This paper presents an experimental study of microwave single-photon transitions that are magnetic-field-insensitive in degenerate Fermi gases of
40K. This contrasts with microwave single-photon clock transitions for 0-0 magnetic-field-insensitive states and two-photon clock transitions for non 0-0 magnetic-field-insensitive states in bosonic alkali metal atoms. We show that there are two sets of special transitions between two different hyperfine ground states (
∣F=9/2,
mF=1/2
⟩ ⇔ $|
7/2,−1/2\rangle$ and $|
9/2,−1/2\rangle$
⇔ $|
7/2,1/2\rangle$), whose microwave single-photon transition frequency is insensitive to low magnetic fields, as the first-order Zeeman shift is almost completely canceled. By using the microwave spectrum and Ramsey interference fringes, we demonstrate the long-time stability of the coherent transition under magnetic field fluctuations. These magnetic-field-insensitive microwave hyperfine transitions in ultracold
40K Fermi gases offer promising applications in quantum information and precision measurements.
The spontaneous emission spectrum of a three-level $\ensuremath{\Lambda}$-type atom driven by a microwave field was studied. For the two transitions coupled to the same modified reservoir, we discussed the influence of photonic band gap and Rabi frequency of the microwave field on the emission spectrum. The emission spectrum is given for different locations of the upper band-edge frequency. With the transition frequencies moving from outside the band gap to inside, the number of peaks decreases in the emission spectrum and the multipeak structure of spectral line is finally replaced by a strong non-Lorentzian shape. With increase of the Rabi frequency of the microwave field, we find the spectral line changes from a multipeak structure to a two-peak structure, originating from the inhibition of spontaneous emission for the corresponding decay channel.
Previous measurements of single photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2)f$ transitions by two of us were described as microwave transitions made possible by configuration interaction (CI) between the
nd5/2nd5/2 and the nearly degenerate $(n+2){p}_{3/2}(n\ensuremath{-}2)f$ states [Lee and Gallagher, Phys. Rev. A 93, 062509 (2016)]. Here we report the observation of the one photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){s}_{1/2}(n\ensuremath{-}2)f$, two photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){p}_{j}(n\ensuremath{-}2)f$, and three photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+4){s}_{1/2}(n\ensuremath{-}2)f$ microwave transitions. We show that both single and multiphoton microwave transitions are conveniently described as Forster resonant energy transfers between resonant Floquet states, and we show that the Floquet-Forster model reduces to the CI model used previously. Finally, to show that the transitions observed previously are by no means unique, we report pair transitions with different initial and final states as well as radio instead of microwave frequencies.