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Physical Review A

Precision test of the ac Stark shift in a rubidium atomic vapor

Filippo Levi, James C. Camparo, B. Francois, Claudio Eligio Calosso, Salvatore Micalizio, A. Godone

Published Feb 29, 2016• 25 citations
Publisher

Abstract

The ac Stark shift (also known as the ``light shift'') is one of the most important physical processes that arises in precision spectroscopy, affecting the basic understanding of field-matter interactions, measurements of fundamental constants, and even the atomic clocks onboard GPS satellites. Although the theory of the ac Stark shift was fully developed by the 1960s and 1970s, precision tests of theory have, for the most part, been few. Taking advantage of recent developments in atomic clock technology, specifically the pulsed approach to atomic signal generation, which allows frequency measurements with a resolution of $\ensuremath{\sim}{10}^{\ensuremath{-}15}$, we demonstrate a methodology for measuring the ac Stark shift. Here, we report results from a precision examination of the ac Stark shift in a vapor phase system, examining the resonant frequency of the $^{87}\text{Rb}$ 0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the ${D}_{1}$ absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.

DOI
10.1103/physreva.93.023433

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The ac Stark shift (also known as the ``light shift'') is one of the most important physical processes that arises in precision spectroscopy, affecting the basic understanding of field-matter interactions, measurements of fundamental constants, and even the atomic clocks onboard GPS satellites. Although the theory of the ac Stark shift was fully developed by the 1960s and 1970s, precision tests of theory have, for the most part, been few. Taking advantage of recent developments in atomic clock technology, specifically the pulsed approach to atomic signal generation, which allows frequency measurements with a resolution of \ensuremath∼10\ensuremath−15\ensuremath{\sim}{10}^{\ensuremath{-}15}\ensuremath∼10\ensuremath−15, we demonstrate a methodology for measuring the ac Stark shift. Here, we report results from a precision examination of the ac Stark shift in a vapor phase system, examining the resonant frequency of the 87Rb^{87}\text{Rb}87Rb 0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the D1{D}_{1}D1​ absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than 5\ifmmode×\else\texttimes\fi10\ensuremath−25\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}5\ifmmode×\else\texttimes\fi10\ensuremath−2), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.
The dynamic Stark shift of an inhomogeneously broadened spectral transition has been studied. Our measurements show a shift in the observed 87 Rb ground-state hyperfine transition, which has a nonlinear dependence on light intensity when the conditions for inhomogeneous broadening are met. The nonlinearity is the result of light-intensity gradients in the signal volume, which produce an inhomogeneously broadened asymmetric microwave transition. We show that our measurements are in full agreement with the second-order perturbation-theory treatment of light-induced energy-level shifts when the effects of inhomogeneities are properly taken into consideration. The effects of inhomogeneous broadening must be carefully considered when one extracts oscillator strengths from light-shift data, or performs high-precision laser spectroscopy. Originator-supplied keywords include: AC stark effect, Atomic clocks, Atomic line shapes, Light shifts.
One of the important subjects in coherent-population- trapping-based (CPT-based) vapor cell frequency standards is the light shift (ac Stark shift). We calculate the light shift using a numerical method and perturbation approximation. Experimentally, we measure light shift using a pair of phase-locked diode lasers as well as a frequency-modulated diode laser. There is good agreement between theory and experiment. A method of controlling light shift in CPT-based frequency standards is proposed and implemented in Agilent Laboratories. The short-term stability of our CPT-based rubidium vapor cell frequency standard is measured as 1.3 x 10(-12) tau (-1/2), which is limited by the phase noise of the reference local oscillator used.
We report on a precision measurement of the DDD line tune-out wavelength of 87Rb^{87}\text{Rb}87Rb in the hyperfine ground state $\left|F=1,{m}_{F}=0,\ifmmode\pm\else\textpm\fi{}1\right\ensuremath{\rangle}$ manifold at 790nm790\phantom{\rule{0.16em}{0ex}}\mathrm{nm}790nm, where the scalar ac Stark shifts of the D1{D}_{1}D1​ and the D2{D}_{2}D2​ lines cancel. This wavelength is sensitive to usually neglected contributions from vector and tensor ac Stark shifts, transitions to higher principle quantum numbers, and core electrons. The ac Stark shift is probed by Kapitza-Dirac scattering of a rubidium Bose-Einstein condensate in a one-dimensional optical lattice in free space and controlled magnetic environment. The tune-out wavelength of the magnetically insensitive mF=0{m}_{F}=0mF​=0 state was determined to 790.01858(23)nm790.01858(23)\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{m}790.01858(23)nm with sub-pm accuracy. An in situ absolute polarization, and magnetic background field measurement is performed by employing the ac vector Stark shift for the ${m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ states. Comparing our findings to theory, we get quantitative insight into atomic physics beyond commonly used two-level atom approximations or the neglect of inner shell contributions.
The energy shift of an atom due to its interaction with the oscillating electric field of an electromagnetic wave, or a laser light, is called the ac Stark shift. It has been studied both in the field of precision spectroscopy and atom optics. When the laser intensity is not constant spatially, its gradient gives rise to a dipole force. The force was used either to trap atoms in an optical trap or to reflect or guide atoms. We studied the ac Stark effect taking into account the fine structure of an alkali atom. We found that when the laser light is circularly polarized and properly detuned between the D1 and D2 transitions, the ac Stark shift can take the form of a pure Zeeman shift, hence the name analogous Zeeman shift.
Atomic clocks are based on highly stable and well-characterized atomic transitions, mak-ing precise control and understanding of systematic frequency shifts essential for improved timekeeping performance. This thesis presents an experimental study of light-induced Stark shifts in rubidium and their impact on precision laser spectroscopy relevant to atomic frequency standards, as well as the effects of residual amplitude modulation on the laser lock point and the resulting sensitivity of both short- and long-term stability. A laser-based spectroscopy system was developed to probe rubidium transitions while enabling controlled variation of optical intensity. The optical beam was experimentally characterized through calculations of beam waist and measurements of power to accurately determine the intensity at the interaction region. Frequency shifts arising from the AC Stark effect were measured as a function of optical power, allowing extraction of the differential polarizability between atomic energy levels using a theoretical model relating energy shifts to electric-field intensity. Uncertainty analysis was performed through systematic propagation of experimental errors associated with beam geometry, optical power calibration, and frequency measurements. In addition, residual amplitude modulation generated by electro-optic phase modulation was investigated as a significant source of systematic error in frequency stabilization systems used in atomic clocks. The magnitude and behavior of RAM were experimentally characterized, and its impact on frequency stability was quantified by measuring the sensitivity of the laser lock point to controlled variations in RAM. Potential mitigation strategies were then explored through active pre-compensation of RAM using an amplitude electro-optic modulator in a closed-loop feedback system.