Introductory Quantum Optics - Errata

List of corrections for Gerry and Knight ”Introductory Quantum Optics” (Cambridge University Press 2005, reprinted with corrections 2006) Chapter 2: p. 11 text above Eq. (2.6): dimension of  q   q (t) is [mkg [mkg 1/2] as you can check by dimensional dimensional analysis of Eq.(2.5); likewise, likewise, the dimension of q ˙(t) =  p(  p (t) is 1/2 −1 [mkg s ] as it needs to be to have the Hamilton function in Eq.(2.8) with dimensions of energy, the commutator in Eq.(2.9) with dimensions of action, and the creation and annihilation operators in Eqs.(2.13-14) dimensionless. p. 13 Eq. (2.20): missing minus sign in fourth line of the equation p. 16 Eq. (2.47): square root sign only over 2 p. 16: missing |  at the end of footnote p. 19 Eq. (2.73): replace ω 2 k by ω by  ω k2  on the r.h.s. p. 20 line after Eq. (2.81): change ”The” to ”A” p. 21 Eq. (2.89): remove the hats on unit vectors p. 21 Eqs. (2.91) and (2.92): change k to κ  (four places) p. 23 Eq. (2.121): change κ to κ p. 25 below Eq. (2.131): replace ”...given in Eq.(2.131)...” by ”...given in Eq.(2.34)...” p. 28 Eq. (2.152): change ω 3 to ω to  ω 2 p. 29 Eq. (2.155): change h ¯ 2 to h ¯  in second line of equation p. 30 line above Eq. (2.163): change δ (r ) to δ (r) p. 31 Eq. (2.167): remove minus sign p. 32-33 the discussion of the Casimir effect is incomplete. A minimal set of corrections are: keep a prime on the summation signs up to and including Eq. (2.177), define the dimensionless dimensionless variable variable w   above above Eq. (2.177) (2.177) as w =  2 2 2 2 r d /π , write F  (z ) =  −2  − 2z  in line after Eq. (2.180), and replace L3 in Eq. (2.181) by L2 p. 33 Eq. (2.183): in the second line i  multiplies the whole exponent (in both exponentials) exponentials) p. 35 Eq. (2.200): replace i by −ih ¯  on the r.h.s Chapter 3: p. 45 Eq. (3.20): replace 4 by 2 −|α| /2 p. 46 Eq. (3.28): remove the factor e−|α on left hand side p. 50 Eq. (3.46): multiply right hand side by e by  e −ξ /2 p. 52 Eq. (3.52): replace ω0 by ω  in the denominator on the r.h.s p. 52 Eq. (3.53): remove minus sign on the r.h.s. 2

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p. 52 Eq. (3.55): swap u(t) and u∗ (t) in the 2nd line of the equation p. 52 Eq. (3.56): replace u(t) by u ∗ (t) on the l.h.s., replace global minus sign by i/¯h  on the r.h.s. p. 55 4th line below Eq. (3.73) replace Ψn (z ) by Ψ(z ) p. 60 Eq. (3.93): in the 3rd line replace a∗ by α∗ in the exponential p. 65 below Eq. (3.125) replace ”...just the Fourier transform...” by ”...just the reverse Fourier transform...” p. 71 Problem 2: replace 1/(2¯n)1/2 by 1/(4¯n)1/2 Chapter 4: p. 74 two lines below Eq. (4.1): h ¯  is missing p. 76 Eq. (4.14): remove last minus sign p. 85 4th line from below: replace |b by |a p. 89 Fig. 4.4: replace Ωn  on horizontal axis by V /h ¯  and add to caption ”∆ is given in units of  V /¯h” p. 94 Fig. 4.6: label on the x-axis should read λt Chapter 5: p. 116 Eq. (5.2): multiply r.h.s by 0 c K  K  p. 116 Eq. (5.7): replace K 1 K 2 by |K  ||K  |  on the r.h.s. p. 118 Eq. (5.21): divide r.h.s by T  p. 122 Eq. (5.39): replace first = by ∝; the r.h.s. is not of dimensions of  an intensity (0 c missing) p. 125 1st line: replace ”Maximum visibility...occurs...” by ”Maxima of  the...occur...”. Note that the visibility does not drop at all, but rather the intensity in the maxima does! p. 133 Problem 1: replace ”Eq.(5.66)” by ”Eq.(5.67)” ∗

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Chapter 6: p. 136 Remove the sentence ”The photons, to conserve momentum, are emitted in opposite directions.” (This is just wrong physics! Since one can excite the atom with two collinear beams, it can also decay by emitting two photons in the same direction. The angular momenta of initial and final atomic state put constraints on the joint polarization state of the emitted photons.)

Chapter 7: p. 168 Eq. (7.92): put brackets around operators on the r.h.s. Chapter 10: p. 240 three lines below Eq. (10.6): change (1 + 4/n) to (1 − 4/n) p. 244 two lines below Eq. (10.20): replace Ω0  by (Ω20 − ω02 /4Q2 )1/2 p. 245 two lines below Eq. (10.21): replace (4.87) by (4.90) p. 245 Eq. (10.25): remove  0