Quantum metric unveils defect freezing in non-Hermitian systems
The fundamental postulates of quantum mechanics rest upon the fact that the Hamiltonian, which quantifies the energy of the system, is given by a Hermitian operator. This means that the complex conjugate and transpose of the Hamiltonian should be equal to itself. Almost a century after the formulation of quantum mechanics, researchers are now trying to break free from this constraint — non-Hermitian Hamiltonians, which do not satisfy the aforementioned property, are now a new frontier of exploration in both theoretical and experimental physics. Paolo Molignini is part of the project and is a Postdoctor in Condensed Matter and Quantum Optics at Fysikum.
Non-Hermitian systems where these fundamental postulates are relaxed offer an ideal playground to discover new paradigms of physics, as evinced by the plethora of unconventional phenomena reported recently. Importantly, this departure from the established notions in quantum mechanics necessitates a consistent mathematical reformulation of non-Hermitian quantum mechanics. The physical implications of such a mathematical theory remain relatively unexplored.
Our Letter bridges this gap by adopting the mathematician’s approach to solve a physics problem. In our model, we change a parameter in a non-Hermitian system in time, and quantify the amount by which the system gets excited (we call these excitations “defects”). We unveil novel physical consequences, including a phenomenon which we coin “defect freezing”. What this means is that no matter how slowly we change the parameter in a non-Hermitian system, the system always manages to get excited — even in the limit of an infinitely slow change, in stark contrast to a conventional quantum system. For an analogy of this, imagine you’re walking around in an old house with squeaky floors. In non-Hermitian systems, you always end up making some noise no matter how slowly you move!
Our study is a timely addition to the flourishing field of non-Hermitian quantum mechanics, since it highlights the need for a mathematically consistent formulation to reveal certain aspects of non-Hermitian systems. We expect our model to be readily realisable in a wide array of experimental platforms, such as in a system of qubits, the building blocks of quantum computers. Given the novelty and breadth of our results, we believe that this work opens up new possibilities in studying the dynamics of non-Hermitian systems."
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Quantum metric unveils defect freezing in non-Hermitian systems - Physical Review Letters
Last updated: October 4, 2023
Source: Fysikum