Publisher Correction: Control of semiconductor emitter frequency by increasing polariton momenta

Correction to: Nature Photonics https://doi.org/10.1038/s41566-018-0176-6, published online 4 June 2018.

In the version of this Article originally published, in the PDF, in equations (1) and (3b), the superscript ‘ρ’ was mistakenly set as ‘j’; the equations should have read:

$${\mathbf{E}}_{\mathbf{q}}\left( {\mathbf{r}} \right) \propto {\mathrm{e}}^{ - q\left| z \right|}{\mathrm{e}}^{ - i{\mathbf{q}} \cdot {\mathbf{\rho}}}\left( {{\hat{\mathbf q}} \pm i{\hat{\mathbf z}}} \right)$$

(1)

$$\psi _{n{\mathbf{k}}}\left( {\mathbf{r}} \right) = {\mathrm{e}}^{ - i{\mathbf{k}} \cdot {\mathbf{\rho}}}\phi _n\left( {z - z_0} \right)$$

(3b)

The equation number (5) was missing from the following equation:

$$\begin{array}{*{20}{l}}\cr {\it{\Gamma }}_{\begin{array}{*{20}{c}} {{\mathrm{em}}} \cr {{\mathrm{ab}}} \end{array}} = & \frac{{2{\rm{\pi}}}}{\hbar }\mathop {\sum}\nolimits_{{\mathbf{k}}_{\mathrm{i}},{\mathbf{k}}_{\mathrm{f}}} {\left| {\left\langle {n_{\mathrm{f}},{\mathbf{k}}_{\mathrm{f}},n_{\mathbf{q}} \pm 1\left| {H_{{\mathrm{int}}}} \right|n_{\mathrm{i}},{\mathbf{k}}_{\mathrm{i}},n_{\mathbf{q}}} \right\rangle } \right|} ^2\\\cr & f\left( {{\mathbf{k}}_{\mathrm{i}}} \right)\delta \left( {E_{n_{\mathrm{i}}{\mathbf{k}}_{\mathrm{i}}} - E_{n_{\mathrm{f}}{\mathbf{k}}_{\mathrm{f}}} \mp \hbar \omega _q} \right)\cr \end{array}$$

(5)

In equation (6), the proportional sign ‘∝’ was mistakenly included in term (i), the equation should have read:

$$\begin{array}{*{20}{l}}\langle n_{\mathrm{f}},{{\boldsymbol{k}}}_{\mathrm{f}},n_{\mathbf{q}} \pm 1\left| {H_{{\mathrm{int}}}} \right|n_{\mathrm{i}},{{\boldsymbol{k}}}_{\mathrm{i}},n_{\mathbf{q}}\rangle\propto \\ {{({\mathrm{i}})} \atop \overbrace { \left\langle {n_{\mathrm{f}}\left| {{\rm{e}}^{ - qz}\partial _z} \right|n_{\mathrm{i}}} \right\rangle}} {{({\mathrm{ii}})} \atop \overbrace{\left\langle {{{\boldsymbol{k}}}_{\mathrm{f}}\left| {{\mathrm{e}}^{ \pm i{\mathbf{q}} \cdot {\it{\rho }}}} \right|{{\boldsymbol{k}}}_{\mathrm{i}}} \right\rangle }}\cr \end{array}$$

(6)

And, in both the PDF and HTML versions, in the equation in the sentence beginning “The results presented are normalized to yield...”, the denominator ‘π²’ was incorrect; it should have been ‘(2π)²’. These errors have now been corrected online.