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arXiv:2102.02719 · Physical Review Letters

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

Giuseppe Buonaiuto, Federico Carollo, Beatriz Olmos, Igor Lesanovsky

Published Sep 21, 2021• 53 citations
arXivHTMLPDF

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 for the generation of 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.

DOI
10.1103/physrevlett.127.133601

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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 for the generation of 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.
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In this thesis three different approaches to control the quantum statistics in nanoscopic devices are investigated. In the first part of the thesis, mechanical oscillations in solid state devices are manipulated by an external laser to show bistabilities, coherent amplification, and enhanced damping. The dynamics is controlled by the frequency of the external laser. This study is performed in a semiclassical approximation, where expectation values of operators are factorized. These effects are used to show the similarities and differences between optomechanical systems and phonon cavities. In the regime of coherent amplification of phonons the theoretical description is extended to a fully quantum mechanical model. This reveals additional resonances due to collective processes that can be addressed via the frequency of the external laser. In the second part, a quantum light source is considered for manipulation of the emission statistics of a second quantum optical system serving as target. A Jaynes-Cummings system is used as a source that may be tuned from nonclassical to thermal emission via the pump strength. The target consists of a cavity with two emitters. The nature of the imprinted statistics is studied by higher order correlation functions. The resulting statistics deviates strongly from thermal, coherent or antibunched statistics. The third part considers coherent self feedback with time-delay, which is motivated by classical Pyragas control. The finite time delay is used as control parameter. The matrix product state evolution in the picture of the quantum stochastic Schrödinger equation is employed as a systematic way of dealing with quantum self-feedback. In this thesis, the approach is extended to include higher order terms in the time evolution operator. This is done systematically so that arbitrary order can be included enabling faster numerical evaluation. This extension of the matrix product state evolution method allows to investigate efficiently the emission statistics of a single mode cavity containing two emitters. It is shown that feedback can enhance antibunching in the light field while also counter-intuitively increasing the number of emitted photons at the same time. Expressing the time evolution operator as a sum of sparse matrices allows to include time dependent Hamiltonians in an efficient manner. Considering the pulsed excitation of a two level emitter, it is demonstrated that emission statistics may be tuned via feedback. This allows to switch between single photon emission and enhanced two photon emission.
Squeezed light states have a special place in quantum optics with potentially profound applications in emerging quantum technologies. We present a numerically-exact matrix product states (MPS) approach to model quantum pulses of squeezed light, at the few-photon level, interacting with a two-level system in a waveguide environment. We represent the squeezed state as a coherent superposition of Fock states and explore the nonlinear population dynamics as well as multi-photon correlation functions that emerge. We show how the squeezed pulse can create quantum correlations that are unique to squeezed pulses, including ⟨b(t)b(t+t′)⟩\langle b(t) b(t+t')\rangle⟨b(t)b(t+t′)⟩ for transmitted fields as well as ⟨b†(t)b†(t+t′)b(t+t′)b(t)⟩\langle b^\dagger(t) b^\dagger(t+t') b(t+t') b(t) \rangle⟨b†(t)b†(t+t′)b(t+t′)b(t)⟩. We also demonstrate how ⟨b(t)b(t+t′)⟩\langle b(t) b(t+t') \rangle⟨b(t)b(t+t′)⟩, a first-order correlation function, shows nonlinear photon correlations that are similar to those known and measured for two-photon scattering states. Finally, we also study the squeezed spectra of the pulse before and after interacting with the two-level system, and highlight the role of the spectral bandwidth of the incident pulse. The MPS theory allows the modeling of arbitrary bandwidth squeezing without making any Markov and Born approximations for the light-matter interaction processes, and can easily be extended to waveguide systems with multiple emitters and time-delayed feedback.