Dr Juan Ramon Munoz de Nova (IEM-CSIC) gives a webinar on “Andreev-Hawking effect, spontaneous Floquet states & Hawking time crystals” at 4pm UK time. Please note the scheduled day is a Thursday, not the usual Tuesday.

Zoom link: https://us02web.zoom.us/j/84769510659 Meeting ID: 847 6951 0659

The field of analogue gravity simulates otherwise inaccessible gravitational phenomena in laboratory setups [1]. This has eventually led to the first observation of the Hawking effect [2], using atomic condensates, where one can also study the analogue of the Andreev reflection [3]. One of the biggest remaining challenges is the observation of the black-hole laser (BHL) effect, in which Hawking radiation is exponentially self-amplified due to successive internal reflections between two horizons [4]. Of particular interest is the dynamical pase diagram of a BHL, after the initial instability has saturated, where it may exhibit an intriguing periodic state of continuous emission of solitons (CES), representing the bona fide BHL. In fact, the CES state is a universal feature of flowing condensates, which has inspired the more general concept of spontaneous Floquet state (SFS): a state of a time-independent Hamiltonian which oscillates like a Floquet state due to interactions [5].

We discuss how SFS provide a new paradigm of quantum matter [6]. For instance, due to energy conservation, they present a novel conserved charge, the Floquet charge, whose thermodynamic conjugate is the oscillation frequency. This allows to characterize spontaneous and driven Floquet states as “isofloquetic” or “isoperiodic”, in analogy to standard isochoric and isobaric thermodynamic systems. Another hallmark of a SFS is the presence of a temporal Floquet-NambuGoldstone (FNG) mode with zero quasifrequency, whose quantum amplitude represents a rare tangible realization of time operator in Quantum Mechanics. The CES state is then a time supersolid, breaking U(1) and time-translation symmetry.

Finally, we demonstrate how a bona fide time crystal, exhibiting a genuinely spontaneous symmetry breaking of time-translation symmetry, can be achieved in the CES state emerging from a quantum BHL [7]. Such a Hawking time crystal provides a nonlinear periodic analogue of the Andreev-Hawking effect. Remarkably, we prove that a time operator can be defined in any parametric amplifier, which enables a unique understanding of a time-crystallization process in terms of two time operators: one for the initial BHL and another for the final CES state.

[1] W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981). [2] JRMdN, K. Golubkov, V. I. Kolobov, J. Steinhauer, Nature 569, 688 (2019). [3] I. Zapata, F. Sols, Phys. Rev. Lett. 102, 180405 (2009). [4] S. Corley and T. Jacobson, Phys. Rev. D 59, 124011 (1999). [5] JRMdN, Fernando Sols, Phys. Rev. A 105, 043302 (2022). [6] JRMdN, Fernando Sols, Quantum 9, 1850 (2025). [7] JRMdN, Fernando Sols, Phys. Rev. Lett. 136, 170402 (2026)