Chirped-Pulse Millimeter-Wave Spectroscopy of Rydberg-Rydberg Transitions

Transitions between Rydberg states of Ca atoms, in a pulsed, supersonic atomic beam, are directly detected by chirped-pulse millimeter-wave spectroscopy. Broadband, high-resolution spectra with accurate relative intensities are recorded instantly. Free induction decay (FID) of atoms, polarized by the chirped pulse, at their Rydberg-Rydberg transition frequencies, is heterodyne detected, averaged in the time domain, and Fourier transformed into the frequency domain. Millimeter-wave transient nutations are observed, and the possibility of FID evolving to superradiance is discussed.

Figure 1

Rydberg CPmmW experimental setup. Ca atoms are produced by laser ablation and supersonically co-expanded with He gas into vacuum [19]. The diverging laser beams, delivered through a 12 mm aperture in the metal mirror, excite Ca atoms to a selected Rydberg state. The chirped mm-wave pulses are broadcast from the source horn, and the FID is collected by the receiving horn. The pulsed lasers and gas nozzle operate at a 20 Hz repetition rate, and are synchronized with the mm-wave pulses.

Figure 2

CPmmW spectrum of Ca atoms. (a) The 10 ns duration, $3.9\mathrm{V}/\mathrm{m}$ ($\approx 1.4\times {10}^{-5}\mathrm{W}$), 0.5 GHz bandwidth chirped pulse centered around the $\nu =76.9293\mathrm{GHz}$ $36p\mathrm{\text{−}}36s$ transition [21], is followed by FID. Fine modulation is due to the 10 MHz frequency standard [16]. (b) The spectrum is a (rectangular window) magnitude Fourier transform of the FID. The inserts show an up-close view of the line, which is split into the three Zeeman components with $\Delta {\nu }_{\mathrm{FWHM}}=420\mathrm{kHz}$ of the central peak, and the level diagram of Ca atoms.

Figure 3

 Millimeter-wave transient nutations (only the top portion is shown). (a) The FID is initiated when the frequency of the chirped excitation pulse (500 ns duration) tunes through the Rydberg-Rydberg resonance. The frequency of the chirp is swept linearly in time away from resonance while that of the FID is constant; hence the frequency of the beat increases. (b),(c) Single frequency excitation pulse. (b) ${\mathcal{E}}_0=0.69\mathrm{V}/\mathrm{m}$ is determined by measuring $T_{\mathrm{nut}}=84\mathrm{ns}$; (c) ${\mathcal{E}}_0=0.23\mathrm{V}/\mathrm{m}$, $T_{\mathrm{nut}}=250\mathrm{ns}$. When deducing ${\mathcal{E}}_{\mathrm{FID}}$ we took into account that approximately 60% of the detected signal comes from the mm waves that pass outside of the interaction volume.

Figure 4

Evidence of superradiant decay. The excitation pulse ($0–0.5\mu \mathrm{s}$) followed by FID (superradiance) ($0.5–3.9\mu \mathrm{s}$) is a continuation of the Figs. 3b, 3c series with ${\mathcal{E}}_0=0.039\mathrm{V}/\mathrm{m}$ ($\approx 1.4\times {10}^{-9}\mathrm{W}$), as determined by the tunable power attenuator. The line splitting in (1) is due to Zeeman effect. The observed ($1/e$) decay time of 190 ns is close to the predicted $T_{\mathrm{sr}}=350\mathrm{ns}$. The inserts show Fourier transforms of different time intervals of the time-domain signal. (1) $0.5–3.9\mu \mathrm{s}$: broader, Lorentzian-type line shape; (2) $1.0–3.9\mu \mathrm{s}$: narrower, Gaussian-type line shape. This measurement is consistent with fast initial superradiant decay followed by slower, Doppler dephasing.