Measuring the Rydberg Constant Using Circular Rydberg Atoms in an Intensity-Modulated Optical Lattice

Abstract

A method for performing a precision measurement of the Rydberg constant, $R_{\infty }$, using cold circular Rydberg atoms is proposed. These states have long lifetimes, as well as negligible quantum-electrodynamics (QED) and no nuclear-overlap corrections. Due to these advantages, the measurement can help solve the "proton radius puzzle" [Bernauer, Pohl, Sci. Am. 310, 32 (2014)]. The atoms are trapped using a Rydberg-atom optical lattice, and transitions are driven using a recently-demonstrated lattice-modulation technique to perform Doppler-free spectroscopy. The circular-state transition frequency yields $R_{\infty }$. Laser wavelengths and beam geometries are selected such that the lattice-induced transition shift is minimized. The selected transitions have no first-order Zeeman and Stark corrections, leaving only manageable second-order Zeeman and Stark shifts. For Rb, the projected relative uncertainty of $R_{\infty }$ in a measurement under the presence of the Earth's gravity is $10^{-11}$, with the main contribution coming from the residual lattice shift. This could be reduced in a future micro-gravity implementation. The next-important systematic arises from the Rb${}^{+}$ polarizability (relative-uncertainty contribution of $\approx 3\times 10^{-12}$).

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• Theory and applications of atomic and ionic polarizabilities
• Fundamental constants and tests of theory in Rydberg states of hydrogen-like ions
• Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium
• Coherent transfer between low-angular momentum and circular Rydberg states
• Review of experimental and theoretical status of the proton radius puzzle
• Fundamental constants and tests of theory in Rydberg states of one-electron ions
• Forbidden atomic transitions driven by an intensity-modulated laser trap

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• Probing new physics using Rydberg states of atomic hydrogen
• Measurement of Rb g-series quantum defect using two-photon microwave spectroscopy
• Photoionization of Rydberg Atoms in Optical Lattices
• Metrology of Rydberg states of the hydrogen atom
• Modulation spectroscopy of Rydberg atoms in an optical lattice
• A magneto-optical trap with millimeter ball lenses
• Photoionization of $nS$ and $nD$ Rydberg atoms of Rb and Cs from the near-infrared to the ultraviolet spectral region
• Baryon asymmetry constraints on Extended Symmetric Teleparallel Gravity
• Determination of Quantum Defects and Core Polarizability of Atomic Cesium via Terahertz and Radio-Frequency Spectroscopy in Thermal Vapor
• Driving alkali Rydberg transitions with a phase-modulated optical lattice
• Gauge effects in bound-bound Rydberg-transition matrix elements
• Forces on alkali Rydberg atoms due to non-linearly polarized light
• Blackbody radiation Zeeman shift in Rydberg atoms