Fig. 1. Experimental setup and procedure. (a) Energy levels of the two-photon Rydberg excitation of ⁴⁰K. The three energy levels are shown as |4S_1/2, F = 9/2, m_F = 9/2〉 ≡ |g〉 → |4P_3/2, F = 11/2, m_F = 11/2〉 ≡ |e〉 → |nl〉 ≡ |r〉, with l = 0 (S) or 2 (D). (b) Optical setup. The laser beam for absorption imaging is σ⁺-polarized and collimated with a Gaussian waist of 2 cm propagating along the z^. The probe laser polarized linearly along x^ for the EIT propagates along the y axis and is collimated with a Gaussian waist of 2 mm. The coupling laser for exciting from intermediate state |e〉 to Rydberg states |r〉 is linearly polarized along z^ with 1/e² radii of 200 µm and illuminates the atom cloud in the x–y plane. (c) Time sequence for the EIT; after applying the probe and coupling light, the atoms ballistically expand to take the TOF absorption image with a CCD.

Fig. 2. Schematic of the laser system for 767 and 457 nm. (a) Locking scheme for 767 and 457 nm. The probe laser beam with wavelength 767 nm is produced by an ECDL, which can be locked to the transition between |F = 9/2, m_F = 9/2〉 state of 4S_1/2 and |F^′ = 11/2, m_F^′ = 11/2〉 state of 4P_3/2. The coupling laser beam is derived from a commercial frequency-doubled diode laser system (Toptica TA-SHG pro) providing 800 mW output at 455.5–458.5 nm. In order to improve the frequency stability, the probe and coupling lasers are frequency-locked to a thermally stabilized ultralow expansion glass cavity via the PDH method. To shift the arbitrary laser frequency detuning of probe and coupling lasers around the resonant transition, we use an additional signal generator to generate a sideband before PDH locking. (b) Transmitted signal of the phase-modulated 767 nm laser (blue curve) on the cavity, which is obtained by sweeping the carrier frequency of the 767 nm laser; the red curve represents the corresponding error signal. Here, the output signals of MW-FG and RF-FG are 120 and 28 MHz, respectively.

Fig. 3. Measurement of the Rydberg–EIT spectrum. The spectrum as a function of the probe beam detuning δ_p when the weak probe laser is locked to the (a1) SAS and (b1) ultrastable cavity, respectively, in the absence of a coupling laser. The loss profiles correspond to the transition from the F = 9/2 state of 4S_1/2 to |F^′ = 11/2, 9/2, 7/2〉 state of 4P_3/2. The unusual Rydberg–EIT spectrum in the ladder scheme while scanning the coupling detuning δ_c and locking the probe laser to (a2) SAS and (b2) ultrastable cavity; the normal Rydberg–EIT spectrum scanning the probe detuning δ_p when the coupling laser is fixed, where the probe laser is frequency-locked by the (a3) SAS and (b3) ultrastable cavity. The ladder system is shown as |g〉 →|e〉 →|r〉 ≡ |37s〉. The optical density of the remaining atomic sample is normalized to a value of 1 in the absence of the coupling laser. Experimental data in (a2) and (b2) are enlarged by a factor of 3 for comparison with (a3) and (b3) on the same scale. The fitting values for (a1)–(a3) are Ω_c = 2π × 11.93 MHz, γ_eg = 2π × 25 MHz, γ_rg = 2π × 12 MHz, and δ_c = 2π × (−1.55) MHz. The fitting values for (b1)–(b3) are Ω_c = 2π × 11.93 MHz, γ_eg = 2π × 20.1 MHz, γ_rg = 2π × 6.01 MHz, and δ_c = 2π × (−1.48) MHz. The red open squares show the experimental data. The solid lines in (a1) and (b1) serve as a guide to the eye. The blue solid curve is the fitting of data to Eq. (1). The red error bars for uncertainties of the EIT lines indicate the standard deviation of three repeated measurements, which come from the stability of the laser’s locking and the fluctuations of the atomic number.

Fig. 4. Observation of the Rydberg–EIT spectrum on 35d Rydberg state. (a) Unusual Rydberg–EIT spectrum (red) while scanning the coupling detuning δ_c and locking the probe laser to ultrastable cavity resonating at the transition from |g〉 to |e〉. The Rydberg-EIT spectrum (gray) for 37s Rydberg state is from Figs. 3(b2) and 3(b3). (b) The normal Rydberg–EIT spectrum is obtained by scanning the probe detuning δ_p when the coupling laser is fixed, where the probe laser is frequency-locked through the ultrastable cavity, and the coupling laser is locked to the transition between |e〉 and |r〉 ≡ |35d〉. The fitting values are Ω_c = 2π × 14.02 MHz, γ_eg = 2π × 18.5 MHz, γ_rg = 2π × 9.5 MHz, and δ_c = 2π × (−0.68) MHz.

Fig. 5. Observation of the Rydberg–EIT spectrum on 52s Rydberg state. (a) Unusual Rydberg-EIT spectrum while scanning the coupling detuning δ_c and locking the probe laser to the ultrastable cavity resonating at the transition from |g〉 to |e〉. (b) The normal Rydberg–EIT spectrum is obtained by scanning the probe detuning δ_p when the coupling laser is fixed, where the probe laser is frequency-locked through the ultrastable cavity, and the coupling laser is locked to the transition between |e〉 and |r〉 ≡ |52s〉. The fitting values are Ω_c = 2π × 6.8 MHz, γ_eg = 2π × 18.5 MHz, γ_rg = 2π × 2.12 MHz, and δ_c = 2π × (−1.92) MHz. The red open squares show the experimental data. The red error bars indicate the standard deviation of three repeated measurements. The blue solid curve is the fitting of data to Eq. (1).