Quantum frequency locking and down-conversion in a driven cavity-qubit system
arXiv:2003.05648 · doi:10.1103/PhysRevResearch.2.043411
Abstract
We study a periodically driven qubit coupled to a quantized cavity mode. Despite its apparent simplicity, this system supports a rich variety of exotic phenomena, such as topological frequency conversion as recently discovered in [Martin et al, PRX 7, 041008 (2017)]. Here we report on a qualitatively different phenomenon that occurs in this platform, where the cavity mode's oscillations lock their frequency to a rational fraction of the driving frequency . This phenomenon, which we term quantum frequency locking, is characterized by the emergence of -tuplets of stationary (Floquet) states whose quasienergies are separated by , up to exponentially small corrections. The Wigner functions of these states are nearly identical, and exhibit highly-regular and symmetric structure in phase space. Similarly to Floquet time crystals, these states underlie discrete time-translation symmetry breaking in the model. We develop a semiclassical approach for analyzing and predicting quantum frequency locking in the model, and use it to identify the conditions under which it occurs.
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