Alkali D Line Data - Steck

1 rubidium 85 D line DataDaniel Adam SteckOregon Center for Optics and Department of Physics, University of OregonCopyrightc 2008, 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 30 April is revision , 20 September this document as:Daniel A. Steck , rubidium 85 d line data , available online (revision ,20 September 2013).Author contact information:Daniel SteckDepartment of Physics1274 University of OregonEugene, Oregon Introduction31 IntroductionIn this reference we present many of the physical and optical properties of85Rb that are relevant to variousquantum optics experiments.

2 In particular, we give parameters that are useful in treating the mechanical effects oflight on85Rb 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. 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 87 d line data .

3 This is theonlypermanent URL for thisdocument at present; please do not link to any others. Please sendcomments, corrections, and suggestions rubidium 85 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 of85Rb are given in 85 has 37 electrons, only one of which is in the outermost is the only stable isotope ofrubidium (although87Rb is only very weakly unstable, and is thus effectively stable), and is the only isotope weconsider in this reference. The mass is taken from the high-precision measurement of [3], and the density, meltingpoint, boiling point, and heat capacities (for the naturally occurringform of Rb) are taken from [4]. The vaporpressure at 25 C and the vapor 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.

4 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 energyrequired to ionize a85Rb atom; this value is taken from Ref. [8].The optical properties of the85Rb 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 trapping85Rb. The frequency 0of the D2is acombination of the87Rb measurement of [9] with the isotope shift quoted in [10], while the frequency of the D1transition is an average of values given by [10] and [11]; the vacuum wavelengths and the wave numberskLarethen determined via the following relations: =2 c 0kL=2.

5 (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 85 Physical and Optical Propertiesto typical laboratory conditions (100 kPa pressure, 20 C temperature, and 50% relative humidity). 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]).

6 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; 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. 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 .

7 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 the85Rb atomic velocity when absorbing or emitting a resonant photon,and is given byvr=~kLm.(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)because 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 (8) gives sw= 4 r. Two temperatures that are useful in cooling and1 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. See Refs. [16,17] for more Hyperfine Structure5trapping 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 [24]. Of course, in Zeeman-degenerate atoms, sub-Doppler coolingmechanisms permit temperatures substantially below this limit [25].

9 3 Hyperfine Energy Level SplittingsThe 52S1/2 52P3/2and 52S1/2 52P1/2transitions are the components of a fine-structure doublet, andeachof these transitions additionally have hyperfine structure. The fine structure is a result of the coupling between theorbital angular momentumLof the outer electron and its spin angular momentumS. The total electron angularmomentum is then given byJ=L+S,(11)and the corresponding quantum numberJmust lie in the range|L S| J L+S.(12)(Here we use the convention that the magnitude ofJispJ(J+ 1)~, and the eigenvalue ofJzismJ~.) For theground state in85Rb,L= 0 andS= 1/2, soJ= 1/2; for the first excited state,L= 1, soJ= 1/2 orJ= 3 energy of any particular level is shifted according to the value ofJ, so theL= 0 L= 1 (D line ) transitionis split into two components, the D1line (52S1/2 52P1/2) and the D2line (52S1/2 52P3/2). The meaningof the energy level labels is as follows: the first number is the principal quantum number of the outer electron, thesuperscript is 2S+ 1, the letter refers toL( , S L= 0, P L= 1, etc.)

10 , and the subscript gives the hyperfine structure is a result of the coupling ofJwith the total nuclear angular momentumI. The totalatomic angular momentumFis then given byF=J+I.(13)As before, the magnitude ofFcan take the values|J I| F J+I.(14)For the85Rb ground state,J= 1/2 andI= 5/2, soF= 2 orF= 3. For the excited state of the D2line (52P3/2),Fcan take any of the values 1, 2, 3, or 4, and for the D1excited state (52P1/2),Fis either 2 or 3. Again, theatomic energy levels are shifted according to the value the fine structure splitting in85Rb is large enough to be resolved by many lasers ( 15 nm), the twoD- line components are generally treated separately. The hyperfine splittings, however, are much smaller, and itis useful to have some formalism to describe the energy shifts. TheHamiltonian that describes the hyperfinestructure for each of the D- line components is [23,26 28]Hhfs=AhfsI J+Bhfs3(I J)2+32(I J) I(I+ 1)J(J+ 1)2I(2I 1)J(2J 1)+Chfs10(I J)3+ 20(I J)2+ 2(I J)[I(I+ 1) +J(J+ 1) + 3] 3I(I+ 1)J(J+ 1) 5I(I+ 1)J(J+ 1)I(I 1)(2I 1)J(J 1)(2J 1),(15) Interaction with Static External Fieldswhich leads to a hyperfine energy shift of Ehfs=12 AhfsK+Bhfs32K(K+ 1) 2I(I+ 1)J(J+ 1)4I(2I 1)J(2J 1)+Chfs5K2(K/4 + 1) +K[I(I+ 1) +J(J+ 1) + 3 3I(I+ 1)J(J+ 1)] 5I(I+ 1)J(J+ 1)I(I 1)(2I 1)J(J 1)(2J 1),(16)whereK=F(F+ 1) I(I+ 1) J(J+ 1),(17)Ahfsis the magnetic dipole constant,Bhfsis the electric quadrupole constant, andChfsis the magnetic octupoleconstant (although the terms withBhfsandChfsapply only to the excited manifold of the D2transition and notto the levels withJ= 1/2).