Real-Time Dynamic Atomic Spectroscopy Using Electro-Optic Frequency Combs

Spectroscopy is a key technology for both fundamental and applied science. A long-held desire has been the development of a means to continuously acquire broadband spectral data with simultaneous high time and frequency resolution. Frequency-comb technology can open this door: here, we use a spectroscopic technique based on an electro-optic comb to make continuous observations of cesium vapor across a 3.2-GHz spectral bandwidth with a 2-$\mu \mathrm{s}$ time resolution and with 10-MHz frequency sampling. We use a rapidly switched pump laser to burn narrow features into the spectral line and study the response to this step perturbation. This examination allows us to see a number of unexpected effects, including the temporal evolution of the bandwidth, the amplitude, and the frequency of these burnt features. We also report on the previously unobserved effect of radiation reabsorption, which slowly produces a broad pedestal of perturbation around each feature. We present models that can explain these dynamical effects.

Figure 1

(a) Experimental setup. The probe laser is split into two signals—one path is modulated with a pseudorandom number code to produce a user-controllable frequency comb, while the second is frequency shifted by an AOM to provide a local oscillator. The combined optical signals are then incident on a vapor cell. We separately detect the incident ($D1$) and transmitted ($D2$) light in two channels of a fast oscilloscope and then calculate the transmittance. (b) Cesium energy-level diagram showing the four possible arrangements for optical pumping between the two ground states and the two excited states, together with the transitions probed by the frequency comb. (c) Simplified three-level diagram which aids the calculation of the expected temporal response.

Figure 2

Spectrogram showing the frequency-temporal response of the cesium $F=4\to F^{\prime }=3$, 4 transitions. A strong pump laser tuned to the $F=4\to F^{\prime }=4$ transition is switched on at $t=0$ and switched off at $t=250\mu \mathrm{s}$.

Figure 3

Measured transmittance of the $F=4\to F^{\prime }=3$, 4 transitions. The left-hand column shows the outcome when pumping on the $F=4\to F^{\prime }=4$ transition, while the right-hand column displays pumping on the $F=3\to F^{\prime }=3$ transition. The top row shows $2.2\mu \mathrm{s}$ after the pump is switched on, the middle row shows the transmission at $t=168\mu \mathrm{s}$, and the bottom row at $t=260\mu \mathrm{s}$ ($10\mu \mathrm{s}$ after the pump is switched off). In each panel, we superimpose the unperturbed transmission spectrum (at $t=0$, the blue line), together with a nonlinear fit to the experimental data (the black line). The wavelength markers are retrieved from Ref. [47].

Figure 4

Inclusion of a broad pedestal. (a) Fit using spectral holes only. The absence of the pedestal forces the widths of the resonant features to around 36 MHz. (b) Fit allowing for both spectral holes and pedestals. The returned width values for the resonant features are around 27 MHz. The displayed residuals are expressed in terms of the optical-depth difference between the model and fitted curves.

Figure 5

Temporal evolution of the spectral modifications. (a) Pump tuned to the $F=3\to F^{\prime }=3$ transition. The left plot shows the fractional height (the fractional change in optical depth) of the spectral hole in the $F=4\to F^{\prime }=3$ (red) and $F=4\to F^{\prime }=4$ (blue) transitions. The amplitude of the pedestal feature is also shown as measured in the $F=4\to F^{\prime }=4$ (brown) and $F=4\to F^{\prime }=3$ (black) transitions. The right-hand-side plot shows the bandwidth of the burnt feature as measured in the $F=4\to F^{\prime }=3$ (red) and $F=4\to F^{\prime }=4$ (blue) transitions. (b) Pump tuned to the $F=4\to F^{\prime }=4$ transition. Color codes are the same as in (a). See Fig. 1 in the Supplemental Material [48] for the cases where the pump is tuned to the $F=3\to F^{\prime }=4$ and $F=4\to F^{\prime }=3$ transitions.

Figure 6

Frequency splitting between spectral holes as a function of time when pumped on the $F=4\to F^{\prime }=3$ (blue) and $F=4\to F^{\prime }=4$ (red) transitions.

Figure 7

Simulations of the atomic response using a three-level atomic model. (a) Pump tuned to the $F=3\to F^{\prime }=3$ transition. (b) Pump tuned to the $F=4\to F^{\prime }=4$ transition. In both cases, the pumping rate has been set at 7 MHz and transit-time relaxation at $7.5\mu \mathrm{s}$. The theory shows good qualitative agreement with the experimental curves in Fig. 5.