Coherence-Assisted Resonance with Sub-Transit-Limited Linewidth

We demonstrate a novel approach to obtain a resonance linewidth below the transit limit. The cross correlation between the induced intensity modulation of two lasers coupling the target resonance exhibits a narrow spectrum. $1/30$ of the transit-limited width is achieved in a proof-of-principle experiment where two ground states are the target resonance levels. Attainable linewidth is only limited by laser shot noise in principle. The experimental results qualitatively agree with an intuitive analytical model and numerical calculations. This technique can be easily implemented and should be applicable to many atomic, molecular, and solid state spin systems for spectroscopy, metrology, and resonance-based sensing and imaging.

Figure 1

Principle of the sub-transit-width resonance, shown between $|1⟩$ and $|2⟩$ in a three-level $\Lambda$ configuration. $\delta$ is the averaged one-photon detuning, and $\Delta$ is the two-photon detuning, generated by shifting the energy levels with a magnetic field via a Zeeman shift (as shown) or by varying the frequency difference of $E_1$ and $E_2$. (See the text for details.)

Figure 2

Measured offset between the transmission minima of $E_1$ and $E_2$ vs $\Delta$ for two input laser powers. Lines are to guide the eye.

Figure 3

ac transmitted signals of the two $CPT$ fields (blue and red) for (a) $\Delta =0$ and (b) $\Delta =15\mathrm{kHz}$. (c) An example of a $g^{(2)}(0)$ spectrum with FWHM 2.4 kHz, about $1/30$ of the transit width ${\gamma }_2/\pi =75\mathrm{kHz}$. The input laser power was $300\mu \mathrm{W}$.

Figure 4

Dependence of the $g^{(2)}(0)$ FWHM on (a) input laser power, (b) the power ratio of the two $CPT$ beams for a laser power of $300\mu \mathrm{W}$, and (c) the modulation range for two different laser powers. The full modulation range $2\lambda \nu$ is 5 MHz for (a), (b). The lines in (c) are linear fits. In (a), (b), an overall scaling factor was applied to the linewidth in the fitting to account for broadening from optical depth and other noises. The transit width is 75 kHz.

Figure 5

Measured $g^{(2)}(0)$ FWHM vs modulation frequency in the nonadiabatic regime. The laser power is $800\mu \mathrm{W}$, and the transit width is ${\gamma }_2/\pi =63\mathrm{kHz}$.