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arXiv:1307.5891 · Physical Review Letters

Synchronization of Two Ensembles of Atoms

Minghui Xu, David Tieri, E. C. Fine, James K. Thompson, Murray Holland

Published Oct 6, 2014• 217 citations
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Abstract

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.

DOI
10.1103/physrevlett.113.154101

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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.
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 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.
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.
Driven-dissipative quantum systems can undergo transitions from stationary to dynamical phases, reflecting the emergence of collective nonequilibrium behavior. We study such a transition in a Bose-Einstein condensate coupled to an optical cavity and develop a cavity-assisted Bragg spectroscopy technique to resolve its collective modes. We observe dissipation-induced synchronization at the quasiparticle level, where two rotonlike modes coalesce at an exceptional point. This reveals how dissipation microscopically drives collective dynamics and signals a precursor to a dynamical phase transition.
Superradiant lasers may soon achieve state-of-the-art frequency purity, with linewidths of 1 mHz or less. In a superradiant (or bad-cavity) laser, coherence is primarily stored in the atomic gain medium instead of the optical field. This phase storage is characterized by spontaneous quantum synchronization of the optical dipole moments of each atom. To observe this synchronization, we create two independent superradiant atomic ensembles lasing in a single optical cavity and observe the dynamics of phase realignment, collective power enhancement, and steady-state frequency locking. This work introduces superradiant ensembles as a testbed for fundamental study of quantum synchronization as well and informs research on narrow linewidth superradiant lasers.
We theoretically investigate the quantum phase transition in the collective systems of qubits in a high quality cavity, where the cavity field is squeezed via the optical parametric amplification process. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase transition can be controlled by the nonlinear gain coefficient, which is sensitive to the pump field. These features also lead to an optical switching from the normal phase to the superradiant phase by just increasing the pump field intensity. The signature of these phase transitions can be observed by detecting the phase space Wigner function distribution with different profiles controlled by the squeezed light intensity. Such superradiant phase transition can be implemented in various quantum systems, including atoms, quantum dots, and ions in optical cavities as well as the circuit quantum electrodynamics system.