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arXiv:physics/0409051 · Physical Review Letters

Optical Clocks Based on Ultranarrow Three-Photon Resonances in Alkaline Earth Atoms

Tao Hong, Claire E. Cramer, Warren Nagourney, E. Norval Fortson

Published Feb 10, 2005• 132 citations
arXivHTMLPDF

Abstract

A sharp resonance line that appears in three-photon transitions between the 1S0 and 3P0 states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. With this method, the width and the rate of the clock transition can, in principle, be continuously adjusted from the MHz level to sub-mHz without loss of signal amplitude by varying the intensities of the three optical beams. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams or by point confinement in a lattice trap. Light-shift effects on the clock accuracy can be limited to below a part in 10(18).

DOI
10.1103/physrevlett.94.050801

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An optical atomic clock scheme is proposed that utilizes two lasers to establish coherent coupling between the 5s2 1S0 ground state of 88Sr and the first excited state, 5s5p 3P0. The coupling is mediated by the broad 5s5p 1P1 state, exploiting the phenomenon of electromagnetically induced transparency. The effective linewidth of the clock transition can be chosen at will by adjusting the laser intensity. By trapping the 88Sr atoms in an optical lattice, long interaction times with the two lasers are ensured; Doppler and recoil effects are eliminated. Based on a careful analysis of systematic errors, a clock accuracy of better than 2 x 10(-17) is expected.

arXiv:physics/0411197•Physical Review Letters•May 4, 2005•131 citations
A sharp resonance line that appears in three-photon transitions between the 1S0 and 3P0 states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. With this method, the width and the rate of the clock transition can, in principle, be continuously adjusted from the MHz level to sub-mHz without loss of signal amplitude by varying the intensities of the three optical beams. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams or by point confinement in a lattice trap. Light-shift effects on the clock accuracy can be limited to below a part in 10(18).
We report an experimental observation of the weak 'SO-~PO transition in 171,173Ybl and new approaches for qubits and optical clocks with this single-photon resonance and a three-photon resonance in an even isotope, respectively. Introduction - Optical clocks show great promise as the next generation of precision frequency standards due to the high frequency and correspondingly high line-Q of weakly allowed atomic transitions. Thanks to femtosecond comb technology (l), clocks based on optical transitions in both single trapped ions and neutral atom clouds are poised to exceed the already stringent bounds on precision set by microwave frequency standards. A recent proposal combining the Lamb-Dicke confinement of single ion frequency standards with the high signal-tenoise of neutral atom cLouds, and exploiting a highly forbidden transition insensitive to external magnetic fields and trap light polarization has the potential to do even better (2). The scheme makes use of the 'SO-~P~ electric dipole transition in alkaline-earth atoms, weakly allowed in odd isotopes by the hyperfine interaction of the nuclear spin and completely forbidden by a single-photon process in even isotopes. Trapping the atoms in a Stark-free optical httice will allow a large ensemble of atoms to exhibit a spectrum free of Doppler and recoil shifts, leading to an estimated accuracy of a few parts in lo1* (3, 41. As an additional application, the long atomic coherence times in optical lattices also suggest using the 'SO-~PO pairs of states as an array of qubits for quantum information (5, 61. Yb and Sr are both strong candidates for an optical lattice clock as well as for creating useful qubits. Both atoms have experimentally accessible energy level transitions, allowing the atoms to be readily laser-cooled and trapped, and in the case of Yb, Eose-Einstein condensed. While the Sr clock transition has been studied extensively, both in and out of an optical lattice, the same transition in Yb has thus far remained unexplored experimentally. Here we report the direct excitation of the 578 nm 'SO-~P~ transition in odd isotope 171,173Yb. (We understand that a group at NIST has also observed this transition (7)). We also discuss the possible application of this type of transitions in making qubits for quantum computation and a clock scheme based on three-photon transition in an even isotope (8, 91. - The level structure of Yb and the experimental apparatus are diagrammed in Fig. 1. The experiment is performed on a sample of cold atoms collected in a magneto- optical trap (MOT). To excite the clock transition, we shut off the MOT beams and irradiate the cloud of atoms with a 578 nm probe. JVe t,hen turn the MOT beams back on, continuously monitoring 399 nm fluorescence from the atom cloud. As the probe laser frequency is scanned over the dock transition, there is an observable decrease in MOT fluorescence as atoms are excited into the metastable 3Po state and escape the trap. By chopping trap and probe beams out of phase, we avoid light shifts of the clock transition due to near-resonant 399 nm light while maintaining a steady-state MOT population. The MOT fluorescence reduction of 171Yb is shown in Fig. 2 (a). Since iodine lines have been well measured in Observation of the 1So-3P, Transition in 1713173Yb
Magic-wave-induced 1S0−3P0^1S_0-^3P_01S0​−3P0​ transition in even isotopes of alkaline-earth-like atoms
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the 3P1^3P_13P1​ state into the long-living metastable state 3P0^3P_03P0​, thus enabling the strictly forbidden 1S0^1S_01S0​−-−3P0^3P_03P0​ ''clock'' transition in even isotopes of alkaline-earth-like atoms, without change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the line width of the "clock" transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional "state-mixing" wave, including estimations of the "magic" wavelengths, Rabi frequencies for the ''clock'' and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.
An ultra-stable optical clock based on coherent population trapping effect of alkaline-earth ions, such as Ca+^++, Sr+^++, Ba+^++, is analyzed here. The proposed transitions use the odd isotopes, so that the frequency shift is insensitive to the applied magnetic field. To enhance the signal, a large number of ions are trapped in a linear Paul trap, and laser cooled to crystallize such that the ions are in the Lamb-Dicke regime to avoid first order Doppler shift. Other relevant frequency shifts are also analyzed. Further techniques to improve the stability of the clock signal are discussed.
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the 3P1^{3}P_{1}3P1​ state into the long-living metastable state 3P0^{3}P_{0}3P0​, thus enabling the strictly forbidden $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ ``clock'' transition in even isotopes of alkaline-earth-metal-like atoms, without a change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the linewidth of the clock transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional ``state-mixing'' wave, including estimations of the ``magic'' wavelengths, Rabi frequencies for the clock and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.
The circular polarized laser beam of the “magic” wavelength used to produce an optical lattice for the time-frequency standard on neutral atoms may mix the 3P 1 state to the long-living metastable state 3P 0 thus providing significant enhancement of the strongly forbidden 1S 0 -3P 0 clock transition in even isotopes of alkaline-earth-like atoms. We present a detailed analysis of various factors influencing resolution and uncertainty for this kind of optical standard, including precise estimations of the “magic” wavelengths, transition matrix elements and field induced second- and fourth-order ac Stark shifts for the ground and metastable alkaline-earth-like atoms.
An optical atomic clock scheme is proposed that utilizes two lasers to establish coherent coupling between the 5s2 1S0 ground state of 88Sr and the first excited state, 5s5p 3P0. The coupling is mediated by the broad 5s5p 1P1 state, exploiting the phenomenon of electromagnetically induced transparency. The effective linewidth of the clock transition can be chosen at will by adjusting the laser intensity. By trapping the 88Sr atoms in an optical lattice, long interaction times with the two lasers are ensured; Doppler and recoil effects are eliminated. Based on a careful analysis of systematic errors, a clock accuracy of better than 2 x 10(-17) is expected.