Alkali D Line Data - Steck

1 Rubidium 87 D line DataDaniel Adam SteckOregon Center for Optics and Department of Physics, University of OregonCopyrightc 2001, 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 25 September is revision , 13 January this document as:Daniel A.

2 Steck , Rubidium 87 D line data , available online (revision ,13 January 2015).Author contact information:Daniel SteckDepartment of Physics1274 University of OregonEugene, Oregon Introduction31 IntroductionIn this reference we present many of the physical and optical properties of87Rb that are relevant to variousquantum optics experiments. In particular, we give parameters that are useful in treating the mechanical effects oflight on87Rb 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.

3 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. 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 Cesium DLine data , Sodium D line data , and Rubidium 85 D line data .

4 This is theonlypermanent URL for thisdocument at present; please do not link to any others. Please sendcomments, corrections, and suggestions Rubidium 87 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]. Some of the overall physical properties of87Rb are given in Table2. Rubidium87 has 37 electrons, only one of which is in the outermost is not a stable isotope of rubidium, decayingto +87Sr with a total disintegration energy of MeV [3] (the only stable isotope is85Rb), but has anextremely slow decay rate, thus making it effectively stable.

5 This is the only isotope we consider in this mass is taken from the high-precision measurement of [4], and the density, melting point, boiling point, andheat capacities (for the naturally occurring form of Rb) are takenfrom [3]. The vapor pressure at 25 C and thevapor pressure curve in taken from the vapor-pressure model given by [5], which islog10Pv= + 4215T(solid phase)log10Pv= + 4040T(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.

6 Older, and probably less-accurate, sources of vapor-pressure data include Refs. [6] and [7]. The ionization limit is the minimum energyrequired to ionize a87Rb atom; this value is taken from Ref. [8].The optical properties of the87Rb D line are given in Tables3and4. The properties are given separatelyfor each of the two D- line components; the D2line (the 52S1/2 52P3/2transition) properties are given inTable3, and the optical properties of the D1line (the 52S1/2 52P1/2transition) are given in Table4. Of thesetwo components, the D2transition is of much more relevance to current quantum and atom optics experiments,because it has a cycling transition that is used for cooling and trapping87Rb.

7 The frequency 0of the D2wasmeasured in [9], while the frequency of the D1transition is an average of values given by [10] and [11]; the vacuumwavelengths and the wave numberskLare then determined via the following relations: =2 c 0kL=2 .(2)Due to the different nuclear masses of the two isotopes85Rb and87Rb, the transition frequencies of87Rb areshifted slightly up compared to those of85Rb. This difference is reported as the isotope shift, and the values aretaken from [10]. (See [11,12] for less accurate measurements.) The air wavelength air= /nassumes an indexof refraction ofn= 266 501(30) for the D2line andn= 266 408(30) for the D1line, corresponding42 Rubidium 87 Physical and Optical Propertiesto typical laboratory conditions (100 kPa pressure, 20 C temperature, and 50% relative humidity).

8 The index ofrefraction is calculated from the 1993 revision [13] of the Edl en formula [14]: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 [15]). This formula is appropriate for laboratory conditions and has an estimated (3 )uncertainty of 3 10 8from 350-650 lifetimes are weighted averages1from four recent measurements.

9 The first employed beam-gas-laser spec-troscopy [18], with lifetimes of (4) ns for the 52P1/2state and (4) ns for the 52P3/2state, the secondused time-correlated single-photon counting [19], with lifetimes of (4) ns for the 52P1/2state and (9)ns for the 52P3/2state, the third used photoassociation spectroscopy [20] (as quoted by [19]), with a lifetime (6) ns for the 52P3/2state only, and the fourth also used photoassociation spectroscopy [21], with lifetimesof (8) ns for the 52P1/2state and (8) ns for the 52P3/2state. Note that at present levels of theoretical[22] and experimental accuracy, we do not distinguish between lifetimes of the85Rb and87Rb isotopes.

10 Invertingthe lifetime gives the spontaneous decay rate (EinsteinAcoefficient), which is also the natural (homogenous) line width (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 [23] =e2 202 0mec32J+ 12J + 1f(4)for aJ J fine- structure transition, wheremeis the electron recoil velocityvris the change in the87Rb atomic velocity when absorbing or emitting a resonant photon,and is given byvr=~kLm.