Half-integer vs. integer effects in quantum synchronization of spin systems

Ryan Tan1, Christoph Bruder1, and Martin Koppenhöfer2

1Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
2Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA

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We study the quantum synchronization of a single spin driven by an external semiclassical signal for spin numbers larger than $S = 1$, the smallest system to host a quantum self-sustained oscillator. The occurrence of interference-based quantum synchronization blockade is found to be qualitatively different for integer vs. half-integer spin number $S$. We explain this phenomenon as the interplay between the external signal and the structure of the limit cycle in the generation of coherence in the system. Moreover, we show that the same dissipative limit-cycle stabilization mechanism leads to very different levels of quantum synchronization for integer vs. half-integer $S$. However, by choosing an appropriate limit cycle for each spin number, comparable levels of quantum synchronization can be achieved for both integer and half-integer spin systems.

Classical synchronization has been studied since the 17th century and has applications in many areas of our daily lives, such as in time-keeping devices and power grids. Quantum systems can synchronize, too, and they feature a number of genuinely quantum effects in their synchronization behavior. An example is interference-based quantum synchronization blockade in driven quantum limit-cycle oscillators, where a destructive interference effect prevents synchronization even though an external signal is applied. Spin systems are a convenient platform to study quantum synchronization because of their finite (and typically low-dimensional) Hilbert space.

Here, we analyze how quantum synchronization depends on the size of the spin system. For specific combinations of a quantum limit-cycle oscillator and an applied signal, we find qualitative differences in the number of synchronization blockades and strong oscillations in the maximum amount of synchronization, depending whether the spin is integer or half-integer. However, if one chooses different limit-cycle oscillators depending on the size of the spin system, a monotonic growth of the maximum level of quantum synchronization as a function of the size of the spin of the system is found.

Our results shed light on the complex interference effects in quantum synchronization and are a first step towards studying the quantum-to-classical transition in synchronization.

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Cited by

[1] Parvinder Solanki, Faraz Mohd Mehdi, Michal Hajdušek, and Sai Vinjanampathy, "Symmetries and Synchronization Blockade", arXiv:2212.09388, (2022).

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