Long time universality of black-hole lasers

Abstract

For flowing quantum gases, it has been found that at long times an initial black-hole laser (BHL) configuration exhibits only two possible states: the ground state or a periodic self-oscillating state of continuous emission of solitons. So far, all the works on this subject are based on a highly idealized model, quite difficult to implement experimentally. Here we study the instability spectrum and the time evolution of a recently proposed realistic model of a BHL, thus providing a useful theoretical tool for the clear identification of black-hole lasing in future experiments. We further confirm the existence of a well-defined phase diagram at long times, which bespeaks universality in the long-time behavior of a BHL. Additionally, we develop a complementary model in which the same potential profile is applied to a subsonic homogeneous flowing condensate that, despite not forming a BHL, evolves toward the same phase diagram as the associated BHL model. This result reveals an even stronger form of robustness in the long-time behavior with respect to the transient, which goes beyond what has been described in the previous literature.

Continuous time crystal from a spontaneous many-body Floquet state

“…The passage of the dragged soliton through the well leaves the system in the same configuration, and restarts the process described above. The resulting density pattern shows a periodic behavior for every x, and not just in the emitted trains of solitons (already noticed in the literature [28][29][30]). Therefore, since the whole density profile oscillates periodically, the effective GP Hamiltonian becomes a Floquet Hamiltonian.…”

“…Nevertheless, a quench in the external potential is not the only way to reach the CES state: for fixed background parameters (v, X, V 0 ), the CES state, and particularly its period, is insensitive to the details of the transient, including stochastic dynamics starting from unstable black-hole laser solutions [28,30,39]. This independence with respect to the transient further demonstrates that the CES state is indeed an intrinsic state of the system, satisfying Eq.…”

“…CES state.-The question is now: does a non-trivial SMBF state exist? We identify here one example using a model previously studied in the literature [28], consisting of a 1D initially homogeneous flowing condensate (IHFC) with density n 0 and velocity v, in which, at t = 0, an attractive square well of amplitude −V 0 and size X is suddenly introduced. A schematic representation of the IHFC at t = 0 is given in Fig.…”

“…The quench in the external potential induces a deterministic dynamics in the condensate, numerically computed by integrating the time-dependent GP equation. Specifically, there are only two possible choices for the final state of the system as a function of the parameters (v, X, V 0 ): the ground state (GS), or a periodic regime of continuous emission of solitons (CES) [28]. A typical phase diagram is represented in Fig.…”

Confirmation of stimulated Hawking radiation, but not of black hole lasing

“…In this way, the quantity of Hawking radiation exceeds the spontaneous emission. This process was first suggested in the context of black hole lasing, in which the partner particles are reflected from an inner horizon deep inside the analogue black hole, and become the superluminal particles, which then stimulate additional Hawking/partner pairs [5,[8][9][10][11][12][13][14][15][16].…”