PHYSICAL REVIEW A 83, 039907(E) (2011)

Erratum: Squeezing the collective spin of a dilute atomic ensemble by cavity feedback[Phys. Rev. A 81, 021804(R) (2010)]

Monika H. Schleier-Smith, Ian D. Leroux, and Vladan Vuletic(Received 2 March 2011; published 28 March 2011)

DOI: 10.1103/PhysRevA.83.039907 PACS number(s): 42.50.Dv, 06.20.−f, 32.80.Qk, 42.50.Lc, 99.10.Cd

An error in our expression for S+ (second column of page 2)led us to miscalculate by a factor of 2 the spin variance due tophoton shot noise. The correction of this error alters numericalfactors but does not affect the conclusions of the paper.

We should have defined S+ ≡ S+(t)e−iRe[f1(0)]t , and thusEqs. (7)–(11) should read

〈S+〉β = e−Q/(2S)eiQSz/SS+(0), (7)

〈S2+〉β = e−(2+i)Q/Se2iQSz/SS2

+(0), (8)

�S2y = S2

2+ S

4−

(S2

2− S

4

)e−2Q/SGS(Q), (9)

〈SySz + SzSy〉 = (2S2 − S)e−Q/(2S) sin

(Q

2S

)GS(Q/2),

(10)

and

�S2y ≈ S

2

(1 + 2Q + Q2

). (11)

The second term in Eq. (11) indicates the spin variance QS

due to photon shot noise, twice the value given in our originalpublication.

Although the numerical prefactors in subsequent expres-sions are of little consequence, we correct them here forcompleteness:

σ 2α0

≈ 2/Q + Q4/(24S2),

σα0σα0+π/2 ≈√

2Q,

Qcurv = 121/5S2/5,

σ 2curv = (5/2)12−1/5S−2/5,

σ 2α0,r

≈(

2

Q+ Q

3Sη

)=

(1

2Sηr+ 4r

3

),

Qscatt =√

6Sη,

σ 2α0,r

|Q=Qscatt =√

8/(3Sη),

ropt =√

3/(8Sη).

The corrected version of Fig. 2 still indicates substantialsqueezing, and the caption is unchanged.

0 50 100 150 2000.01

0.1

1

Q

σα

0

20.001

0.01

0.11

FIG. 2. (Color online) Minimum normalized variance σ 2α0,r as a

function of shearing strength Q for S = 104 and various single-atomcooperativities η = 0.001, 0.01, 0.1, 1 (solid lines). The dashed lineshows the limit σ 2

curv due to the curvature of the Bloch sphere whenfree-space scattering is ignored. The dotted line shows the varianceneglecting both free-space scattering and curvature, scaling as 1/Q

for Q � 1.

039907-11050-2947/2011/83(3)/039907(1) ©2011 American Physical Society