long-range interactions between Rydberg atoms. Technically, the ion trap will need to stay active while exciting the ions into the Rydberg state, else the strong Coulomb repulsion will quickly push the ions apart. Thus, a thorough understanding of the trap effects on Rydberg ions is essential for future applications. Here we report the observation of two fundamental trap effects. First, we investigate the interaction of the Rydberg electron with the quadrupolar electric trapping field. This effect leads to Floquet sidebands in the spectroscopy of Rydberg D-states whereas Rydberg S-states are unaffected due to their symmetry. Second, we report on the modified trapping potential in the Rydberg state compared to the ground state which results from the strong polarizability of the Rydberg ion. We observe the resultant energy shifts as a line broadening which can be suppressed by cooling the ion to the motional ground state in the directions orthogonal to the excitation laser.
Highly excited Rydberg states are usually extremely polarizable and exceedingly sensitive to electric fields. Because of this Rydberg ions confined in electric fields have state-dependent trapping potentials. We engineer a Rydberg state that is insensitive to electric fields by coupling two Rydberg states with static polarizabilities of opposite sign, in this way we achieve state-independent magic trapping. We show that the magically-trapped ion can be coherently excited to the Rydberg state without the need for control of the ion's motion.
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.