Alkali D Line Data - Steck

1 Cesium D line DataDaniel Adam SteckOregon Center for Optics and Department of Physics, University of OregonCopyrightc 1998, by Daniel Adam Steck . All rights material may be distributed only subject to the terms and conditions set forth in the Open Publication License, or later (the latest version is presently available ). Distributionof substantively modified versions of this document is prohibited without the explicit permission of the copyrightholder. Distribution of the work or derivative of the work in any standard (paper) book form is prohibited unlessprior permission is obtained from the copyright revision posted 23 January is revision , 23 December this document as:Daniel A. Steck , Cesium d line data , available online (revision , 23 December 2010).

2 Author contact information:Daniel SteckDepartment of Physics1274 University of OregonEugene, Oregon Introduction31 IntroductionIn this reference we present many of the physical and optical properties of cesium that are relevant to variousquantum optics experiments. In particular, we give parameters that are useful in treating the mechanical effects oflight on cesium atoms. The measured numbers are given with their original references, and the calculated numbersare presented with an overview of their calculation along with references to more comprehensive discussions oftheir underlying theory. At present, this document isnota critical review of experimental data , nor is it evenguaranteed to be correct; for any numbers critical to your research, you should consult the original references.

3 Wealso present a detailed discussion of the calculation of fluorescencescattering rates, because this topic is often nottreated clearly in the literature. More details and derivations regarding the theoretical formalism here may befound in Ref. [1].The current version of this document is available , along with Sodium DLine data , Rubidium 87 d line data , and Rubidium 85 d line data . This istheonlypermanent URL forthis document at present; please do not link to any others. Please send comments, corrections, and suggestions Cesium Physical and Optical PropertiesSome useful fundamental physical constants are given in Table1. The values given are the 2006 CODATA recommended values, as listed in [2].

4 Some of the overall physical properties of cesium are given in has 55 electrons, only one of which is in the outermost is the only stable isotope of cesium,and is the only isotope we consider in this reference. The mass is taken from the high-precision measurementof [3], and the density, melting point, boiling point, and heat capacities aretaken from [4]. The vapor pressure at25 C and the vapor pressure curve in taken from the vapor-pressure model given by [5], which islog10Pv= + 3999T(solid phase)log10Pv= + 3830T(liquid phase),(1)wherePvis the vapor pressure in torr (forPvin atmospheres, simply omit the term), andTis the temperaturein K. This model is specified to have an accuracy better than 5% from 298 550K.

5 Older, and probably less-accurate, sources of vapor-pressure data include Refs. [6] and [7]. The ionization limit is the minimum energyrequired to ionize a cesium atom; this value is taken from Ref. [8] (another measurement of 31 (7) cm 1[9] is not included due to substantial disagreement with the more recent value quoted here).The optical properties of the cesium D line are given in Tables3and4. The properties are given separately foreach of the two D- line components; the D2line (the 62S1/2 62P3/2transition) properties are given in Table3,and the optical properties of the D1line (the 62S1/2 62P1/2transition) are given in Table4. Of these twocomponents, the D2transition is of much more relevance to current quantum and atom optics experiments, becauseit has a cycling transition that is used for cooling and trapping frequencies 0of the transitions weremeasured using an optical frequency comb [10,11]; the vacuum wavelengths and the wave numberskLare thendetermined via the following relations: =2 c 0kL=2.

6 (2)The air wavelength air= /nassumes an index of refraction ofn= 266 094(30) for the D2line andn= 265 900(30) for the D1line, corresponding to typical laboratory conditions (100 kPa pressure, 20 Ctemperature, and 50% relative humidity). The index of refraction iscalculated from the 1993 revision [12] of the42 Cesium Physical and Optical PropertiesEdl en formula [13]:nair= 1 +" 8 +2 406 147130 2+15 2 P96 1 + 10 8( 72T)P1 + 6610T f 345 401 2 # 10 8.(3)Here,Pis the air pressure in Pa,Tis the temperature in C, is the vacuum wave numberkL/2 in m 1, andfis the partial pressure of water vapor in the air, in Pa (which can be computed from the relative humidity viathe Goff-Gratch equation [14]).

7 This formula is appropriate for laboratory conditions and has an estimated (3 )uncertainty of 3 10 8from 350-650 lifetimes are weighted averages1from recent measurements; the first [17] used a fast beam laser technique,yielding lifetimes of (10) ns for the 62P1/2state and (7) ns for the 62P3/2state; the second [18] used aphoton-counting method, giving lifetimes of (7) ns (62P1/2) and (10) ns (62P3/2) state; the third [19]used a static polarizability to obtain (6) ns (62P1/2) and (5) ns (62P3/2), after combining statisticaland systematic errors in quadrature. The first measurement is taken to supersede several measurements by someof the same experimenters using the same technique [20,21], and another measurement of comparable quoteduncertainty ( (2) ns for the 62P3/2state) [22] is excluded because of a substantial disagreement with all recentprecision measurements [17].

8 Another precise measurement of the ratios of the D1and D2transition strengths [23]of|hJ= 1/2kerkJ = 3/2i|2/|hJ= 1/2kerkJ = 1/2i|2= (9) was not factored into the weighted averagesquoted here. A general discussion of precision lifetime measurement methods can be found in [24]. Inverting thelifetime gives the spontaneous decay rate (EinsteinAcoefficient), which is also the natural (homogenous) linewidth (as an angular frequency) of the emitted spontaneous emission rate is a measure of the relative intensityof a spectral line . Commonly, the relativeintensity is reported as an absorption oscillator strengthf, which is related to the decay rate by [25] =e2 202 0mec32J+ 12J + 1f(4)for aJ J fine-structure transition, wheremeis the electron recoil velocityvris the change in the cesium atomic velocity when absorbing or emitting aresonant photon,and is given byvr=~kLm.

9 (5)The recoil energy~ ris defined as the kinetic energy of an atom moving with velocityv=vr, which is~ r=~2k2L2m.(6)The Doppler shift of an incident light field of frequency Ldue to motion of the atom is d=vatomc L(7)for small atomic velocities relative toc. For an atomic velocityvatom=vr, the Doppler shift is simply 2 r. Finally,if one wishes to create a standing wave that is moving with respect tothe lab frame, the two traveling-wavecomponents must have a frequency difference determined by the relationvsw= sw2 2,(8)1 Weighted means were computed according to = ( jxjwj)/( jwj), where the weightswjwere taken to be the inversevariances of each measurement,wj= 1/ 2j. The variance of the weighted mean was estimated according to 2 = ( jwj(xj )2)/[(n 1) jwj], and the uncertainty in the weighted mean is the square rootof this variance.

10 See Refs. [15,16] for more Hyperfine Structure5because sw/2 is the beat frequency of the two waves, and /2 is the spatial periodicity of the standing a standing wave velocity ofvr, Eq. (8) gives sw= 4 r. Two temperatures that are useful in cooling andtrapping experiments are also given here. The recoil temperatureis the temperature corresponding to an ensemblewith a one-dimensional rms momentum of one photon recoil~kL:Tr=~2k2 LmkB.(9)The Doppler temperature,TD=~ 2kB,(10)is the lowest temperature to which one expects to be able to cool two-level atoms in optical molasses, due to abalance of Doppler cooling and recoil heating [26]. Of course, in Zeeman-degenerate atoms, sub-Doppler coolingmechanisms permit temperatures substantially below this limit [27].