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Physical Review Letters

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

Kirill Prozument, Anthony P. Colombo, Yan Zhou, George Barratt Park, Vladimir Petrović, Stephen L. Coy, Robert W. Field

Published Sep 26, 2011• 27 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.107.143001

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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.
We apply the chirped-pulse millimeter-wave (CPmmW) technique to transitions between Rydberg states in calcium atoms. The unique feature of Rydberg-Rydberg transitions is that they have enormous electric dipole transition moments (~5 kiloDebye at n* ~ 40, where n* is the effective principal quantum number), so they interact strongly with the mm-wave radiation. After polarization by a mm-wave pulse in the 70-84 GHz frequency region, the excited transitions re-radiate free induction decay (FID) at their resonant frequencies, and the FID is heterodyne-detected by the CPmmW spectrometer. Data collection and averaging are performed in the time domain. The spectral resolution is ~100 kHz. Because of the large transition dipole moments, the available mm-wave power is sufficient to polarize the entire bandwidth of the spectrometer (12 GHz) in each pulse, and high-resolution survey spectra may be collected. Both absorptive and emissive transitions are observed, and they are distinguished by the phase of their FID relative to that of the excitation pulse. With the combination of the large transition dipole moments and direct monitoring of transitions, we observe dynamics, such as transient nutations from the interference of the excitation pulse with the polarization that it induces in the sample. Since the waveform produced by the mm-wave source may be precisely controlled, we can populate states with high angular momentum by a sequence of pulses while recording the results of these manipulations in the time domain. We also probe the superradiant decay of the Rydberg sample using photon echoes. The application of the CPmmW technique to transitions between Rydberg states of molecules is discussed.
The 106^{6}6 increase in spectral velocity allowed by the combination of chirped pulse millimeter-wave spectroscopy with a buffer gas cooled molecular beam source qualitatively expands the classes of possible experiments. As an example, it allows for investigation of cooperative radiation effects (such as superradiance and subradiance) in large samples of atoms in Rydberg states in a single shot. However, these same effects can present obstacles to the application of the full increase in spectral velocity to high-resolution spectroscopic experiments through both frequency (chirps, broadenings, and shifts) and intensity effects.
We have directly detected millimeter-wave (mm-wave) free-space superradiant emission from Rydberg states (principal quantum number $n\ensuremath{\sim}30$) of barium atoms in single-shot experiments. We trigger the cooperative effects with a weak initial pulse and detect the time-dependent amplitude and phase of the emitted radiation with single-shot sensitivity and 20 ps time resolution. This allows measurement and shot-by-shot analysis of the statistical distribution of decay rates, time delays, and time-dependent frequency shifts. Cooperative line shifts and decay rates are observed that exceed the 250 kHz Doppler width by a factor of 20 and the 50 Hz spontaneous emission rate by a factor of 105{10}^{5}105.
Transitions between high Rydberg states of 133{}^{133}133Cs atoms have been studied by high-resolution millimeter-wave spectroscopy of an ultracold sample. The spectroscopic measurements were performed after releasing the atoms from a magneto-optical trap. Switching off all trapping fields and compensating the stray electric and magnetic fields to below 1 mV/cm and 2 mG, respectively, prior to the spectroscopic measurement enabled the recording of millimeter-wave spectra of Rydberg states with principal quantum number beyond n=100n=100n=100 under conditions where the inhomogeneous broadening by stray fields is minimal and no dephasing of the Rydberg-atom sample can be detected over measurement times up to 60 $\ensuremath{\mu}$s. The Fourier-transform-limited line widths of better than 20 kHz enabled the observation of the hyperfine structure of nSnSnS and nPnPnP Rydberg states of Cs beyond n=90n=90n=90. The analysis of the line shapes of transitions to Rydberg states with $n\ensuremath{\approx}230$ indicated that field inhomogeneities across the atomic sample represent the dominant cause of spectral broadening at high nnn values. The analysis also revealed that the initial polarization of the atomic sample (F=4F=4F=4, MF=4{M}_{F}=4MF​=4) is preserved for several tens of microseconds, the depolarization being caused by slow precession along the magnetic stray fields.
The operation of maser devices using highly excited Rydberg atoms as active medium is investigated. These systems, working in a transient regime reminiscent of super-radiance generate few-hundred-ns-long bursts of mm-wave radiation. They are characterized by extremely low inversion density thresholds (${N}_{0}\ensuremath{\sim}{10}^{4}$ atoms typically) and very small peak power outputs (in the ${10}^{\ensuremath{-}11}$- to ${10}^{\ensuremath{-}13}$-watt range). This study is interesting in the context of new tests of super-radiance and electrodynamics theory. It also opens new possibilities in the important domain of mm-wave amplification and detection. In this paper, we present a simple semiclassical theory of transient Rydberg maser operation and we report the experimental observation of a large number of maser emission lines on Na atoms, spanning a wide frequency interval ($60<\ensuremath{\nu}<950$ GHz). The technique used to monitor the emission is the indirect field ionization procedure which reveals fast radiative transfers occurring between Rydberg levels. Another method involving the direct detection of the maser radiation by a heterodyne receiver is described in a subsequent paper, along with a report on the investigation of various effects related to the triggering of the transient maser emission by external radiation.
Most chirped-pulse experiments refer to a theoretical study from McGurk, Schmalz, and Flygare [J. Chem. Phys. 60, 4181 (1974)] which is well tailored to interpret the signals obtained with very fast chirped pulses, but is not sufficient to account for the signals in the case of slower chirped pulses used in spectroscopy to increase the signal-to-noise ratio. A theoretical study of the polarization of molecules subjected to a chirped pulse in a cell, uniform supersonic flow, or molecular beam is presented. Three degrees of approximation for the polarization are introduced and are compared with the numerical solution of the optical Bloch equations. These expressions enter the analytic expression of the free-induction-decay signal which is validated against experimental data on the rotational emission spectra of OCS molecules. A relation among the pulse duration, the line position in the chirped pulse, and the signal amplitude is proposed in the thermalized case. It assists in the optimization of the chirped-pulse parameters and in the estimation of the error associated with the line intensity.