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Journal of the Korean Physical Society

Analytical approach to dynamic cancelation of the AC Stark shift in a pulsed three-level optical lattice clock

Tai Hyun Yoon

Published Aug 1, 2013• 0 citations
Publisher

Abstract

We study analytically the dynamic cancelation of the AC Stark shift in a three-level pulsed optical lattice clock by solving the time-dependent density-matrix equations in the adiabatic following limit. We found an optimum value of the common detuning Δ 0 of two coherent driving fields at which the dynamic AC Stark shift cancelled completely at an arbitrary field strength. The optimum value of Δ 0 for the well-studied Sr atoms agreed well with the values obtained by using other methods, for instance, a numerical calculation and a wave-function formalism. We give an optimum value of common detuning, Δ 0 = 65.3 MHz, for the pulsed Raman Yb optical lattice clock.

DOI
10.3938/jkps.63.877

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We study analytically the dynamic cancelation of the AC Stark shift in a three-level pulsed optical lattice clock by solving the time-dependent density-matrix equations in the adiabatic following limit. We found an optimum value of the common detuning Δ 0 of two coherent driving fields at which the dynamic AC Stark shift cancelled completely at an arbitrary field strength. The optimum value of Δ 0 for the well-studied Sr atoms agreed well with the values obtained by using other methods, for instance, a numerical calculation and a wave-function formalism. We give an optimum value of common detuning, Δ 0 = 65.3 MHz, for the pulsed Raman Yb optical lattice clock.
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 propose a combination of electromagnetically induced transparency-Raman and pulsed spectroscopy techniques to accurately cancel frequency shifts arising from electromagnetically induced transparency fields in forbidden optical clock transitions of alkaline earth atoms. At appropriate detunings, time-separated laser pulses are designed to trap atoms in coherent superpositions while eliminating off-resonance ac Stark contributions, achieving efficient population transfer up to 60% with inaccuracy <10(-17). Results from the wave-function formalism are confirmed by the density matrix approach.
We analyze both the s- and p -wave collision induced frequency shifts and propose an over- π pulse scheme to cancel the shifts in optical lattice clocks interrogated by a Rabi pulse. The collisional frequency shifts are analytically solved as a function of the pulse area and the inhomogeneity of the Rabi frequencies. Experimentally measured collisional frequency shifts in an Yb optical lattice clock are in good agreement with the analytical calculations. Based on our analysis, the over- π pulse combined with a small inhomogeneity below 0.1 allows a fractional uncertainty on a level of 10 −18 in both Sr and Yb optical lattice clocks by canceling the collisional frequency shift.
Magnetic-dipole, electric-quadrupole, and hyperpolarizability effects on clock energy levels are analyzed in detail for Sr atoms in Stark potentials of red-detuned and blue-detuned magic-wavelength optical lattices. A difference between ac Stark shifts in traveling and standing waves is determined numerically. Differences between magic wavelengths for atoms in traveling and standing waves are presented and strategies for minimizing uncertainties of the clock frequency are indicated explicitly. Significant suppression of hyperpolarizability effect is demonstrated analytically for a blue-detuned in comparison with a red-detuned lattice, thus enabling essential deepening of trap potentials, reducing tunneling between lattice wells and collision effects.
Quantum engineering of time-separated Raman laser pulses in three-level systems is presented to produce an ultranarrow optical transition in bosonic alkali-earth clocks free from light shifts and with a significantly reduced sensitivity to laser parameter fluctuations. Based on a quantum artificial complex wave-function analytical model and supported by a full density-matrix simulation including a possible residual effect of spontaneous emission from the intermediate state, atomic phase shifts associated with Ramsey and hyper-Ramsey two-photon spectroscopy in optical clocks are derived. Various common-mode Raman frequency detunings are found in which the frequency shifts from off-resonant states are canceled, while their uncertainties at the ${10}^{\ensuremath{-}18}$ level of accuracy are strongly reduced.
Atomic mirrors and beam splitters based on adiabatic following by delayed laser pulses in a three-level Raman configuration are analyzed. We show that in a pure three-level system of two ground states and one excited state, laser pulses tuned precisely on resonance with the excited state do not produce any accumulated phase shifts due to ac Stark shifts even if the process is nonadiabatic. A numerical simulation suggests that multiple delayed laser pulses are attractive for precision interferometry since high transfer efficiencies (up to 98.7% per pulse for the cesium D1 line) and low ac Stark shifts are expected. A possible application to optical two-photon spectroscopy for an optical clock is discussed.