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Bulletin of the American Physical Society

Time-dependent analysis of pulsed EIT processes in atomic clocks

T. Zanon-Willette, Andrew D. Ludlow, Martin M. Boyd, Tanya Zelevinsky, Sebastian Blatt, T. Ido, Jun Ye

Published May 19, 2006• 0 citations
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In the atomic frequency standard, the light shift inevitably affects the long-term stability of the atomic clock. In this work, we accurately calculated the light shifts of electromagnetically induced transparency (EIT) and coherent population trapping (CPT) clocks operating under continuum and pulse sequence regimes by numerically solving the Liouville density matrix equation, including all the relaxation terms of a three-level system. The results show that the light shifts under pulse excitation are smaller than those under continuous excitation and the light shifts of the CPT process are much smaller than those of the EIT process under both excitations. It is also found that the light shifts in the continuous excitation increase and those in the pulse excitation decrease with an increase in the Rabi frequency. The light shifts will increase with an increase of the relaxations of the ground states for both the processes under both regimes. Compared to all process atomic clocks, the light shift of pulse-excited atomic clocks is the smallest, which will be suitable for many applications.

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We have simultaneously studied electromagnetically induced transparency (EIT) and Raman Ramsey fringes (RRF) in sodium vapor, in the same theoretical framework and the same experimental scheme. RRF spectra and EIT spectra can be simply distinguished by whether the gate timing of the detection is set at the beginning (RRF) or at the end (EIT) of the excitation pulses. The EIT spectral peaks exhibited pronounced ac Stark shifts linearly depending upon the pumping power (8.8 kHz/mW), while in the RRF spectra such shifts were almost negligible (0.19 kHz/mW), provided that the pulse separation is sufficiently large. This fact promotes RRF as a strong candidate for next-generation compact atomic clocks. Transient spectra in between RRF and EIT have also been investigated by changing the gate timing within the excitation pulse, and the transition time from RRF to EIT was found to be of the order of a few microseconds.

Physical Review A•Feb 22, 2013•19 citations
In the atomic frequency standard, the light shift inevitably affects the long-term stability of the atomic clock. In this work, we accurately calculated the light shifts of electromagnetically induced transparency (EIT) and coherent population trapping (CPT) clocks operating under continuum and pulse sequence regimes by numerically solving the Liouville density matrix equation, including all the relaxation terms of a three-level system. The results show that the light shifts under pulse excitation are smaller than those under continuous excitation and the light shifts of the CPT process are much smaller than those of the EIT process under both excitations. It is also found that the light shifts in the continuous excitation increase and those in the pulse excitation decrease with an increase in the Rabi frequency. The light shifts will increase with an increase of the relaxations of the ground states for both the processes under both regimes. Compared to all process atomic clocks, the light shift of pulse-excited atomic clocks is the smallest, which will be suitable for many applications.
We study analytically the dynamic cancellation of ac Stark shift in the recently proposed pulsed electromagnetically-induced-transparency (EIT-)Raman optical lattice clock based on the wave-function formalism. An explicit expression for the time evolution operator corresponding to the effective two-level interaction Hamiltonian has been obtained in order to explain the atomic phase shift cancellation due to the ac Stark shift induced by the time-separated laser pulses. We present how to determine an optimum value of the common detuning of the driving fields at which the atomic phase shift cancels completely with the parameters for the practical realization of the EIT-Raman optical lattice clock with alkaline-earth-metal atoms.
We have simultaneously studied electromagnetically induced transparency (EIT) and Raman Ramsey fringes (RRF) in sodium vapor, in the same theoretical framework and the same experimental scheme. RRF spectra and EIT spectra can be simply distinguished by whether the gate timing of the detection is set at the beginning (RRF) or at the end (EIT) of the excitation pulses. The EIT spectral peaks exhibited pronounced ac Stark shifts linearly depending upon the pumping power (8.8 kHz/mW), while in the RRF spectra such shifts were almost negligible (0.19 kHz/mW), provided that the pulse separation is sufficiently large. This fact promotes RRF as a strong candidate for next-generation compact atomic clocks. Transient spectra in between RRF and EIT have also been investigated by changing the gate timing within the excitation pulse, and the transition time from RRF to EIT was found to be of the order of a few microseconds.