Radiation-Field-Dependent Frequency Shifts of Atomic Beam Resonances

Abstract

Radiation-fielddependent frequency shifts arising in atomic-beam spectroscopy are treated theoretically and experimentally. Shifts due to fundamental and unavoidable interactions between the radiation field and the atoms comprising the beam are distinguished from those due to various "apparatus effects." Precise measurements of frequency shifts are made for a cesium beam experiencing Ramsey-type excitation. For the magnetic-field-sensitive transitions ( F , M F ) = (4, f l ) -( 3 , fl), the magnitude of the shifts is about 1 part in 1Olo of the resonance frequency value, per milliwatt variation of input power to the radiation field. The shifts vary with input intensity in a nonmonotonic fashion and are shown to result from nonuniformity in the static magnetic c-field of the apparatus. Much smaller shifts of about 5 parts in 1013 per milliwatt are observed for the magnetic-field-insensitive transition ( F , M F ) = (4,O) -(3,0). The major features of these shifts are shown to arise from spectral impurities in the radiation exciting the transition and a small phase daerence between the pair of separated radiation fields. The bearing these results have on evaluating the accuracy of an atomic beam frequency standard is discussed.

Frequency shifts due to ramsey type interrogation in atomic beam tubes

“…Frequency changes due to changes in the microwave power level are quite pronounced, which is contrary to the result of a previous treatment of this subject [5]. In fact, the power dependence could be utilized to determine the frequency bias when other causes for frequency bias are known to be absent, e.g., microwave spectrum effects (see Section 5).…”

“…In this case the measurement of the frequency change with reduction of the microwave power to, for example, P /2 yields directly the frequency bias according to eq (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) This factor has a maximum of unity for br = 77/4. Since the perturbation amplitude b is proportional to the square root of the applied power, the higher the applied microwave power, the higher is the velocity of the atoms for which the transition probability is maximum.…”

“…We can use eq (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)) to obtain the dependence of the frequency bias Av on the microwave power P. Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) The results, as summarized in eqs (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) and (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and in figure 2, show that frequency shifts caused by cavity phase differences, the microwave power level, the resonance linewidth (velocity of atoms), and the frequency modulation amplitude are closely interrelated.…”

“…We are interested In the coefficient of that term in I { t } which varies as (1)(2) and eq (1)(2)(3) into eq (1-7) we obtain (1)(2)(3)(4)(5)(6)(7)(8) Equation (I' 8) gives us the frequency bias Af which we define v = A v o (1)(2)(3)(4)(5)(6)(7)(8)(9) In order to evaluate eq(I-8) we have to express B/C in terms of the operating conditions. Following eq(I-l)we.…”