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## Reversing the Pump-Dependence of a Laser at an Exceptional Point

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, S. Rotter

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”, since 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 micro-disk quantum cascade lasers, we demonstrate that in the vicinity of these Exceptional Points the laser shows a characteristic reversal of its pump-dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power. This result establishes photonic molecule lasers as promising tools for exploring many further fascinating aspects of Exceptional Points, like a strong line-width enhancement and the coherent perfect absorption of light in their vicinity as well as non-trivial mode-switching and the accumulation of a geometric phase when encircling an Exceptional Point parametrically.

http://arxiv.org/abs/1404.1837
Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Chaotic Dynamics (nlin.CD)

## Coherent perfect absorption with and without lasing in complex potentials

Zafar Ahmed

We study the coherent scattering from complex potentials to find that the coherent perfect absorption (CPA) without lasing is not possible in the PT-symmetric domain as the s-matrix is such that $$|\det S(k)|=1$$. We confirm that in the domain of broken PT-symmetry$$|\det S(k)|$$ can become indeterminate 0/0 at the spectral singularity (SS), k=k∗, of the potential signifying CPA with lasing at threshold gain. We also find that in the domain of unbroken symmetry (when the potential has real discrete spectrum) neither SS nor CPA can occur. In this, regard, we find that exactly solvable Scarf II potential is the unique model that can exhibit these novel phenomena and their subtleties analytically and explicitly. However, we show that the other numerically solved models also behave similarly.

http://arxiv.org/abs/1404.1679

Quantum Physics (quant-ph)

## Spectral Singularities and CPA-Laser Action in a Weakly Nonlinear PT-Symmetric Bilayer Slab

We study optical spectral singularities of a weakly nonlinear PT-symmetric bilinear planar slab of optically active material. In particular, we derive the lasing threshold condition and calculate the laser output intensity. These reveal the following unexpected features of the system: 1. For the case that the real part of the refractive index η of the layers are equal to unity, the presence of the lossy layer decreases the threshold gain; 2. For the more commonly encountered situations when η−1 is much larger than the magnitude of the imaginary part of the refractive index, the threshold gain coefficient is a function of η that has a local minimum. The latter is in sharp contrast to the threshold gain coefficient of a homogeneous slab of gain material which is a decreasing function of η. We use these results to comment on the effect of nonlinearity on the prospects of using this system as a CPA-laser.

http://arxiv.org/abs/1404.1737
Quantum Physics (quant-ph); Mathematical Physics (math-ph); Optics (physics.optics)

## Exceptional points and lasing self-termination in photonic molecules

Ramy El-Ganainy, Mercedeh Khajavikhan, Li Ge

We investigate the rich physics of photonic molecule lasers using a non-Hermitian dimer model. We show that several interesting features, predicted recently using a rigorous steady state ab-initio laser theory (SALT), can be captured by this toy model. In particular, we demonstrate the central role played by exceptional points in both pump-selective lasing and laser self-terminations phenomena. Due to its transparent mathematical structure, our model provides a lucid understanding for how different physical parameters (optical loss, modal coupling between microcavities and pump profiles) affect the lasing action. Interestingly, our analysis also confirms that, for frequency mismatched cavities, operation in the proximity of exceptional points (without actually crossing the square root singularities) can still lead to laser self-termination. We confirm this latter prediction for two coupled slab cavities using scattering matrix analysis and SALT technique. In addition, we employ our model to investigate the pump-controlled lasing action and we show that emission patterns are governed by the locations of exceptional points in the gain parameter space. Finally we extend these results to multi-cavity photonic molecules, where we found the existence of higher-order EPs and pump-induced localization.

http://arxiv.org/abs/1404.1242

Optics (physics.optics)

## Mathematical and physical aspects of complex symmetric operators

Stephan Ramon Garcia, Emil Prodan, Mihai Putinar

Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugate-linear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics, and complex variables.

http://arxiv.org/abs/1404.1304
Functional Analysis (math.FA); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph); Operator Algebras (math.OA); Spectral Theory (math.SP)