Terahertz Molecular Frequency References: Theoretical Analysis of Optimal Instability

We report a comprehensive theoretical analysis of the instability achievable by using phase modulation spectroscopy to lock a terahertz local oscillator to an absorptive reference consisting of the rotational transition of molecules at room temperature. We find that the signal-to-noise ratio of the THz detector provides the limitation to the instability that can be achieved and analyze a number of viable candidate molecules, identifying several as being of particular interest, including OCS and HI. We find that a one-second instability in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-13}$</tex-math></inline-formula> decade is achievable for molecules confined to waveguide, while instability at the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-14}$</tex-math></inline-formula> level can be reached for molecules in free space. We also present calculations of the intermodulation effect for spectroscopy taking place far outside the quasistatic regime and find that this source of noise presents constraints on which THz local oscillators are appropriate to be used for such frequency references.