1 INTRODUCTION 1 Introduction In this reference we present many of the physical and optical properties of sRb that are relevant to various quantum optics experiments. In particular, we give parameters that are useful in treating the mechanical effects of light on Rb atoms. The measured numbers are given with their original references, and the calculated numbers are presented with an overview of their calculation along with references to more comprehensive discussions of their underlying theory. At present, this document is not a critical review of experimental data, nor is it even guaranteed to be correct; for any numbers critical to your research, you should consult the original references. We also present a detailed discussion of the calculation of fuorescence scattering rates, because this topic is often not treated clearly in the literature. More details and derivations regarding the theoretical formalism here may be found in Ref. 1 Thecurrentversionofthisdocumentisavailableathttp://steck.us/alkalidata,alongwithcesiumD Line Data, " Sodium D Line Data, " and"Rubidium 85 D Line Data. This is the only permanent URL for this document at present: please do not link to any others. Please send comments, corrections, and suggestions to dsteck@oregon. edu. 2 Rubidium 87 Physical and Optical Properties Some useful fundamental physical constants are given in Table 1. The values given are the 2006 COdaTa recommended values, as listed in [2]. Some of the overall physical properties of Rb are given in Table 2.Rubidium 87 has 37 electrons, only one of which is in the outermost shell. sTRb is not a stable isotope of rubidium, decaying to B-+ 87Sr with a total disintegration energy of 0.283 Mev [3(the only stable isotope is sRb), but has an extremely slow decay rate, thus making it effectively stable. This is the only isotope we consider in this reference. The mass is taken from the high-precision measurement of [4, and the density, melting point, boiling point, and heat capacities(for the naturally occurring form of Rb)are taken from 3. The vapor pressure at 25 C and the por pressure curve in Fig. I are taken from the vapor-pressure model given by 5, which is 4215 log1o Pv=2.881+4.857-T(solid phase) 1og10P=2.881+43124040 (liquid phase) where P is the vapor pressure in torr(for Pv in atmospheres, simply omit the 2.881 term), and T is the temperature in K. This model is specified to have an accuracy better than +5% from 298-550K. Older, and probably less- accurate, sources of vapor-pressure data include Refs. 6 and 7. The ionization limit is the minimum energy required to ionize a SRb atom; this value is taken from Ref [8] for he optical properties of the sTRb D line are given in Tables 3 and 4. The properties are given separately each of the two D-line components; the D2 line(the 52S1/2 52P 3/2 transition o properties are given in Table 3, and the optical properties of the DI line(the 5-S1/2-452P1/2 transition) are given in Table 4. Of these two components, the D2 transition is of much more relevance to current quantum and atom optics experiments because it has a cycling transition that is used for cooling and trapping Rb. The frequency wo of the D2 was measured in 9, while the frequency of the Di transition is an average of values given by [10 and [11; the vacuum wavelengths A and the wave numbers k are then determined via the following relations Due to the different nuclear masses of the two isotopes srB and 87Rb, the transition frequencies of 87Rb are shifted slightly up compared to those of 85Rb. This difference is reported as the isotope shift, and the values are taken from [10.( See 11, 12 for less accurate measurements. The air wavelength Aair A/n assumes an index of refraction of n= 1.000 266 501(30) for the D2 line and n= 1.000 266 408 (30) for the D1 line, corresponding1 Introduction 3 1 Introduction In this reference we present many of the physical and optical properties of 87Rb that are relevant to various quantum optics experiments. In particular, we give parameters that are useful in treating the mechanical effects of light on 87Rb atoms. The measured numbers are given with their original references, and the calculated numbers are presented with an overview of their calculation along with references to more comprehensive discussions of their underlying theory. At present, this document is not a critical review of experimental data, nor is it even guaranteed to be correct; for any numbers critical to your research, you should consult the original references. We also present a detailed discussion of the calculation of fluorescence scattering rates, because this topic is often not treated clearly in the literature. More details and derivations regarding the theoretical formalism here may be found in Ref. [1]. The current version of this document is available at http://steck.us/alkalidata, along with “Cesium D Line Data,” “Sodium D Line Data,” and “Rubidium 85 D Line Data.” This is the only permanent URL for this document at present; please do not link to any others. Please send comments, corrections, and suggestions to dsteck@uoregon.edu. 2 Rubidium 87 Physical and Optical Properties Some useful fundamental physical constants are given in Table 1. The values given are the 2006 CODATA recommended values, as listed in [2]. Some of the overall physical properties of 87Rb are given in Table 2. Rubidium 87 has 37 electrons, only one of which is in the outermost shell. 87Rb is not a stable isotope of rubidium, decaying to β − + 87Sr with a total disintegration energy of 0.283 MeV [3] (the only stable isotope is 85Rb), but has an extremely slow decay rate, thus making it effectively stable. This is the only isotope we consider in this reference. The mass is taken from the high-precision measurement of [4], and the density, melting point, boiling point, and heat capacities (for the naturally occurring form of Rb) are taken from [3]. The vapor pressure at 25◦C and the vapor pressure curve in Fig. 1 are taken from the vapor-pressure model given by [5], which is log10 Pv = 2.881 + 4.857 − 4215 T (solid phase) log10 Pv = 2.881 + 4.312 − 4040 T (liquid phase), (1) where Pv is the vapor pressure in torr (for Pv in atmospheres, simply omit the 2.881 term), and T is the temperature in K. This model is specified to have an accuracy better than ±5% from 298–550K. Older, and probably less￾accurate, sources of vapor-pressure data include Refs. [6] and [7]. The ionization limit is the minimum energy required to ionize a 87Rb atom; this value is taken from Ref. [8]. The optical properties of the 87Rb D line are given in Tables 3 and 4. The properties are given separately for each of the two D-line components; the D2 line (the 52S1/2 −→ 5 2P3/2 transition) properties are given in Table 3, and the optical properties of the D1 line (the 52S1/2 −→ 5 2P1/2 transition) are given in Table 4. Of these two components, the D2 transition is of much more relevance to current quantum and atom optics experiments, because it has a cycling transition that is used for cooling and trapping 87Rb. The frequency ω0 of the D2 was measured in [9], while the frequency of the D1 transition is an average of values given by [10] and [11]; the vacuum wavelengths λ and the wave numbers kL are then determined via the following relations: λ = 2πc ω0 kL = 2π λ . (2) Due to the different nuclear masses of the two isotopes 85Rb and 87Rb, the transition frequencies of 87Rb are shifted slightly up compared to those of 85Rb. This difference is reported as the isotope shift, and the values are taken from [10]. (See [11, 12] for less accurate measurements.) The air wavelength λair = λ/n assumes an index of refraction of n = 1.000 266 501(30) for the D2 line and n = 1.000 266 408(30) for the D1 line, corresponding