Nonexistence of PT-symmetric gain-loss photonic quantum systems (Vol. 49 No.5-6)

Our common understanding of quantum mechanics relies on the Hamiltonian operator describing any quantum mechanical system to be Hermitian. This has been challenged 20 years ago by the discovery that, for an operator to possess real eigenvalues, it only needs to be invariant under combined parity-time (PT) symmetry operations. This had profound impact on photonics where potential landscapes with tailored gain and loss for electromagnetic waves can easily be implemented.

However, this is as far as the analogy to quantum mechanics can be taken. A straightforward implementation of gain-loss structures for quantum states of light - even for the most classical ones, coherent states - fails. As the authors show in this article, concatenating lossy and amplifying media turn coherent states into thermally broadened quantum states, whose first moments (i.e. their amplitudes) are retained, but whose variances are increased proportional to the amount of gain.

This shows that PT-symmetric quantum optics cannot be implemented within the prevailing paradigm of using distributed gain and loss. The wider consequence of this simple result hints at the limits of simulating quantum physics beyond wave mechanics using photonic quantum systems.

S. Scheel and A. Szameit, PT-symmetric photonic quantum systems with gain and loss do not exist, EPL 122, 34001 (2018)
[Abstract]