Scientists demonstrate first experimental evidence of non-Hermitian edge burst in photonic quantum walks

In a new Physical Exam Letters In a study, scientists have demonstrated the first experimental observation of a non-Hermitian edge burst in quantum dynamics using a carefully designed photonic quantum walk setup.

The growing interest in non-Hermitian systems reflects their role in understanding real-world systems characterized by dissipation, interactions with the environment, or gain and loss mechanisms.

They reveal new physical properties that do not exist in Hermitian systems, such as boundary localization, which may have interesting applications in photonics and condensed matter physics. The PRL study researchers focused on a non-Hermitian skin effect (NHSE), where a system exhibits unique behavior at edges or boundaries.

Phys.org spoke with the study’s co-authors, Professor Wei Yi of the University of Science and Technology of China, Professor Zhong Wang of Tsinghua University, and Professor Peng Xue of the Beijing Research Center for Computer Science.

Speaking about their motivation to study non-Hermitian systems, Professor Xue said: “One of the main motivations for its rise was the discovery of NHSE.” The term NHSE was coined by Professor Wang and his colleague in an earlier PRL study, and the team has been actively working on it since its discovery.

Professor Yi added: “As NHSE revealed intriguing static properties (such as the energy spectrum) of non-Hermitian systems, we became very curious about the possible existence of new dynamical phenomena with extreme boundary sensitivity.”

Real-time dynamics

In non-Hermitian systems, operators are not equal to their Hermitian conjugates. Therefore, the eigenvalues ​​are complex, giving rise to special phenomena such as NHSE.

In NHSE, the eigenstates of a non-Hermitian system accumulate at the edges or boundaries. This differs from the global properties observed in Hermitian systems. NHSE is typically observed in open systems with energy gain or loss, i.e. Hamiltonians.

Previous studies have investigated this effect under static conditions, meaning that the properties of the system, such as the Hamiltonian, do not change over time. However, Wang and his team focused on examining how the dynamics of the edges evolve over time.

“While previous studies focused on more static aspects (such as the energy spectrum) of non-Hermitian systems, our work unveils an intriguing dynamic phenomenon,” said Professor Wang.

The study of real-time dynamics can offer insight into real-world systems where the Hamiltonian evolves over time, reflecting changes in the energy and behavior of the system.

One-dimensional quantum walk

To study real-time edge dynamics in non-Hermitian systems, the researchers used a setup involving a one-dimensional quantum walk with photons. Each step or move is determined by a quantum coin toss, which introduces probabilistic motion.

A boundary or wall was part of the experimental setup, segmenting the system into two regions, where each region followed different rules for quantum walking.

The quantum walk of the photon has been managed using different optical tools, including beam splitters, waveplates and beam shifters.

Their goal was to study the boundary loss mechanism, for which they used partially polarizing beam splitters. This introduces a loss of photons, which they can then measure as the photons exit the system.

With this measurement, they are able to determine the occurrence of the loss at different positions and times, which sheds light on the dynamics of the edge. In addition, the researchers studied how different initial conditions (where the photons start) affect the dynamics of the edge of the non-Hermitian system.

Edge dynamics

The researchers detected an increase in the probability of photon loss at the boundary, confirming the existence of non-Hermitian edge explosion. However, they found that this only occurs when two conditions are simultaneously met.

The first condition is that the non-Hermitian skin effect, where eigenstates accumulate near the edges, is present. Second, the imaginary gap in the energy spectrum must be closed. This means that the difference between the real and imaginary parts of the energy spectrum decreases.

The need for both conditions to be met simultaneously highlights the interaction between static localization (NHSE) and dynamic evolution (imaginary gap).

Professor Yi explained: “These phenomena provide a comprehensive view of the correspondence between the non-Hermitian topology of the volume and the sharp features, both static and dynamic, at the boundaries.”

They also concluded that the initial position of the photos plays a role in enhancing edge blowout. The probability of losing a photon at the boundary wall is reduced when the photon starts further away from the boundary, compared to when it starts close to it.

By successfully mapping the time evolution of the edge explosion, the researchers showed that it occurs precisely when the particle reaches the boundary. Furthermore, they showed that the phenomena are consistent even when the initial position of the particle varies.

Future work

Experimental observation of real-time edge bursts in non-Hermitian systems reveals a novel interplay between topological physics and dynamical phenomena.

According to Professor Wang, this could open up new research avenues in this field. He said: “The spatial and spectral sensitivity of edge bursting paves the way for exploring localized light harvesting or quantum sensing using this phenomenon.”

Professor Xue added: “Our work paves the way for studying rich real-time dynamics in non-Hermitian topological systems, hinting at the possible existence of other universal scaling relations in non-Hermitian systems.”

According to the team, the edge-shattering effect could be used in practical ways to harvest light or particles at precise locations, with implications for photonics and other wave-based fields.

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