Fig. 1. (a) LO locking scheme, where 6.834 682… GHz with ±0.5  Hz modulation is multiplied from a 5 MHz OCXO oscillator and delivered to the fountain. The feedback signal is directly applied to the OCXO oscillator every two launch cycles to lock its frequency to the resonance spectra of Rb87 atoms. (b) CISC scheme with atomic fountain switching between two states with different sets of parameters. Error signals from the two states are recorded to lock the LO and used to identify the frequency difference of the two states. (c) Transfer function in time domain where the averaging time is 4Tc. The blue line is the case in a normal Allan variance, while the black line is the case in CISC with extra modulation on the effect of interest. (d) Frequency conjugate of the transfer function with different averaging times, which are determined by 2nTc.

Fig. 2. (a) Confirmation of CISC method. The black solid line given by the result of CISC between two identical states has a 7.2×10−13  τ−1/2 dependence. It is twice that of the LO locking depicted by the blue dotted line, which is measured by comparison with a hydrogen maser. The red dashed line is the CISC scheme confirmed by a comparison with the same hydrogen maser. (b) Allan deviation of y2-y1 given as the uncertainty for the collisional frequency shifts.

Table 1. Comparison at Different Periods of Time for Light Shift (×10−15)

Table 2. Comparison at Different Periods of Time for Cold Collisional Shift (×10−15)