**Precision Measurements Using Rydberg Atoms**

** Raithel Lab, University of Michigan **

Participating Students: Ryan Cardman, Andira Ramos '19, Kaitlin Moore '17

Rydberg atoms are great candidates for precision measurements. Their long lifetimes enable longer interaction times with probing fields. This leads to narrower peak linewidths, which, in precision measurements, is key for determining transition frequencies accurately. Moreover, their weakly bound electron makes it possible to trap Rydberg atoms and drive microwave transitions between these states using optical ponderomotive potentials. These lead to more efficient trapping and to Fourier-limited linewidths. To exploit the advantages of Rydberg atoms, we have built an ultra-high vacuum, cold-atom spectroscopy apparatus equipped with three dimensional electric and magnetic field controls that allows us to perform precision measurements (shown below). Additionally, the experiment is in thermal contact with a liquid-helium cryostat for shielding blackbody radiation and extending the radiative lifetimes of our Rydberg ensembles.

*Our in-vacuum spectroscopy enclosure consists of six plate electrodes for electric-field control.*

Rydberg Constant Measurement (RCM)

The Rydberg constant is a key physical constant which is employed in
determining atomic energy levels of any atom and is related to other
fundamental constants. The current value of the Rydberg constant started to
be questioned with the appearance of the "proton radius puzzle". In order to
help solve this puzzle, we have proposed performing a precision measurement
of the Rydberg constant using cold circular Rydberg atoms. Circular atoms are
in the highest *l* and *m*-state possible for a given *n*.
This provides us with a measurement independent from the proton size and QED
effects, which, in turn, should help in solving the proton radius puzzle. The
atoms are trapped using a Rydberg-atom optical lattice and transitions are
driven using a recently demonstrated lattice-modulation technique (explained
below) to perform Doppler-free spectroscopy. The circular-state transition
frequency yields the Rydberg constant.

*Our apparatus for precision spectroscopy.*

Spectroscopy and Coherent Control of Rydberg Atoms with Optical Lattices

When Rydberg atoms are trapped in optical lattices that are periodically modulated at resonant frequencies between two Rydberg levels, Fourier-
limited, Doppler-free transitions can be driven, free of *l* selection
rules. This effect comes from the fact that a Rydberg atom's electronic wave
function sees a spatially dependent potential within a standing wave of
light. Therefore, this provides an angular-momentum coupling to a state with
the same or opposite parity. Using an amplitude-modulated optical lattice, we
have already demonstrated this technique and will use it for a Rydberg
constant measurement. Furthermore, we have recently developed the theoretical
framework for using one and two-dimensional time-dependent ponderomotive
optical potentials to initialize Rydberg atoms in circular states for
spectroscopy.

*Optical molasses of ^{85}Rb at sub-Doppler
temperatures.*

Recent Breakthroughs

As a demonstration of how well we can make measurements with our apparatus, we obtained the hyperfine coupling constant for the * nS _{1/2}* states of

*a) Fourier-limited 45S _{1/2} hyperfine peaks
obtained by mm-wave spectroscopy. *

*b) Splitting of those peaks as a function of
1/n ^{*3}. *

Publications

1. V.S. Malinovsky, K.R. Moore, and G. Raithel, Phys. Rev. A **101**, 033414 (2020).

2. R. Cardman and G. Raithel, Phys. Rev. A **101**, 013434 (2020).

3. A. Ramos,
R. Cardman, and G. Raithel, Phys. Rev. A **100**, 062515 (2019).

4. A. Ramos, K. Moore, and G. Raithel, Phys. Rev. A **96**, 032513 (2017).

5. K.R.
Moore and G. Raithel, Phys. Rev. Lett. **115**, 163003 (2015).

6. K.R.
Moore, S.E. Anderson, and G. Raithel, Nat. Commun.** 6**, 6090 (2015).

This work is supported by NASA, the NSF, and NIST.

Webpage author: Ryan Cardman