Frequency Measurements of Superradiance from the Strontium Clock Transition

We present the first characterization of the spectral properties of superradiant light emitted from the ultranarrow, 1-mHz-linewidth optical clock transition in an ensemble of cold ${}^{87}\mathrm{Sr}$ atoms. Such a light source has been proposed as a next-generation active atomic frequency reference, with the potential to enable high-precision optical frequency references to be used outside laboratory environments. By comparing the frequency of our superradiant source to that of a state-of-the-art cavity-stabilized laser and optical lattice clock, we observe a fractional Allan deviation of $6.7(1)\times {10}^{-16}$ at 1 s of averaging, establish absolute accuracy at the 2-Hz ($4\times {10}^{-15}$ fractional frequency) level, and demonstrate insensitivity to key environmental perturbations.

Popular Summary

Atomic clocks are currently our most precise way of keeping time. These clocks can be categorized as active or passive (depending on whether they work by absorbing or emitting electromagnetic radiation) and as microwave or optical (depending on the frequency range of the radiation involved). While passive clocks have superior accuracy, active clocks can offer advantages in terms of bandwidth, dynamic range, and insensitivity to environmental perturbations. Optical frequencies offer a large advantage in precision that has allowed passive optical clocks to surpass the performance of their microwave counterparts. However, until now, precision active clocks have been confined to the microwave domain. In this work, we present the first characterization of a high-precision active clock operating in the optical domain.

We use an ensemble of laser-cooled strontium atoms that collectively emit radiation from an ultranarrow (1-mHz linewidth) optical clock transition. This emission process is referred to as superradiance, and the frequency of the superradiant light constitutes the clock signal. We compare the frequency of the superradiant light to a state-of-the-art cavity-stabilized laser and optical lattice clock. We find that the frequency stability of the superradiant light already surpasses that of active microwave clocks, and we confirm its absolute frequency at the hertz level and demonstrate a high degree of insensitivity to important environmental perturbations.

Our observations suggest a compelling path to extend optical frequency metrology to applications outside of carefully controlled laboratory environments.

Figure 1

Passive and active optical frequency references. (a) In a passive optical frequency reference, the clock transition in the atomic medium is driven by radiation from a laser at frequency $f_{\ell }$. The laser frequency is then determined relative to the clock transition frequency through a population measurement of the two clock states using a fluorescence signal ($I$) obtained from a separate atomic transition. The fluorescence signal provides information about the atomic response at frequency $f_{\ell }$, which can be used to stabilize the frequency of the laser. (b) In an active optical frequency reference, light is collected directly from the atomic clock transition. This light can be compared to the reference laser by forming a heterodyne beat note. The power spectral density of the resulting signal ($\tilde{I}$) provides information about the atomic system at all offset frequencies from $f_{\ell }$ within a large detection bandwidth set by the detection electronics. In our system, we use ${}^{87}\mathrm{Sr}$ atoms emitting into a high-finesse optical cavity on a roughly 1-mHz-linewidth clock transition as the active atomic medium. The clock transition frequency $f_a$ is nearly equal to a cavity resonance frequency $f_c$, up to a tunable offset ${\delta }_c=f_a-f_c$. The cavity linewidth $\kappa =2\pi \times 145\mathrm{kHz}$ greatly exceeds the atomic linewidth, placing the system in a highly damped, “superradiant” regime.

Figure 2

Superradiant pulses in the time and frequency domains with different initial nuclear spin state populations. Atomic state population is initialized (a) with all atoms in a single stretched state, (b) with atoms in both stretched states, and (c) with all ten spin states populated. Columns represent the output power measured in the time domain (left), the initial spin state population (inset), and power spectrum of output power measured relative to a stable reference laser up to an arbitrary frequency offset (right), for single trials of the experiment. In the frequency domain, we observe a single peak in the power spectrum when we populate only one stretched state, two peaks when we populate both stretched states, and many peaks when we populate all ten Zeeman sublevels.

Figure 3

Stability and accuracy of the superradiant laser. (a) Short-term stability of superradiant light source expressed as fractional Allan deviation $\sigma (\tau )$. We populate both stretched states and compute the Allan deviation for two quantities: the average frequency of the two lasing transitions $f_m$ (black and blue points) and half the difference of the two lasing transition frequencies $f_d$ (red points). During a longer data set, we measure a short-term fractional instability of $\sigma (\tau )=1.04(4)\times {10}^{-15}/\sqrt{\tau /s}$ for the average frequency (black dashed line) and a value of $\sigma (\tau )=6.7(1)\times {10}^{-16}/\sqrt{\tau /s}$ for a shorter data set taken under particularly quiet conditions (blue dashed line). (b) Real-time insensitivity to changing magnetic fields is obtained by simultaneously fitting the frequencies of two radiating transitions. Perturbations to the two individual transitions $\mathrm{\Delta }{f}_{\pm 9/2}$ (black points) are suppressed to below the half-percent level in the sum frequency $\mathrm{\Delta }{f}_m$ (red points). (c) Lattice-induced frequency shifts, with the frequency difference between the superradiant laser and an optical lattice clock for different lattice laser detunings and power levels. Different colored points correspond to different lattice depths: $U=1025$, 760, $570{\mathrm{E}}_{\mathrm{rec}}$ for green, red, and blue points, respectively, where ${\mathrm{E}}_{\mathrm{rec}}$ is the lattice recoil energy. The horizontal axis shows $\mathrm{\Delta }{f}_{\mathrm{lat}}=f_{\mathrm{lat}}-f_{\text{magic}}^{\mathrm{wm}}$, where $f_{\text{magic}}^{\mathrm{wm}}$ is the expected value for the magic wavelength as measured by our wave meter. A simultaneous fit (see text) to all data points returns a nominal frequency offset consistent with zero, represented by the horizontal dashed line, with the uncertainty of the fit represented by the red band. The vertical dashed line represents the fit magic wavelength, relative to $f_{\text{magic}}^{\mathrm{wm}}$, with fit uncertainty given by the green band.

Figure 4

(a) Sensitivity of superradiant light frequency $f_m$ to detuning of the cavity from resonance ${\delta }_c$ for different initial population inversions, as shown in the side insets. An offset frequency $f_0$ set by the detuning of the reference laser from the strontium transition is subtracted for each data set. When tuned to minimize sensitivity to cavity detuning (red line and points) we observe a pulling coefficient $P=\mathrm{\Delta }{f}_m/{\delta }_c=2(3)\times {10}^{-6}$. Changing the duration of the state preparation pulse leads to an increased absolute value of $P$ (black and blue points). (b) Atomic inversion changes throughout the superradiant pulse, leading to a chirp in the frequency of the emitted light for finite cavity detuning. The emitted power for a single shot is shown in the upper panel for the first 45 ms of the pulse. The pulling coefficient at different time intervals is computed from frequency measurements made on subsets of the pulse (as indicated by colored vertical bands) for the red data set shown in (a). The pulling coefficient of the entire pulse can be made insensitive to cavity detuning by choosing an initial inversion for which the time-averaged (weighted by instantaneous power) frequency shift is zero.

Figure 5

Light from a state-of-the-art stabilized cavity laser system is transported by phase stabilized a 75-m optical fiber and is combined with the superradiant pulse light to originate an optical beat-note detected at the photodiode. An IQ demodulation step is performed before data acquisition (FFT). The reference path for the phase stabilization is referenced to the back cavity mirror.

Figure 6

Frequency noise aliasing. (a) Sensitivity function $r(t)$ for a superradiant (SR) pulse with a Gaussian power profile with duration characterized by $\sigma =28\mathrm{ms}$ and centered at $t=15\mathrm{ms}$ (blue), and for a Ramsey sequence with duration $T=40\mathrm{ms}$ (red). (b) Modulus squared of the normalized Fourier transform of the sensitivity functions shown in (a). (c) Contribution to fractional Allan deviation from the reference laser, under different measurement scenarios: the Allan deviation of the reference laser, assuming no dead time in measurement (green) [33, 34]; the Allan deviation contribution of the reference laser for the SR pulse as in (a) and (b) (dashed blue); the Allan deviation contribution of the reference laser for the Ramsey sequence in (a) and (b) (dashed red); the quadrature sum of laser noise and frequency aliasing for the SR pulse (solid blue); and the quadrature sum of laser noise and frequency aliasing for the Ramsey sequence (solid red).