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Physical Review A

Robust Ramsey sequences with Raman adiabatic rapid passage

Krish Kotru, Justin M. Brown, David L. Butts, Joseph M. Kinast, Richard E. Stoner

Published Nov 10, 2014• 14 citations
Publisher

Abstract

We present a method for robust timekeeping in which alkali-metal atoms are interrogated in a Ramsey sequence based on stimulated Raman transitions with optical photons. To suppress systematic effects introduced by differential ac Stark shifts and optical intensity gradients, we employ atom optics derived from Raman adiabatic rapid passage (ARP). Raman ARP drives coherent transfer between the alkali-metal hyperfine ground states via a sweep of the Raman detuning through the two-photon resonance. Our experimental implementation of Raman ARP reduced the phase sensitivity of Ramsey sequences to Stark shifts in $^{133}\mathrm{Cs}$ atoms by about two orders of magnitude, relative to fixed-frequency Raman transitions. This technique also preserved Ramsey fringe contrast for cloud displacements reaching the $1/{e}^{2}$ intensity radius of the laser beam. In a magnetically unshielded apparatus, second-order Zeeman shifts limited the fractional frequency uncertainty to $\ensuremath{\sim}3.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ after about 2500 s of averaging.

DOI
10.1103/physreva.90.053611

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We present a method for robust timekeeping in which alkali-metal atoms are interrogated in a Ramsey sequence based on stimulated Raman transitions with optical photons. To suppress systematic effects introduced by differential ac Stark shifts and optical intensity gradients, we employ atom optics derived from Raman adiabatic rapid passage (ARP). Raman ARP drives coherent transfer between the alkali-metal hyperfine ground states via a sweep of the Raman detuning through the two-photon resonance. Our experimental implementation of Raman ARP reduced the phase sensitivity of Ramsey sequences to Stark shifts in 133Cs^{133}\mathrm{Cs}133Cs atoms by about two orders of magnitude, relative to fixed-frequency Raman transitions. This technique also preserved Ramsey fringe contrast for cloud displacements reaching the 1/e21/{e}^{2}1/e2 intensity radius of the laser beam. In a magnetically unshielded apparatus, second-order Zeeman shifts limited the fractional frequency uncertainty to \ensuremath∼3.5\ifmmode×\else\texttimes\fi10\ensuremath−12\ensuremath{\sim}3.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\ensuremath∼3.5\ifmmode×\else\texttimes\fi10\ensuremath−12 after about 2500 s of averaging.
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.
Over the past 30 years, optical manipulation of neutral atoms has been primarily performed with a monochromatic laser beam. The simplest tool for the control of atomic motion is the radiative force exerted by a monochromatic laser on a twolevel atom. The radiative force arises from absorption followed by spontaneous emission, and its magnitude is limited by the atom's excited state lifetime. The coherent momentum exchanges between light elds and atoms can be exploited to produce long-range optical forces much greater than the radiative force through the use of absorption-stimulated emission processes. Adiabatic Rapid Passage (ARP) is a long-existing method to invert the population of a two-level nuclear spin system. Its extension to the optical domain necessitates a frequency chirped light pulse to interact with a two-level atom via the dipole interaction. I will first present a numerical study of the properties of optical forces on moving atoms derived from purely stimulated processes produced by multiple ARP sequences. This will be followed by experimental observations of long-range ARP forces much larger than the radiative force in metastable helium. Sequences of properly timed laser pulses may be used for rapid deceleration of neutral atomic (or molecular) beams. | 171 pages
Sophisticated Ramsey-based interrogation protocols using composite laser pulse sequences have been recently proposed to provide next-generation high-precision atomic clocks with a near perfect elimination of frequency shifts induced during the atom-probing field interaction. We propose here a simple alternative approach to the autobalanced Ramsey interrogation protocol and demonstrate its application to a cold-atom microwave clock based on coherent population trapping (CPT). The main originality of the method, based on two consecutive Ramsey sequences with different dark periods, is to sample the central Ramsey fringes with frequency jumps finely adjusted by an additional frequency-displacement concomitant parameter, scaling as the inverse of the dark period. The advantage of this displaced frequency-jump Ramsey method is that the local oscillator (LO) frequency is used as a single physical variable to control both servo loops of the sequence, simplifying its implementation and avoiding noise associated with controlling the LO phase. When tested using a CPT cold-atom clock, the DFJR scheme reduces the sensitivity of the clock frequency to variations of the light shifts by more than an order of magnitude compared with the standard Ramsey interrogation. This simple method can be applied in a wide variety of Ramsey-spectroscopy based applications including frequency metrology with CPT-based and optical atomic clocks, mass spectrometry, and precision spectroscopy.
We demonstrate that when laser light is circularly polarized and properly detuned, the ac Stark shift of an alkali-metal atom in its ground state takes the form of a pure Zeeman shift. The condition is satisfied when the laser frequency is between the D1D1D1 and D2D2D2 transition frequencies, with the size of the detuning from the D2D2D2 resonance twice that from the D1D1D1 resonance. The direction of the effective magnetic field is along the laser propagation axis, and its magnitude is proportional to the vector polarizability of the atom and to the laser intensity. We use stimulated Raman spectroscopy on an optically pumped slow atomic beam from a magneto-optical trap to measure the vector polarizability and saturated absorption spectroscopy to show that the scalar polarizability vanishes at the particular detuning.
Ramsey spectroscopy and geometric operations on the released sodium Bose–Einstein condensates consisting of 10 7 atoms were demonstrated using copropagating two-photon stimulated Raman pulses, which were resonant to the clock transition between the F =1, m F =0 and F =2, m F =0 states of sodium atoms. The Ramsey fringes with a visibility close to 1 were obtained for two Raman pulses separated by 10 ms. A relative frequency resolution of Ramsey resonance was 6×10 -10 and a phase uncertainty of fringes was 0.06 rad for single measurement. Using resonant laser-controlled Raman pulses, geometric operations for rotations of the two-level Bose–Einstein condensates around axes 2 and 3 on the Bloch sphere were also demonstrated with a relative phase uncertainty of 4%.
The mid-term fractional frequency stability of miniaturized atomic clocks can be limited by light-shift effects. In this Letter, we demonstrate the implementation of a symmetric auto-balanced Ramsey (SABR) interrogation sequence in a microcell-based atomic clock based on coherent population trapping. Using this advanced protocol, the sensitivity of the clock frequency to laser power, microwave power, and laser frequency variations is reduced, at least by one order of magnitude, in comparison with continuous-wave or Ramsey interrogation schemes. Light-shift mitigation obtained with the SABR sequence benefits greatly to the clock Allan deviation for integration times between 102 and 105 s. These results demonstrate that such interrogation techniques are of interest to enhance the timekeeping performance of chip-scale atomic clocks.