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.
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…
We present a precise measurement of the rubidium ionic core polarizability. The results can be useful for interpreting experiments such as parity violation or black-body radiation shifts in atomic clocks since the ionic core electrons contribute significantly to the total electrical polarizability of rubidium. We report a dipole polarizability $α_d$ = $9.116 \pm 0.009$ $a_0^3$ and quadrupole polarizability $α_q$ = $38.4 \pm 0.6$ $a_{0}^{5}$ derived from microwave and radio-frequency spectroscopy measurements of Rydberg states with large angular momentum. By using a relatively low principal qua…
We investigate the phenomenon of optical bistability in a driven ensemble of Rydberg atoms. By performing two experiments with thermal vapors of rubidium and cesium, we are able to shed light onto the underlying interaction mechanisms causing such a non-linear behavior. Due to the different properties of these two atomic species, we conclude that the large polarizability of Rydberg states in combination with electric fields of spontaneously ionized Rydberg atoms is the relevant interaction mechanism. In the case of rubidium, we directly measure the electric field in a bistable situation via tw…
The response of matter to fields underlies the physical sciences, from particle physics to astrophysics, and from chemistry to biophysics. We observe an atom's response to an electric quadrupole field to second- and higher orders; this arises from the atom's electric quadrupole polarizability and hyperpolarizabilities. We probe a single atomic ion which is excited to Rydberg states and confined in the electric fields of a Paul trap. The quadrupolar trapping fields cause atomic energy level shifts and give rise to spectral sidebands. The observed effects are described well by theory calculation…
We introduce a scheme to entangle Rydberg ions in a linear ion crystal, using the high electric polarizability of the Rydberg electronic states in combination with mutual Coulomb coupling of ions that establishes common modes of motion. After laser-initialization of ions to a superposition of ground- and Rydberg-state, the entanglement operation is driven purely by applying a voltage pulse that shuttles the ion crystal back and forth. This operation can achieve entanglement on a sub-$μ$s timescale, more than two orders of magnitude faster than typical gate operations driven by continuous-wave …
We propose a method for reducing the sensitivity of atomic ground to Rydberg transitions to stray dc electric fields, using microwave-induced dressing of Rydberg states. Calculations are presented for the Cs $\state{90S}{1/2}$ and $\state{90P}{3/2}$ states. With zero dc bias electric field, a two-frequency ac field is used to simultaneously reduce the sensitivity of both states to dc field variations. The sensitivity reduction is a factor of 95 for the $\state{90S}{1/2}$ state and a factor of 1600 for the $\state{90P}{3/2}, m_J=3/2$ state. We also show how the two-frequency ac field can be use…
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 …
Electrometry is performed using Rydberg states to evaluate the quadratic Stark shift of the $5s^2$ $^1\textrm{S}_0-5s5p$ $^3\textrm{P}_0$ clock transition in strontium. By measuring the Stark shift of the highly excited $5s75d\;^1\textrm{D}_2$ state using electromagnetically induced transparency, we characterize the electric field with sufficient precision to provide tight constraints on the systematic shift to the clock transition. Using the theoretically derived, and experimentally verified, polarizability for this Rydberg state we can measure the residual field with an uncertainty well belo…
On-resonance Rydberg atom-based radio-frequency (RF) electric field sensing methods remain limited by the narrow frequency signal detection bands available by resonant transitions. The use of an additional RF tuner field to dress or shift a target Rydberg state can be used to return a detuned signal field to resonance and thus dramatically extend the frequency range available for resonant sensing. Here we investigate three distinct tuning level schemes based on adjacent Rydberg transitions, which are shown to have distinct characteristics and can be controlled with mechanisms based on the tuni…
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 $\sim$~eight 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 prop…
We employ doubly-resonant two-photon excitation into the 74S Rydberg state to spectroscopically measure the dynamic scalar polarizability, alpha 0, and tensor polarizability, alpha 2, of rubidium 5P3/2. To reach the necessary high intensities, we employ a cavity-generated 1064 nm optical-lattice light field, allowing us to obtain intensities near 2x10^11 W/m^2. In the evaluation of the data we use a self-referencing method that renders the polarizability measurement largely free from the intensity calibration of the laser light field. We obtain experimental values alpha 0 =-1149 (pm 2.5 percen…
