Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity (1603.02325v1)

Abstract: Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional point" occurs, around which many fascinating phenomena have recently been reported to arise. Particularly intriguing behavior is predicted to appear when encircling an exceptional point sufficiently slowly, like a state-flip or the accumulation of a geometric phase. Experiments dedicated to this issue could already successfully explore the topological structure of exceptional points, but a full dynamical encircling and the breakdown of adiabaticity inevitably associated with it remained out of reach of any measurement so far. Here we demonstrate that a dynamical encircling of an exceptional point can be mapped onto the problem of scattering through a two-mode waveguide, which allows us for the first time to access the elusive effects occurring in this context. Specifically, we present experimental results from a waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way mode transitions are induced that make this device perfectly suited as a robust and asymmetric switch between different waveguide modes. Our work opens up new and exciting avenues to explore exceptional point physics at the crossroads between fundamental research and practical applications.

• The paper demonstrates that dynamically encircling exceptional points via a modulated waveguide overcomes the breakdown of adiabaticity to achieve asymmetric mode switching.
• The experimental setup maps non-Hermitian Hamiltonian dynamics onto a two-mode scattering problem, validating chiral mode transitions with directional injection.
• Enhanced design reduces the waveguide’s length-to-width ratio and offers robust, frequency-independent performance, paving the way for advances in telecommunications and quantum technologies.

Dynamically Encircling Exceptional Points in Waveguides: Implications for Asymmetric Mode Switching

The paper entitled "Dynamically Encircling Exceptional Points in a Waveguide: Asymmetric Mode Switching from the Breakdown of Adiabaticity" presents an empirical exploration of exceptional points (EPs) by harnessing waveguide physics. Exceptional points are non-Hermitian degeneracies significant in systems with gain or loss, leading to phenomena like unidirectional invisibility and single-mode lasers. This paper bridges foundational quantum mechanics and practical applications, demonstrating a robust method for dynamically encircling EPs to achieve mode switching in waveguides.

Theoretical Background and Research Foundation

Exceptional points occur in systems described by non-Hermitian Hamiltonians where resonant modes coalesce. Traditionally, systems are expected to evolve adiabatically around EPs—leading to a state-flip—under slow parametric tunings. However, non-Hermitian components lead to a breakdown of adiabaticity, resulting in chiral dynamics. Encircling an EP in opposing directions produces different final states, which has yet to be effectively realized in experiments until now.

The theoretical framework employed by the authors is grounded on mapping the dynamic encircling of an EP onto the scattering problem within a two-mode waveguide. Their innovative design translates the Hamiltonian dynamics of EPs into waveguide mode propagation, elegantly solving the complexity associated with experimentally resolving non-adiabatic contributions.

Experimental Approach and Results

The authors implement their theoretical model practically through a controlled waveguide setup. They modulate the waveguide boundary to simulate the dynamic encircling of an EP. This design facilitates a potent means to control the interaction between propagating modes, thus allowing the manifest chiral behavior predicted by theory.

Experimental results validate the theoretical predictions: injecting waves from opposing ends results in definitive mode selection, demonstrating the asymmetric mode switching capability of the waveguide system. The mode transitions are robust, showcasing strong frequency-independent behavior over a broad range. Remarkably, the implementation provides significant optimization over previous models, reducing the waveguide's length-to-width ratio and enhancing throughput by multiple orders of magnitude.

Implications and Future Directions

The authors propose further exploration of EP-encirclement in waveguides for a range of waveforms, including light, sound, micro and matter waves. The current method rivals existing technologies, providing a new lens on EP-based switching devices. This advancement opens pathways for innovation in mode switching applications, potentially influencing telecommunications, signal processing, and quantum computing.

This research, while focusing primarily on two-mode systems, may extend to multi-mode waveguides, where the effects of non-Hermitian dynamics induced by EPs could yield even more intriguing phenomena. Future work might address enhancing the compactness and integration of such technologies in real-world applications, alongside investigating the roles of additional parameters, such as polarization and coherence length, in the EP-encircling process.

In conclusion, this paper provides a significant empirical contribution to the field of non-Hermitian quantum mechanics by demonstrating a dynamic approach to EP encircling in waveguides, achieving asymmetric mode switching. This research stands poised to influence both fundamental studies of EPs and practical advancements in adaptive wave propagation technologies.