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Fundamental linewidth limit of electromagnetically induced transparency in a thermal Rydberg ladder

Noah Schlossberger, Nikunjkumar Prajapati, Alexandra B. Artusio-Glimpse, Samuel Berweger, Christopher L. Holloway

Abstract

Spectroscopy of Rydberg states has become a popular platform for quantum sensing, with the most common readout scheme being two-photon electromagnetically induced transparency (EIT) using counter-propagating laser beams. In this scheme, the energy resolution of the Rydberg state is set by the spectral linewidth of the EIT feature. While selection criteria for the two-photon resonance can narrow the linewidth to the order of the Rydberg state decay rate for a single atom, the Doppler shift from thermal velocity of the atoms broadens the ensemble linewidth to the order of the decay rate of the intermediate state. Here, we derive an analytic expression for the Doppler residual lineshape in the low-power limit and corroborate the results with experiment. For Rb, we find the full-width at half-maximum linewidth limit to be 1.84 MHz when scanning the coupling laser and measure an experimental linewidth of 2.04 MHz. These linewidths are around a factor of two narrower than previous theoretical estimates as well as previously reported measured linewidths. With this, we demonstrate the most precise two-photon energy resolution of a Rydberg state in thermal vapor to date. We then map out broadening mechanisms near this limit.

Fundamental linewidth limit of electromagnetically induced transparency in a thermal Rydberg ladder

Abstract

Spectroscopy of Rydberg states has become a popular platform for quantum sensing, with the most common readout scheme being two-photon electromagnetically induced transparency (EIT) using counter-propagating laser beams. In this scheme, the energy resolution of the Rydberg state is set by the spectral linewidth of the EIT feature. While selection criteria for the two-photon resonance can narrow the linewidth to the order of the Rydberg state decay rate for a single atom, the Doppler shift from thermal velocity of the atoms broadens the ensemble linewidth to the order of the decay rate of the intermediate state. Here, we derive an analytic expression for the Doppler residual lineshape in the low-power limit and corroborate the results with experiment. For Rb, we find the full-width at half-maximum linewidth limit to be 1.84 MHz when scanning the coupling laser and measure an experimental linewidth of 2.04 MHz. These linewidths are around a factor of two narrower than previous theoretical estimates as well as previously reported measured linewidths. With this, we demonstrate the most precise two-photon energy resolution of a Rydberg state in thermal vapor to date. We then map out broadening mechanisms near this limit.
Paper Structure (9 sections, 20 equations, 4 figures, 1 table)

This paper contains 9 sections, 20 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction.
  2. Theoretical linewidth.
  3. Experimental lineshapes.
  4. Misalignment broadening.
  5. Power broadening.
  6. Other broadening mechanisms.
  7. Methods.
  8. Acknowledgements.
  9. Data availability.

Figures (4)

  • Figure 1: Two-photon EIT configuration. a) The energy level diagram. b) The beam orientations and the resulting Doppler shift on each beam for a moving atom.
  • Figure 2: Experimental lineshapes of the two-photon EIT resonance when scanning the coupling (left) or probe (right) lasers using the $5S_{1/2}(F=3) \rightarrow 5P_{3/2}(F=4) \rightarrow 48S_{1/2}$ ladder in $^{85}$Rb. The theoretical lineshape given by Eq. \ref{['eq:analtyicImChi']} is overlayed in red, with only the amplitude floated between the theory and data. We also display the FWHM predicted by Eq. \ref{['eq:original_FWHM']} ($2\pi\times3.79$ MHz scanning $\Delta_c$ and $2\pi\times2.33$ MHz scanning $\Delta_p$) and by Eq. \ref{['eq:EITLW']} ($2\pi\times1.84$ MHz scanning $\Delta_c$ and $2\pi\times1.13$ MHz scanning $\Delta_p$).
  • Figure 3: Misalignment broadening of the two-photon EIT lineshape. Left: Measured lineshapes at various angles, with the numeric evaluation of Eq. \ref{['eq:misalignmentchi']} overlayed in red. Right: The extracted linewidths are plotted as a funciton of the misalignment angle.
  • Figure 4: Probe power broadening of the two-photon EIT lineshape. Left: Measured lineshapes at various probe powers, with the numeric evaluation of Eq. \ref{['eq:doppint']} overlayed in red. Right: The extracted linewidths are plotted as a function of probe Rabi frequency.