Magnetically Induced Optical Transparency on a Forbidden Transition in Strontium for Cavity-Enhanced Spectroscopy

In this Letter we realize a narrow spectroscopic feature using a technique that we refer to as magnetically induced optical transparency. A cold ensemble of ${}^{88}\mathrm{Sr}$ atoms interacts with a single mode of a high-finesse optical cavity via the 7.5 kHz linewidth, spin forbidden ${}^1{S}_0$ to ${}^3{P}_1$ transition. By applying a magnetic field that shifts two excited state Zeeman levels, we open a transmission window through the cavity where the collective vacuum Rabi splitting due to a single level would create destructive interference for probe transmission. The spectroscopic feature approaches the atomic transition linewidth, which is much narrower than the cavity linewidth, and is highly immune to the reference cavity length fluctuations that limit current state-of-the-art laser frequency stability.

Figure 1

(a) Simplified experimental diagram. The system is probed with horizontally polarized probe light. The light can be coherently absorbed by the atoms (the brown ovals) and reemitted into the cavity at collective vacuum Rabi frequency $\mathrm{\Omega }$. The transmitted power is detected on a single photon counting module (black). A magnetic field is applied along the vertical direction. (b) The atomic energy level diagram of the ground ${}^1{S}_0$ and excited states ${}^3{P}_1$ $|m_j⟩$ with a quantization axis $\widehat{q}$ parallel to the applied magnetic field $\overrightarrow{B}$. The applied magnetic field creates a Zeeman splitting $\mathrm{\Delta }$ between the excited states $|\pm 1⟩$. Both of these transitions interact equally with the horizontally polarized light inside the cavity with the collectively enhanced Rabi frequency $\mathrm{\Omega }/\sqrt{2}$. The transmitted probe light is measured as the probe’s detuning ${\delta }_p$ is swept. The $|0⟩$ state is shown, but it does not interact with the horizontally polarized cavity field.

Figure 2

(a) The transmitted power $P_T$ through the cavity versus the probe detuning ${\delta }_p$, with ${\delta }_c=0$. Each trace was taken for different applied magnetic fields, creating different Zeeman splittings $\mathrm{\Delta }$ labeled on the vertical. The central red trace is taken for $\mathrm{\Delta }=0$ and displays a collective vacuum Rabi splitting $\mathrm{\Omega }/2\pi =5\mathrm{MHz}$. When a magnetic field is applied perpendicular to the probe polarization, inducing a Zeeman splitting $\mathrm{\Delta }$, a new transmission feature appears between the two original resonances of the vacuum Rabi splitting. (b) Linearized theory showing the power $P_T$ and phase $\psi$ of the transmitted light, plotted here for $\mathrm{\Omega }/2\pi =5\mathrm{MHz}$ and $\mathrm{\Delta }/2\pi =1\mathrm{MHz}$.

Figure 3

(a) The measured linewidth of the central MIT transmission feature versus the induced Zeeman splitting between excited states. The traces are taken for three different collective vacuum Rabi frequencies $\mathrm{\Omega }/2\pi =4.6(5)$ (red), 10(1) (blue), and 16(1) (green) MHz, with values set by changing the total atom number $N$. The upper dashed line is the empty cavity’s linewidth $\kappa$, and the lower dashed line is the atomic transition’s linewidth $\gamma$. The minimum observed linewidth was 11 kHz. The shaded regions are no-free parameter predictions from the linearized model introduced in the text, indicating the $\pm 1$ standard deviation uncertainty bands based on independent measurements of $\mathrm{\Omega }$. (b) The measured peak transmitted power of the central MIT transmission feature for the same collective Rabi frequencies. Here, the transmitted power is normalized to the peak transmitted power when the cavity is empty. Again, the shaded regions indicate the $\pm 1$ standard deviation uncertainty bands for the predictions.

Figure 4

The pulling coefficient $P$ versus Zeeman splitting $\mathrm{\Delta }$ for several collective vacuum Rabi frequencies $\mathrm{\Omega }/2\pi =5(1)$ (red), 10(1) (blue), and 17(1) (green) MHz. The prediction from the linearized theory is shown with $\pm 1$ standard deviation bands.