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arXiv:1811.02148 · Physical Review A

Chaotic synchronization between atomic clocks

Aniket Patra, B. L. Altshuler, Emil A. Yuzbashyan

Published Aug 28, 2019• 11 citations
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Abstract

We predict synchronization of the chaotic dynamics of two atomic ensembles coupled to a heavily damped optical cavity mode. The atoms are dissipated collectively through this mode and pumped incoherently to achieve a macroscopic population of the cavity photons. Even though the dynamics of each ensemble are chaotic, their motions repeat one another. In our system, chaos first emerges via quasiperiodicity and then synchronizes. We identify the signatures of synchronized chaos, chaos, and quasiperiodicity in the experimentally observable power spectra of the light emitted by the cavity.

DOI
10.1103/physreva.100.023418

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We predict synchronization of the chaotic dynamics of two atomic ensembles coupled to a heavily damped optical cavity mode. The atoms are dissipated collectively through this mode and pumped incoherently to achieve a macroscopic population of the cavity photons. Even though the dynamics of each ensemble are chaotic, their motions repeat one another. In our system, chaos first emerges via quasiperiodicity and then synchronizes. We identify the signatures of synchronized chaos, chaos, and quasiperiodicity in the experimentally observable power spectra of the light emitted by the cavity.
We propose a system for observing the correlated phase dynamics of two mesoscopic ensembles of atoms through their collective coupling to an optical cavity. We find a dynamical quantum phase transition induced by pump noise and cavity output coupling. The spectral properties of the superradiant light emitted from the cavity show that at a critical pump rate the system undergoes a transition from the behavior of two independent oscillators to the phase locking that is the signature of quantum synchronization.
Superradiant lasers based on atomic ensembles exhibiting ultranarrow optical transitions can emit light of unprecedented spectral purity and may serve as active atomic clocks. We consider two frequency-detuned active atomic clocks, which are coupled in a cascaded setup, i.e., as master and slave lasers, and study the synchronization of the slave to the master clock. In a setup where both atomic ensembles are coupled to a common cavity mode, such synchronization phenomena have been predicted by Xu et al. [M. Xu, D. A. Tieri, E. C. Fine, J. K. Thompson, and M. J. Holland, Phys. Rev. Lett. 113, 154101 (2014).] and experimentally observed by Weiner et al. (J. M. Weiner et al., arXiv:1503.06464). Here we demonstrate that synchronization still occurs in cascaded setups but exhibits distinctly different phase diagrams. We study the characteristics of synchronization in comparison to the case of coupling through a common cavity. We also consider synchronization through a classical channel where light of the master laser is measured phase sensitively and the slave laser is injection locked by feedback and compare to the results achievable by coupling through quantum channels.
Summary form only given. We perform a theoretical and numerical analysis of a system comprising a Bose-Einstein condensate (BEC) interacting with a laser beam in an optical cavity. Recent studies have modelled this system with two motional modes coupled with a light mode and have shown nonlinear behaviour, e.g. bistability [1,2]. Our approach tackles the full Gross-Pitaevskii equation coupled to the cavity field as well as expansions in a number of motional modes.We consider a fixed value of the cavity-pump detuning and increase the pump intensity to cross the region of bistability (see Fig. 1 left panel). The system then displays a variety of behaviours, including regular oscillations, chaotic dynamics, and quasi-periodic behaviour, as displayed in the right panel of Fig. 1. In Fig. 1 we have used a coupled-equation system comprising the Schrödinger wave equation and a cavity-field evolution [3], where we have adiabatically eliminated the latter leading to a conservative dynamics. The chaotic dynamics here is not induced by the detector noise and is an intrinsic property of the light-BEC interaction.Our second model considers a multiple-modes expansion. By using just three modes, the chaotic dynamics observed in the full simulation is recovered. The bifurcation structure, typical of conservative dynamics in the vicinity of a separatrix, is identified through the use of projections and power spectra. Our results suggest that chaotic oscillations in this system are deterministic in nature and arise purely from nonlinear effects. In more general terms, the model is a novel example of quantum matter exhibiting chaotic behaviour and invites further research.
We investigate Ramsey spectroscopy performed on a synchronized ensemble of two-level atoms. The synchronization is induced by the collective coupling of the atoms to a heavily damped mode of an optical cavity. We show that, in principle, with this synchronized system it is possible to observe Ramsey fringes indefinitely, even in the presence of spontaneous emission and other sources of individual-atom dephasing. This could have important consequences for atomic clocks and a wide range of precision metrology applications.
We analyze the dynamics leading to radiative cooling of an atomic ensemble confined inside an optical cavity when the atomic dipolar transitions are incoherently pumped and can synchronize. Our study is performed in the semiclassical regime and assumes that cavity decay is the largest rate in the system dynamics. We identify three regimes characterizing the cooling. At first hot atoms are individually cooled by the cavity friction forces. After this stage, the atoms' center-of-mass motion is further cooled by the coupling to the internal degrees of freedom while the dipoles synchronize. In the latest stage dipole-dipole correlations are stationary and the center-of-mass motion is determined by the interplay between friction and dispersive forces due to the coupling with the collective dipole. We analyze this asymptotic regime by means of a mean-field model and show that the width of the momentum distribution can be of the order of the photon recoil. Furthermore, the internal excitations oscillate spatially with the cavity standing wave forming an antiferromagnetic-like order.
We theoretically analyze superradiant emission of light from an ultracold gas of bosonic atoms confined in a bad cavity. A metastable dipolar transition of the atoms couples to the cavity field and is incoherently pumped, and the mechanical effects of cavity-atom interactions tend to order the atoms in the periodic cavity potential. By means of a mean-field model we determine the conditions on the cavity parameters and pump rate that lead to the buildup of a stable macroscopic dipole emitting coherent light. We show that this occurs when the superradiant decay rate and the pump rate exceed threshold values of the order of the photon recoil energy. Above these thresholds superradiant emission is accompanied by the formation of stable matter-wave gratings that diffract the emitted photons. Outside of this regime, instead, the optomechanical coupling can give rise to dephasing or chaos, for which the emitted light is respectively incoherent or chaotic. These behaviors exhibit the features of a dynamical phase transitions and emerge from the interplay between global optomechanical interactions, quantum fluctuations, and noise.