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arXiv:1801.04442

Emission and Absorption Spectrum of Pulse-Driven Two-Level Systems in Dynamic Environments

Herbert F. Fotso

Published Jan 13, 2018• 0 citations
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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 $π_x$ pulses, the periodic sequence of $π_xπ_y$ 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 $π_xπ_y$ 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 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 the solid state.

DOI
10.48550/arxiv.1801.04442

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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 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 investigate how the quantum control of a two-level system (TLS) coupled to photons can modify and tune the TLS's photon absorption spectrum. Tuning and controlling the emission and the absorption are of great interest, e.g., for the development of efficient interfaces between stationary and flying qubits in modern architectures for quantum computation and quantum communication. We consider periodic pulse control, where the TLS is subjected to a periodic sequence of the near-resonant Rabi driving pulses, each pulse implementing a ${180}^{\ensuremath{\circ}}$ rotation. For small interpulse delays, the absorption spectrum features a pronounced peak of stimulated emission at the pulse frequency, similar satellite peaks with smaller spectral weights, and the net absorption peaks on the sides. As long as the detuning between the carrier frequency of the driving and the TLS transition frequency remains moderate, this spectral shape shows little change. Therefore, the pulse control allows shifting the absorption peak to a desired position and locks the overall absorption spectrum to the carrier frequency of the driving pulses. A detailed description of the spectrum and its evolution as a function time, the interpulse spacing, and the detuning is presented.
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.
The interaction of a resonant light field with a quantum two-level system is of key interest both for fundamental quantum optics and quantum technological applications employing resonant excitation. While emission under resonant continuous-wave excitation has been well-studied, the more complex emission spectrum of dynamically dressed states, a quantum two-level system driven by resonant pulsed excitation, has so far been investigated in detail only theoretically. Here, we present the first experimental observation of the complete resonance fluorescence emission spectrum of a single quantum two-level system, in form of an excitonic transition in a semiconductor quantum dot, driven by finite Gaussian pulses. We observe multiple emerging sidebands as predicted by theory with an increase of their number and spectral detuning with excitation pulse intensity and a dependence of their spectral shape and intensity on the pulse length. Detuning-dependent measurements provide additional insights into the emission features. The experimental results are in excellent agreement with theoretical calculations of the emission spectra, corroborating our findings.
Abstract When a two-level system is driven on resonance by a strong incident field, its emission spectrum is characterized by the well-known Mollow triplet. If the absorption from the excited state, in this continuously driven two-level system, to a third, higher energy level, is probed by a weak field, the resulting absorption spectrum features the Autler-Townes doublet with two peaks separated by the Rabi frequency of the strong driving field. It has been shown that when the two-level system is instead driven by a periodic pulse sequence, the emission spectrum obtained has similarities with the Mollow triplet even though the system is only driven during the short application time of the pulses and is allowed to evolve freely between pulses. Here, we evaluate the absorption spectrum of the three-level system in the ladder/cascade configuration when the bottom two levels are driven by a periodic pulse sequence while the transition between the middle and the highest level is probed by a weak field. The absorption spectrum displays similarities with the Autler-Townes doublet with frequency separation between the main peaks defined by the inter-pulse delay. In addition, this spectrum shows little dependence on the pulse carrier frequency. These results demonstrate the capacity to modulate the absorption spectrum of a three-level system with experimentally achievable pulse protocols.