Elena & Fabrice's Web

*Every page brings me hundreds of opportunities to make mistakes and to miss important ideas.*

Donald Knuth, The Art of Computer Programming, Fascicle 1.

Proceedings of SPIE 8255, 825505 (2012)

Only the Hamiltonian term coupling the cavity to the H-polarised quantum dot state should appear in Eq. (1). That is, Eq. (1) should read:

$$H_\mathrm{dot-cav} = \omega_\mathrm{X}\big(|\mathrm{V}\rangle\langle\mathrm{V}|+|\mathrm{H}\rangle\langle\mathrm{H}|\big)+(2\omega_\mathrm{X}-\chi)\mathrm{B}\rangle\langle\mathrm{B}| +\omega_a a^\dagger a + g\big[a^\dagger (|\mathrm{G}\rangle \langle\mathrm{H}|+|\mathrm{H}\rangle \langle\mathrm{B}|)+ \text{h. c.}\big]$$

New J. Phys. 13, 113014 (2011)

In page 8, last paragraph the equation $$L_\mathrm{I}+L_\mathrm{II}\approx2\langle a^{\dagger2}a^2\rangle$$ should read $$L_\mathrm{I}+L_\mathrm{II}\approx2\int_0^{\infty}\,\langle a^{\dagger2}a^2\rangle(t)dt$$ as the dynamics are always time integrated.

Phys. Rev. A 84, 043816 (2011)

An $i$ is missing in Eq. (10c), so these coefficient should read:

$$L_{\pm}+iK_\pm=\frac{\frac{8\Omega_\mathrm{L}^2}{\gamma_\sigma(\gamma_\sigma+\gamma_\phi)}\big[1 \pm i \frac{5\gamma_\sigma-\gamma_\phi}{4 R_\mathrm{L}}\big]-\frac{\gamma_\sigma-\gamma_\phi}{\gamma_\sigma+\gamma_\phi}\big[1\pm i\frac{\gamma_\sigma-\gamma_\phi}{4R_\mathrm{L}}\big]}{4\big(1+\frac{8 \Omega_\mathrm{L}^2}{\gamma_\sigma(\gamma_\sigma+\gamma_\phi)}\big)}$$

Phys. Rev. A 81, 053811 (2010)

Lower transitions (and operators) in the four level system (see for instance Fig. 2(a)) are referred to as $l_1$ and $l_2$ up to Eq. (58) where I inadvertently changed notation to $d_1$ and $d_2$. They should have been $l_1$ and $l_2$ throughout.

Also, in Fig. 11, the parameters $\gamma_2$ and $P_1$ together with the accompanying arrows, should be exchanged in position: $\gamma_2$ should appear in the right hand side and $P_1$ in the left hand one.

Superlattices and Microstructures 47, 16 (2010)

A minus sign is missing in Eq. (3), it should read:

$$\Delta \omega_O=2g\Re\Big\{\sqrt{\sqrt{\Big(1+\frac{P_b}{P_a}\Big)^2-4\frac{\Gamma_+}{g}\Big(-\frac{\Gamma_b}{2g}+\frac{P_b}{P_a}\frac{\Gamma_-}{g}\Big)}-\frac{P_b}{P_a}-\Big(\frac{\Gamma_b}{2g}\Big)^2}\Big\}$$

Eq. (2.62) should read:

$$\omega_{\substack{\mathrm{U}\\\mathrm{L}}}^n=\frac{(2n-1)\omega_a+\omega_\sigma}2\pm\mathcal{R}_n$$

Eqs. (2.46) should read:

$$\sigma(\sigma^\dagger)^\mu\sigma^\nu =(-1)^\mu(1-\nu)(\sigma^\dagger)^\mu\sigma^{\nu+1}+\mu (\sigma^\dagger)^{\mu-1}\sigma^\nu $$

$$(\sigma^\dagger)^\mu\sigma^\nu\sigma^\dagger=(-1)^\nu(1-\mu)(\sigma^\dagger)^{\mu+1}\sigma^\nu+\nu (\sigma^\dagger)^\mu\sigma^{\nu-1}$$

Eq. (3.67) is missing a minus sign, as in the published paper above, so that it should read:

$$\Delta \omega_O=2g\Re\Big\{\sqrt{\sqrt{\Big(1+\frac{P_b}{P_a}\Big)^2-4\frac{\Gamma_+}{g}\Big(-\frac{\Gamma_b}{2g}+\frac{P_b}{P_a}\frac{\Gamma_-}{g}\Big)}-\frac{P_b}{P_a}-\Big(\frac{\Gamma_b}{2g}\Big)^2}\Big\}$$

Shortly after this equation, in the next paragraph, the in-line equation of the direct exciton emission splitting should read:

$$2\sqrt{\sqrt{g^4-2g^2\gamma_a\gamma_+}-\gamma_a^2/4}$$