Nature Reviews Physics (2019) https://doi.org/10.1038/s42254-018-0006-2 Published online 08 January 2019

The following changes have been made to the original article: in the lower-right panel of Fig. 1, opoelectrics has been corrected to optoelectronics; in the Box 1 footnote, rotating wave-approximation has been corrected to rotating-wave approximation; in equation B1.3, an operator symbol has been added to the last term; and in the third paragraph of Box 2, |j → |n was changed to |j → |n. This has been corrected in the HTML and PDF versions of the article.