Dynamical Phases and Quantum Correlations in an Emitter-Waveguide System with Feedback

Buonaiuto, Giuseppe; Carollo, Federico; Olmos, Beatriz; Lesanovsky, Igor

Abstract

We investigate the creation and control of emergent collective behavior and quantum correlations using feedback in an emitter-waveguide system using a minimal model. Employing homodyne detection of photons emitted from a laser-driven emitter ensemble into the modes of a waveguide allows to generate intricate dynamical phases. In particular, we show the emergence of a time-crystal phase, the transition to which is controlled by the feedback strength. Feedback enables furthermore the control of many-body quantum correlations, which become manifest in spin squeezing in the emitter ensemble. Developing a theory for the dynamics of fluctuation operators we discuss how the feedback strength controls the squeezing and investigate its temporal dynamics and dependence on system size. The largely analytical results allow to quantify spin squeezing and fluctuations in the limit of large number of emitters, revealing critical scaling of the squeezing close to the transition to the time-crystal. Our study corroborates the potential of integrated emitter-waveguide systems-which feature highly controllable photon emission channels-for the exploration of collective quantum phenomena and the generation of resources, such as squeezed states, for quantum enhanced metrology. Introduction. The development of techniques for the manipulation of matter with light has undergone rapid progress in the past decade [1-9]. This has enabled the creation of tailored quantum systems for the purpose of quantum simulation and information processing [10-12]. It has also opened an avenue for the investigation of novel phases of matter and of the emergence of collective quantum behavior as it appears in the vicinity of a phase transition [13, 14]. A paradigmatic example is the (open) Dicke model, which describes the interaction of an ensemble of atoms with a single-mode light field [15]. It has received substantial attention in recent years, not only because of its fundamental theoretical interest, but also because it has been realized in various experimental platforms , such as atom-cavity setups [16, 17]. An example of a novel many-body phase is a so-called time crystal. This is a phase of matter in which time-translation invariance is broken [18-21]. It has been theoretically predicted and analyzed in various scenarios, including disordered closed systems [22-24], dissipative systems in continuous time [25-27] as well as periodic driven-dissipative systems [28-32]. Moreover, this state of matter has been studied and characterized in a number of recent experiments [33-36].

Citation

Buonaiuto, G., Carollo, F., Olmos, B., & Lesanovsky, I. (2021). Dynamical Phases and Quantum Correlations in an Emitter-Waveguide System with Feedback. Physical Review Letters, 127(13), 1-8. https://doi.org/10.1103/PhysRevLett.127.133601

• Journal Article Type: Letter
• Acceptance Date: Aug 13, 2021
• Online Publication Date: Sep 21, 2021
• Publication Date: Sep 24, 2021
• Deposit Date: Aug 18, 2021
• Publicly Available Date: Sep 21, 2021
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 127
• Issue: 13
• Article Number: 133601
• Pages: 1-8
• DOI: https://doi.org/10.1103/PhysRevLett.127.133601
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/6057120
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.133601