Stefan Rotter

Strong Interactions in Multimode Random Lasers

Unlike conventional lasers, diffusive random lasers (DRLs) have no resonator to trap light and no high-Q resonances to support lasing. Because of this lack of sharp resonances, the DRL has presented a challenge to conventional laser theory. We present a theory able to treat the DRL rigorously and provide results on the lasing spectra, internal fields, and output intensities of DRLs. Typically DRLs are highly multimode lasers, emitting light at a number of wavelengths. We show that the modal interactions through the gain medium in such lasers are extremely strong and lead to a uniformly spaced frequency spectrum, in agreement with recent experimental observations.

Loss-induced suppression and revival of lasing

Controlling and reversing the effects of loss are major challenges in optical systems. For lasers, losses need to be overcome by a sufficient amount of gain to reach the lasing threshold. In this work, we show how to turn losses into gain by steering the parameters of a system to the vicinity of an exceptional point (EP), which occurs when the eigenvalues and the corresponding eigenstates of a system coalesce. In our system of coupled microresonators, EPs are manifested as the loss-induced suppression and revival of lasing. Below a critical value, adding loss annihilates an existing Raman laser. Beyond this critical threshold, lasing recovers despite the increasing loss, in stark contrast to what would be expected from conventional laser theory. Our results exemplify the counterintuitive features of EPs and present an innovative method for reversing the effect of loss. Introducing loss into a coupled optical system can result in an enhancement of the optical properties. [Also see Perspective by Schwefel] Achieving gain despite increasing loss When energy is pumped into an optically active material, the buildup (or gain) of excitations within the material can reach a critical point where the emission of coherent light, or lasing, can occur. In many systems, however, the buildup of the excitations is suppressed by losses within the material. Overturning conventional wisdom that loss is bad and should be minimized, Peng et al. show that carefully tweaking the coupling strength between the various components of a coupled optical system can actually result in an enhancement of the optical properties by adding more loss into the system (see the Perspective by Schwefel). The results may provide a clever design approach to counteract loss in optical devices. Science, this issue p. 328; see also p. 304

Pump-induced Exceptional Points in Lasers

We demonstrate that the above-threshold behavior of a laser can be strongly affected by exceptional points which are induced by pumping the laser nonuniformly. At these singularities, the eigenstates of the non-Hermitian operator which describes the lasing modes coalesce. In their vicinity, the laser may turn off even when the overall pump power deposited in the system is increased. Such signatures of a pump-induced exceptional point can be experimentally probed with coupled ridge or microdisk lasers.

Reversing the pump dependence of a laser at an exceptional point.

When two resonant modes in a system with gain or loss coalesce in both their resonance position and their width, a so-called exceptional point occurs, which acts as a source of non-trivial physics in a diverse range of systems. Lasers provide a natural setting to study such non-Hermitian degeneracies, as they feature resonant modes and a gain material as their basic constituents. Here we show that exceptional points can be conveniently induced in a photonic molecule laser by a suitable variation of the applied pump. Using a pair of coupled microdisk quantum cascade lasers, we demonstrate that in the vicinity of these exceptional points the coupled laser shows a characteristic reversal of its pump dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power.

Cavity QED with magnetically coupled collective spin states.

We report strong coupling between an ensemble of nitrogen-vacancy center electron spins in diamond and a superconducting microwave coplanar waveguide resonator. The characteristic scaling of the collective coupling strength with the square root of the number of emitters is observed directly. Additionally, we measure hyperfine coupling to (13)C nuclear spins, which is a first step towards a nuclear ensemble quantum memory. Using the dispersive shift of the cavity resonance frequency, we measure the relaxation time of the NV center at millikelvin temperatures in a nondestructive way.

Chiral modes and directional lasing at exceptional points

Significance Exceptional points (EPs) emerge when a system with loss or gain is tuned such that its eigenvalues and the corresponding eigenstates coalesce. By operating close to two EPs, we achieved a dynamic control of the rotation direction of light in a whispering-gallery-mode (WGM) resonator. This enabled us to tune the emission direction of a WGM microlaser from bidirectional, when the system is away from the EPs, to unidirectional emission at EPs and to reverse the emission direction by moving from one EP to the other. This feature provides WGM resonators new functionalities useful for lasing, sensing, optomechanics, and cavity quantum electrodynamics. Our findings will help to develop novel technologies for controlling the light flow on-chip and could affect scientific fields beyond optics. Controlling the emission and the flow of light in micro- and nanostructures is crucial for on-chip information processing. Here we show how to impose a strong chirality and a switchable direction of light propagation in an optical system by steering it to an exceptional point (EP)—a degeneracy universally occurring in all open physical systems when two eigenvalues and the corresponding eigenstates coalesce. In our experiments with a fiber-coupled whispering-gallery-mode (WGM) resonator, we dynamically control the chirality of resonator modes and the emission direction of a WGM microlaser in the vicinity of an EP: Away from the EPs, the resonator modes are nonchiral and laser emission is bidirectional. As the system approaches an EP, the modes become chiral and allow unidirectional emission such that by transiting from one EP to another one the direction of emission can be completely reversed. Our results exemplify a very counterintuitive feature of non-Hermitian physics that paves the way to chiral photonics on a chip.

Dynamically encircling an exceptional point for asymmetric mode switching.

Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an ‘exceptional point’ occurs, giving rise to fascinating phenomena that defy our physical intuition. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly, such as a state-flip or the accumulation of a geometric phase. The topological structure of exceptional points has been experimentally explored, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.

General description of quasiadiabatic dynamical phenomena near exceptional points

The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process predicted for an adiabatic encircling of an exceptional point. In this work we analyze this and related processes for the generic system of two coupled oscillator modes with loss or gain. We identify a characteristic system evolution consisting of periods of quasistationarity interrupted by abrupt nonadiabatic transitions and we present a qualitative and quantitative description of this switching behavior by connecting the problem to the phenomenon of stability loss delay. This approach makes accurate predictions for the breakdown of the adiabatic theorem as well as the occurrence of chiral behavior observed previously in this context and provides a general framework to model and understand quasiadiabatic dynamical effects in non-Hermitian systems.

Constant-intensity waves and their modulation instability in non-Hermitian potentials

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a waves constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

Pump-Controlled Directional Light Emission from Random Lasers

The angular emission pattern of a random laser is typically very irregular and difficult to tune. Here we show by detailed numerical calculations that one can overcome the lack of control over this emission pattern by actively shaping the spatial pump distribution. We demonstrate, in particular, how to obtain customized pump profiles to achieve highly directional emission. Going beyond the regime of strongly scattering media where localized modes with a given directionality can simply be selected by the pump, we present an optimization-based approach which shapes extended lasing modes in the weakly scattering regime according to any predetermined emission pattern.