Symmetries are one of nature's most powerful organizing principles, shaping everything from snowflakes and flowers to the fundamental interactions of particles and the laws of physics governing them. Conventional symmetries such as translation, rotation, or reflection symmetry, manifest in the system’s geometric structure. However, not all symmetries are visible to the naked eye: The novel concept of latent symmetries describes a type of order deeply hidden within the system’s spectral properties. Prof. Alexander Szameit, head of the Rostock team, illustrates this concept with a musical analogy: “Similarly to the entire set of tones that can be played on an instrument, the ‘spectrum’ describes the different ‘frequencies’ with which dynamics can occur in a given network.” Intriguingly, even though latent symmetries are for all intents and purposes invisible, the system hosting them can still behave in symmetric ways. As a result, asymmetric or even apparently random systems can be designed to embody entirely unexpected symmetry-driven properties and functionalities.
In their new paper, “State Transfer in Latent-Symmetric Networks”, a team of physicists from the Universities of Rostock and Hamburg reports the first experimental observation of quantum state transfer enabled by hidden symmetries. Using a network of laser-written optical waveguides, the researchers were able to fabricate photonic circuits that exhibit – or, rather, conceal – this fascinating trait and render it practical for the transfer of non-classical states of light. Typically, in the absence of symmetries, light tends to spread freely across the entire network whenever it is injected into a single site. Jonas Himmel, doctoral candidate and lead author of the paper, explains: “Our system behaves the same way – with a key exception: Photons launched into a specific, yet entirely inconspicuous site of the network almost magically emerge at a second such site.” This efficient crosstalk between two nodes of the network is possible because they share the same “spectral fingerprint,” – the defining characteristic of a latently symmetric structure.
By overcoming the reliance on conventional types of symmetries, the scientists have dramatically expanded the design space for quantum circuits, opening the gates towards a new class of networks for secure quantum communication and cryptography.
This research was funded by Deutsche Forschungsgemeinschaft and the Alfried Krupp von Bohlen und Halbach-Foundation.
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State transfer in latent-symmetric networks