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the light shifts calculated in ref . @xcite are based upon eq . ( 2 ) in ref . the text states that the basis for eq . ( 2 ) is ` spherical ' ( i.e. , irreducible spherical tensors ) . in fact , the basis for eq . ( 2 ) is actually a cartesian basis ( i.e. , @xmath1 ) , which we used to perform all calculations in ref . @xcite .    in eq . ( 2 ) of ref . @xcite , @xmath2,@xmath3 and @xmath4 are the scalar , vector and tensor atomic dynamic polarizabilities defined in ref . the dipole matrix element in ref . @xcite is @xmath5 , as defined in ref . however , as ref . @xcite only considered light shifts of the ground states , the definition for @xmath6 in ref . @xcite becomes problematic when defining @xmath6 for the excited states . @xmath7 and @xmath8 are defined with respect to states of lower to higher energy , respectively , rather than with respect to initial and final states . this notation is therefore ambiguous if the initial state is an excited state . also , the counter - rotating term was not taken into account in ref . therefore , we follow the formalism in refs . @xcite , in which case eq . ( 2 ) of ref . @xcite should be rewritten as follows :    @xmath9 , \end{array } \label{hamiltonian}\ ] ]    where the dipole matrix element in refs . @xcite is @xmath10 , where @xmath11 are for ( lower , upper ) levels , respectively . @xmath2 , @xmath3 , and @xmath4 of eq . include counter - rotating terms . however , in ref . @xcite , we made an error in the definition of the vector polarizability , @xmath3 , by neglecting the rank dependence of the counter - rotating terms . in this errata , we correct the definition of @xmath3 to incorporate the rank dependence of the counter - rotating terms in our calculations of light shifts @xcite . the dynamic polarizabilities are then given by    @xmath12    @xmath13    where @xmath14 is the rank-@xmath15 propagator defined as    @xmath16    we note that the counter - rotating term gains an overall minus sign for @xmath17 in the expression for the vector propagator @xmath18 . we have confirmed that our corrected formula for the dynamic polarizabilities ( i.e. , eqs . ( 1 - 5 ) ) is now consistent with the expressions in ref . in addition to corrections to our formalism discussed above , we correct two numerical errors for the atomic data used to calculate the light shifts in refs . @xcite . these errors stem from a mistake for a partial lifetime @xmath19 and from an error for a transition wavelength @xmath20 . all values for @xmath19 and @xmath20 of ref . @xcite were taken from tables 7.17.3 of j. mckeever s ph.d thesis @xcite . the specific errors are as follows :    1 .   the wavelength for the transition @xmath21 in table 7.2 of ref . @xcite is listed as @xmath22 nm , whereas the correct value is @xmath23 nm . 2 .   the partial lifetime for the transition @xmath24 in table 7.3 of ref . @xcite is listed as @xmath25 @xmath26s , but instead should be @xmath27 @xmath26s .    the corrected values for tables 7.17.3 of ref . @xcite are highlighted with green color in tables [ comparisontable1 ] and [ comparisontable2 ] of this errata . the partial lifetimes and wavelengths from table 7.17.3 of ref . @xcite were obtained from refs . @xcite with the exception of the values for @xmath28 from ref . @xcite and @xmath29 from ref . @xcite .    to further confirm the accuracy of the corrected values from ref . @xcite , we refer to tables v and vi of arora _ et al . _ @xcite ( heretofore , labelled as ` clark ' ) . tables [ comparisontable1 ] and [ comparisontable2 ] in this errata compare the corrected tables from ref . @xcite to tables v  vi of ref . our values agree well with those from ref . @xcite . we note that all previous publications prior to ref . @xcite from our group , including ref . @xcite , have used the correct values in tables [ comparisontable1][comparisontable2 ] and not those from mckeever s thesis @xcite . furthermore , these earlier results are for linearly polarized trapping fields for which the contribution of the vector term @xmath3 vanishes . therefore , these earlier results from our group stand without revision .    using the revised formalism from section i and based on the corrected numerical values in tables [ comparisontable1][comparisontable2 ] from section ii , we present corrected figures to replace those in refs . @xcite as described in the following sections . the figure numbering in this errata mirrors that of ref.@xcite with corrected figures given here in roman numerals . fig . [ fig6 ] relates to magic wavelengths for the cs @xmath0 line and replaces fig . @xcite . the magic wavelength in this note is defined by the weighted average of the zeeman sublevels @xmath30 ( i.e. , not by @xmath2 alone ) .    as in ref . @xcite , we include a surface interaction potential of an atom with the dielectric nanofiber in our calculation of the total atomic trap potential . the surface potential of the ground state cs atom near a planar dielectric surface can be approximated by the van der waals potential @xmath31 , where @xmath32 and @xmath33 @xcite .    in figs . [ fig7 ] , [ fig8 ] , and [ fig9 ] , the two - color evanescent trap from ref . @xcite is constructed from a pair of counter - propagating @xmath34-polarized ( @xmath35 ) red - detuned beams ( @xmath36 mw ) at @xmath37 nm , forming an optical lattice , and a single repulsive @xmath38-polarized ( @xmath39 ) blue - detuned beam ( @xmath40 mw ) at @xmath41 nm . the sio@xmath42 tapered optical fiber has radius @xmath43 nm in the trapping region [ fig7],[fig8 ] , [ fig9 ] replace figures of fig . 7 , 8 , 9 of ref . @xcite .    for the magic , compensated trap in figs .  [ fig10 ] , [ fig11 ] , [ fig12 ] , we use a pair of counter - propagating @xmath34-polarized ( @xmath44 ) red - detuned beams ( @xmath45 mw ) at the magic wavelength @xmath46 nm . counter - propagating , @xmath34-polarized blue - detuned beams at a second magic wavelength @xmath47 nm are used with a power @xmath48 mw . the resulting interference is averaged out by detuning the beams to @xmath49 ghz . figs . [ fig10 ] , [ fig11 ] , [ fig12 ] replace figs . 10 , 11 , 12 of ref . @xcite . because of the errors described in sections i and ii , our experiment in ref . @xcite used red- and blue - detuned beams at wavelengths @xmath50 nm and @xmath51 nm instead of the correct values of @xmath52 nm and @xmath53 nm calculated in the same fashion as fig . [ fig6 ] but now for @xmath54 of @xmath55 to @xmath56 of @xmath57 . [ fig13 ] shows the trapping potentials for the ground and excited states for the correct magic wavelengths of @xmath52 nm and @xmath53 nm for this transition .    for the actual wavelengths @xmath50 nm and @xmath51 nm used in our experiment @xcite , fig.1 and fig . sm5 of ref . @xcite are here replaced by figs . [ fig14 ] and [ fig15 ] , respectively , which incorporate the revisions described in sections i and ii . our emphasis has been to correct the formalism ( section i ) and atomic data ( section ii and tables i , ii ) that are the basis for our calculations in refs . recently a more extensive set of atomic data than in tables i and ii has become available @xcite . we have confirmed that these data with our formalism in eqs . ( 1 - 5 ) reproduce figs . ( 4 , 5 ) from ref . @xcite .    however , the expanded set of atomic levels and lifetimes in ref . @xcite lead to small differences between figs . ( 4 , 5 ) @xcite and corresponding figures computed from our tables i , ii . these differences are most pronounced around @xmath58 nm ( e.g. , our fig . vi(a ) ) principally due to excited - state contributions up to @xmath59 , which are not included in tables i , ii . we therefore recommend that the data set from ref . @xcite be employed for the calculation of ac stark shifts for the @xmath0 line in atomic cesium rather than the less extensive data in our tables i , ii . 30 c. lacroute _ _ new j. phys . _ , * 14 * , 023056 ( 2012 ) . _ , * 109 * , 033603 ( 2012 ) . i. h. deutsch and p. s. jessen _ opt . comm . _ , * 283 * , 681 ( 2010 ) . d. a. steck _ quantum and atom optics textbook_. + http://atomoptics.uoregon.edu/  dsteck / teaching / quantum - optics/ , 2011 . p. rosenbusch _ _ phys . rev . a _ , * 79 * , 013404 ( 2009 ) . k. beloy , _ phd thesis _ , theory of the ac stark effect on the atomic hyper fine structure and applications to microwave atomic clocks , ( 2009 ) . work / beloy _ dissertation _ 2009.pdf fam le kien , p. schneeweiss , and a. rauschenbeutel arxiv:1211.2673v1 ( 2012 ) j. mckeever _ phd thesis _ ( 2004 ) + http://thesis.library.caltech.edu/2421 , 2004 . + in tables [ comparisontable1 ] and [ comparisontable2 ] of this errata , two errors from mckeever s thesis have been corrected and are highlighted in green , as described in section [ comp ] . g. laplanche _ _ phys . rev . a _ , * 30 * , 2881 ( 1984 ) . m. fabry and j. r. cussenot _ can . _ , * 54 * , 836 ( 1976 ) . d. a. steck _ cesium d line data _ + http://steck.us/alkalidata/ , 2003 . c. j. hood _ phd thesis _ ( 2000 ) . + http://thesis.library.caltech.edu/3688 . b. arora , m. s. safronova , c. w. clark _ phys . a _ , * 76 * , 052509 ( 2007 ) . j. mckeever _ _ phys . rev . _ , * 90 * , 133602 ( 2003 ) . stern _ et al . _ _ new j. phys . _ , * 13 * , 085004(2011 ) . e. vetsch _ _ , * 104 * , 203603 ( 2010 ) .
several errors in refs . 
 @xcite are corrected related to the optical trapping potentials for a state - insensitive , compensated nanofiber trap for the @xmath0 transition of atomic cesium . 
 section i corrects our basic formalism in ref . 
 @xcite for calculating dipole - force potentials . 
 section ii corrects erroneous values for a partial lifetime and a transition wavelength in ref . 
 @xcite . 
 sections iii and iv present corrected figures for various trapping configurations considered in refs . 
 @xcite and @xcite , respectively .