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arXiv:2207.02770 · Physical Review A

Tuning spectral properties of individual and multiple quantum emitters in noisy environments

Herbert F. Fotso

Published Feb 21, 2023• 2 citations
arXivHTMLPDF

Abstract

A quantum emitter in a dynamic environment may have its energy levels drift uncontrollably in time with the fluctuating bath. This can result in an emission and/or absorption spectrum that is spread over a broad range of frequencies and presents a challenging hurdle for various applications. We consider a quantum emitter in an environment that alters the energy levels so that the emission frequency is represented by a Gaussian random distribution around a given mean value with given standard deviation and correlation time. We study the emission spectrum of this system when it is placed under the influence of a periodic sequence of finite-width $\ensuremath{\pi}$ pulses. We show that this external field protocol can effectively overcome spectral diffusion in this system by refocusing the bulk of the emission spectrum onto the pulse carrier frequency. We further consider two such emitters in different noisy environments and find that the two-photon interference operation can be made efficient by the sequence of finite-width pulses applied on both systems. Finally, we show that an ensemble of nominally similar emitters, each with its different environment, and thus randomly shifted emission frequency, can have its overall emission spectrum that would otherwise be inhomogeneously broadened according to the random distribution, refocused onto a lineshape with a well-defined central peak that has the linewidth of an individual isolated non-noisy emitter. These results demonstrate for this specific model of noisy environments, the protection of spectral properties by an external control protocol here represented by a periodic sequence of finite-width pulses.

DOI
10.1103/physreva.107.023719

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A quantum emitter in a dynamic environment may have its energy levels drift uncontrollably in time with the fluctuating bath. This can result in an emission and/or absorption spectrum that is spread over a broad range of frequencies and presents a challenging hurdle for various applications. We consider a quantum emitter in an environment that alters the energy levels so that the emission frequency is represented by a Gaussian random distribution around a given mean value with given standard deviation and correlation time. We study the emission spectrum of this system when it is placed under the influence of a periodic sequence of finite-width \ensuremathπ\ensuremath{\pi}\ensuremathπ pulses. We show that this external field protocol can effectively overcome spectral diffusion in this system by refocusing the bulk of the emission spectrum onto the pulse carrier frequency. We further consider two such emitters in different noisy environments and find that the two-photon interference operation can be made efficient by the sequence of finite-width pulses applied on both systems. Finally, we show that an ensemble of nominally similar emitters, each with its different environment, and thus randomly shifted emission frequency, can have its overall emission spectrum that would otherwise be inhomogeneously broadened according to the random distribution, refocused onto a lineshape with a well-defined central peak that has the linewidth of an individual isolated non-noisy emitter. These results demonstrate for this specific model of noisy environments, the protection of spectral properties by an external control protocol here represented by a periodic sequence of finite-width pulses.
The optical spectrum of a quantum system is jointly determined by the properties of the emitter and the driving field. All-optical spectral control can hence be a promising method to engineer the properties of single photon emitters for quantum technological applications. It was proposed that driving a two-level system with a periodic sequence of optical pi-pulses during the excited state lifetime shifts the emission and absorption maximum to an arbitrarily detuned pulse carrier frequency, enabling the mitigation of spectral diffusion in noisy emitters. In this article, we report on the first experimental observation of this effect. We implement the protocol on a solid-state emitter and reduce its inhomogeneously broadened optical linewidth close to the lifetime limit. By detuning the excitation laser, we are able to concentrate approximately half of the absorption to a freely selectable target frequency. Our approach is solely based on properties of coherently evolving quantum systems, rendering it applicable to a wide range of individual and ensembles of quantum emitters.
We study the emission spectrum and absorption spectrum of a quantum emitter when it is driven by various pulse sequences. We consider the Uhrig sequence of πxπ_xπx​ pulses, the periodic sequence of πxπyπ_xπ_yπx​πy​ pulses and the periodic sequence of πzπ_zπz​ pulses (phase kicks). We find that, similar to the periodic sequence of πxπ_xπx​ pulses, the Uhrig sequence of πxπ_xπx​ pulses has emission and absorption that are, with small variations, analogous to those of the resonance fluorescence spectrum. In addition, while the periodic sequence of πzπ_zπz​ pulses produces a spectrum that is dependent on the detuning between the emitter and the pulse carrier frequency, the Uhrig sequence of nonequidistant πxπ_xπx​ pulses and the periodic sequence of πxπyπ_xπ_yπx​πy​ pulses have spectra with little dependence on the detuning as long as it stays moderate along with the number of pulses. This implies that they can also, similar to previously studied periodic sequence of πxπ_xπx​ pulses, be used to tune the emission or absorption of quantum emitters to specific frequencies, to mitigate inhomogeneous broadening and to enhance the production of indistinguishable photons from emitters the solid state.
Abstract We study the emission spectrum and absorption spectrum of a quantum emitter when it is driven by various pulse sequences. We consider the Uhrig sequence of nonequidistant π x pulses, the periodic sequence of π x π y pulses and the periodic sequence of π z pulses (phase kicks). We find that, similar to the periodic sequence of π x pulses, the Uhrig sequence of π x pulses has emission and absorption that are, with small variations, analogous to those of the resonance fluorescence spectrum. In addition, while the periodic sequence of π z pulses produces a spectrum that is dependent on the detuning between the emitter and the pulse carrier frequency, the Uhrig sequence of nonequidistant π x pulses and the periodic sequence of π x π y pulses have spectra with little dependence on the detuning as long as it stays moderate along with the number of pulses. This implies that they can also, similar to the previously studied periodic sequence of π x pulses, be used to tune the emission or absorption of quantum emitters to specific frequencies, to mitigate inhomogeneous broadening and to enhance the production of indistinguishable photons from emitters in the solid state.
The ability to entangle distant quantum nodes is essential for the construction of quantum networks and for quantum information processing. For solid-state quantum emitters used as qubits, it can be achieved by photon interference. When the emitter is subject to spectral diffusion, this process can become highly inefficient, impeding the achievement of scalable quantum technologies. We study two-photon interference in the context of a Hong-Ou-Mandel (HOM)-type experiment for two separate quantum emitters, with different detunings with respect to a specific target frequency. We evaluate the second order coherences that characterize photon indistinguishability between the two emitters. We find that the two-photon interference operation that is inefficient in the absence of a control protocol, when the two detunings are different and spectral overlap is lessened, can be highly improved by a periodic sequence of $\ensuremath{\pi}$ pulses at a set target frequency. Photon indistinguishability in solid state and other quantum emitters subject to spectral diffusion can thus be enhanced by the proposed pulse sequence and similar external control protocols despite the fluctuations in the environment.
In many quantum architectures the solid-state qubits, such as quantum dots or color centers, are interfaced via emitted photons. However, the frequency of photons emitted by solid-state systems exhibits slow uncontrollable fluctuations over time (spectral diffusion), creating a serious problem for implementation of the photon-mediated protocols. Here we show that a sequence of optical pulses applied to the solid-state emitter can stabilize the emission line at the desired frequency. We demonstrate efficiency, robustness, and feasibility of the method analytically and numerically. Taking nitrogen-vacancy center in diamond as an example, we show that only several pulses, with the width of 1 ns, separated by few ns (which is not difficult to achieve) can suppress spectral diffusion. Our method provides a simple and robust way to greatly improve the efficiency of photon-mediated entanglement and/or coupling to photonic cavities for solid-state qubits.