## Nonlinear Phenomena in Complex Photonic Structures - Project 10

### Project Leader: Stefan Rotter

This theoretical project of the SFB NextLite is dedicated to three topics, all of which are strongly connected to the experimental efforts within the SFB:

**Nonlinear effects in highly tunable laser devices**

We have recently demonstrated on a theoretical level how the coupling between two microcavity lasers can lead to very interesting behavior in the pump-dependence of such a coupled laser device [1]**.** When pumping the two laser components separately of each other, so-called “exceptional points” can be induced in this system. These points correspond to singularities of the non-Hermitian operator, which describes the lasing behavior. In the vicinity of these points the counter-intuitive situation is realized that the laser may turn off even when the overall pump power is increased. In collaboration with the groups of Unterrainer (P02) and Strasser (P09) we were now able to observe this phenomenon also in experiments employing quantum cascade lasers [2]. In a next step we will build on this exciting progress to investigate exceptional points in multiple coupled lasers, as well as the many fascinating effects that they give rise to.

**Light scattering in optical resonators**

In a second line of research, we are interested in optical micro-resonators and the physics involved in the coupling to them - be it the evanescent in- and out-coupling of light by means of tapered fiber couplers or the quantum optical aspects involved in an emitter which couples to the resonator field. For this project we are collaborating with the Rauschenbeutel group (P08), which has acquired extensive expertise with so-called “bottle resonators” that can be used to strongly couple light to atomic emitters. For this strong-coupling regime we could recently demonstrate that emitters coupled to multiple resonator modes can feature periodic quantum revivals in their excitation probability on a time scale associated with the resonator round-trip time [3].

**Quantum optics with spin ensembles**

In a joint work with the group of Majer we have recently demonstrated that a superconducting transmission line cavity can be used to strongly couple the cavity-enhanced microwave field to a macroscopic ensemble of nitrogen-vacancy spins in a synthetic diamond [4]. Investigations of this kind are motivated by the desire to store the information encoded in a photon (“flying qubit”) in a solid-state device (“stationary qubit”) with comparatively long coherence times. To describe the dynamics during the storage and retrieval of information in such a quantum memory, we developed a powerful approach that fully captures the strongly non-Markovian dynamical features appearing in such a context. On this basis we could now show both theoretically and experimentally, that the decoherence induced by the inhomogeneous broadening of the considered spin ensemble can be suppressed in the strong-coupling limit – an effect known as “cavity protection” [5]. This effect is key to promising coherent control schemes that can now be employed to perform quantum operations with the spin ensemble without the detrimental influence of decoherence.

[1] M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-Induced Exceptional Points in Lasers”,* Phys. Rev. Lett.*, vol. 108, no. 17, p. 173901, Apr. 2012.

[2] M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point”, *Nat. Commun.*, vol. 5, p. 4034, Jun. 2014.

[3] D. O. Krimer, M. Liertzer, S. Rotter, and H. E. Türeci, “Route from spontaneous decay to complex multimode dynamics in cavity QED”, *Phys. Rev. A*, vol. 89, no. 3, p. 033820, Mar. 2014.

[4] R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, and J. Majer, “Cavity QED with Magnetically Coupled Collective Spin States”, *Phys. Rev. Lett.*, vol. 107, no. 6, p. 060502, 2011.

[5] S. Putz, D. O. Krimer, R. Amsüss, A. Valookaran, T. Nöbauer, J. Schmiedmayer, S. Rotter, and J. Majer, “Protecting a Spin Ensemble against Decoherence in the Strong-Coupling Regime of Cavity QED”, *Nature Physics* 10, 720 (2014).

Sketch of a PT-symmetric system with balanced gain (G) and and loss (L).

We show that the PT-symmetry breaking transition in such structures is independent of the presence of external mirrors

[see Phys. Rev. X 3, 41030 (2013)]

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