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arXiv:2112.15469 · Materials for Quantum Technology

Polariton creation in coupled cavity arrays with spectrally disordered emitters

Jesse Patton, Victoria A. Norman, E C Mann, B Puri, Richard T. Scalettar, Marina Radulaski

Published Apr 5, 2024• 4 citations
arXivHTMLPDF

Abstract

Abstract Integrated photonics has been a promising platform for analog quantum simulation of condensed matter phenomena in strongly correlated systems. To that end, we explore the implementation of all-photonic quantum simulators in coupled cavity arrays with integrated ensembles of spectrally disordered emitters. Our model is reflective of color center ensembles integrated into photonic crystal cavity arrays. Using the Quantum Master equation and the Effective Hamiltonian approaches, we study energy band formation and wavefunction properties in the open quantum Tavis–Cummings–Hubbard framework. We find conditions for polariton creation and (de)localization under experimentally relevant values of disorder in emitter frequencies, cavity resonance frequencies, and emitter-cavity coupling rates. To quantify these properties, we introduce two metrics, the polaritonic and nodal participation ratios, that characterize the light-matter hybridization and the node delocalization of the wavefunction, respectively. These new metrics combined with the Effective Hamiltonian approach prove to be a powerful toolbox for cavity quantum electrodynamical engineering of solid-state systems.

DOI
10.1088/2633-4356/ad3b5d

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Abstract Integrated photonics has been a promising platform for analog quantum simulation of condensed matter phenomena in strongly correlated systems. To that end, we explore the implementation of all-photonic quantum simulators in coupled cavity arrays with integrated ensembles of spectrally disordered emitters. Our model is reflective of color center ensembles integrated into photonic crystal cavity arrays. Using the Quantum Master equation and the Effective Hamiltonian approaches, we study energy band formation and wavefunction properties in the open quantum Tavis–Cummings–Hubbard framework. We find conditions for polariton creation and (de)localization under experimentally relevant values of disorder in emitter frequencies, cavity resonance frequencies, and emitter-cavity coupling rates. To quantify these properties, we introduce two metrics, the polaritonic and nodal participation ratios, that characterize the light-matter hybridization and the node delocalization of the wavefunction, respectively. These new metrics combined with the Effective Hamiltonian approach prove to be a powerful toolbox for cavity quantum electrodynamical engineering of solid-state systems.
Color centers are optically active point defects in semiconductor materials, many of them carrying a spin degree of freedom that couples coherently to emitted photons. This makes them a leading candidate for building quantum computers, networks, and sensors, but realizing that promise depends on the interface between the emitter and light. Color centers must be integrated into nanophotonic structures, such as nanopillars that collect their emission efficiently and optical cavities that couple them to a single mode. This dissertation studies the physics of quantum emitters inside such structures along two complementary threads: the direct cryogenic spectroscopy of color centers integrated into silicon carbide nanostructures, and the study of the physics of many-body cavity quantum electrodynamics (CQED) through simulation on superconducting and trapped-ion quantum hardware. The first thread concerns the nitrogen-vacancy (NV) center in 4H silicon carbide integrated into nanopillars. We show that the sub-wavelength geometry of a nanopillar reshapes the local electromagnetic environment, granting optical access to transitions that selection rules forbid in bulk material: emission from the PL3 divacancy, nearly absent in planar devices, becomes pronounced in nanopillars through a polarization transformation of the excitation field, and the orientation-dependent collection of the pillar resolves the previously ambiguous NV4′ line, establishing nanophotonic integration as a symmetry-sensitive probe of defect structure. We then take up the complementary problem of quantifying how many emitters a device contains, adapting the number-and-brightness technique from fluorescence microscopy to solid-state emitters. This calibration-free method counts dense NV ensembles in silicon carbide nanopillars, a regime beyond the reach of existing optical techniques, and extracts their areal density and formation yield. The second thread turns to many-body cavity QED, in which placing N emitters in a common cavity enhances the light-matter coupling by √N and gives rise to collective effects that are central to strong-coupling applications yet difficult to achieve in solid-state devices based on defects. We realize one such effect on a superconducting circuit, demonstrating photon blockade, the conversion of a coherent drive into a stream of single photons, in a Tavis–Cummings system of N = 1, 2, 3 transmon qubits coupled to a common resonator. To study the open-system dynamics that govern these systems, we digitally simulate the dissipative Tavis–Cummings model on both a superconducting and a trapped-ion processor. Platform-specific compilation and error mitigation yield population dynamics in close agreement with exact solutions, providing a recipe for simulating cavity-emitter systems on contemporary quantum computers. Together, the two threads connect the fabrication and characterization of color-center devices to the many-body cavity-QED physics that will ultimately govern their performance.
The use of quantum light to probe exciton properties in semiconductor and molecular nanostructures typically occurs in the low-intensity regime. A substantial enhancement of exciton-photon coupling can be achieved with photonic cavities, where excitons hybridize with cavity modes to form polariton states. To provide a theoretical framework for interpreting emerging experimental efforts in this direction, we develop a scattering theory describing the interaction of frequency-entangled photon pairs with cavity polariton and bipolariton states under various coupling regimes. Employing the Tavis-Cummings model in combination with our scattering approach, we present a quantitative analysis of how the interaction of the entangled photon pair with the polariton/bipolariton modifies its joint spectral amplitude (JSA). Specifically, we examine the effects of the cavity-mode steady-state population, exciton-cavity coupling strength, and different forms of the input photon JSA. Our results show that the entanglement entropy of the scattered photons is highly sensitive to the interplay between the input JSA and the spectral line shapes of the polariton resonances, emphasizing the cavity filtering effects. We suggest that biphoton scattering quantum light spectroscopy best serves as a sensitive probe of polariton and bipolariton states in the photon-vacuum cavity state. Our approach is not only robust to various regimes of cavity-exciton coupling, but also amenable to extensions beyond the Tavis-Cummings model, enabling the representation of a broad class of molecular systems and solid state quantum materials.
An empirical framework for studying the way vacuum fluctuations in a Fabry–Perot cavity produce collective light–matter hybrid states (polariton states) is reported. The reason that the Tavis–Cummings model, where a single mode of the radiation field couples to all the molecules, succeeds is discussed in terms of the strong phase correlation of the vacuum fluctuations in the cavity, which produces a single effective cavity mode (ECM). The model is used to study the onset of the collective state, or “superradiant phase”, for ensembles of molecules with significant disorder in their transition energies, as a function of cavity strength factor, from low Q cavities to high Q cavities. A key result is the quantification of the coherence of the ensemble of the lowest energy eigenstate. This is assessed, primarily, using an entropy distance measure. The statistical model provides a physical intuition for the formation of coherence of polariton states when the collective coupling is strong enough that they dominate over the tail of the dark-state density-of-states.
The photon blockade (PB) effect in emitter-cavity systems depends on the anharmonicity of the ladder of dressed energy eigenstates. The recent developments in color center photonics are leading toward experimental demonstrations of multiemitter-cavity solid-state systems with an expanded set of energy levels compared to the traditionally studied single-emitter systems. We focus on the case of N=2N=2N=2 nonidentical quasiatoms strongly coupled to a nanocavity in the bad cavity regime (with parameters within reach of the color center systems), and discover three PB mechanisms: polaritonic, subradiant, and unconventional. The polaritonic PB, which is the conventional mechanism studied in single-emitter-cavity systems, also occurs at the polariton frequencies in multiemitter systems. The subradiant PB is a new interference effect owing to the inhomogeneous broadening of the emitters which results in a purer and a more robust single-photon emission than the polaritonic PB. The unconventional PB in the modeled system corresponds to the suppression of the single- and two-photon correlation statistics and the enhancement of the three-photon correlation statistic. Using the effective Hamiltonian approach, we unravel the origin and the time-domain evolution of these phenomena.