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Physical Review Research

Unveiling the interplay of Mollow physics and perturbed free induction decay by nonlinear optical signals of a dynamically driven two-level system

Jan M. Kaspari, Thomas K. Bracht, Katarina Boos, Sang Kyu Kim, Friedrich Sbresny, Kai Müller, Doris E. Reiter

Published May 13, 2024• 3 citations
Publisher

Abstract

Nonlinear optical signals in optically driven quantum systems can reveal coherences and thereby open up the possibility for manipulation of quantum states. While the limiting cases of ultrafast and continuous-wave excitation have been extensively studied, the time dynamics of finite pulses bear interesting phenomena. In this paper, we explore the nonlinear optical probe signals of a two-level system excited with a laser pulse of finite duration. In addition to the prominent Mollow peaks, the probe spectra feature several smaller peaks for certain time delays. Similar features have been recently observed for resonance fluorescence signals [K. Boos , ]. We discuss that the emergent phenomena can be explained by a combination of Mollow triplet physics and perturbed free induction decay effects, providing an insightful understanding of the underlying physics. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023155

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Nonlinear optical signals in optically driven quantum systems can reveal coherences and thereby open up the possibility for manipulation of quantum states. While the limiting cases of ultrafast and continuous-wave excitation have been extensively studied, the time dynamics of finite pulses bear interesting phenomena. In this paper, we explore the nonlinear optical probe signals of a two-level system excited with a laser pulse of finite duration. In addition to the prominent Mollow peaks, the probe spectra feature several smaller peaks for certain time delays. Similar features have been recently observed for resonance fluorescence signals [K. Boos , ]. We discuss that the emergent phenomena can be explained by a combination of Mollow triplet physics and perturbed free induction decay effects, providing an insightful understanding of the underlying physics. Published by the American Physical Society 2024
Nonlinear optical signals in optically driven quantum systems can reveal coherences and thereby open up the possibility for manipulation of quantum states. While the limiting cases of ultrafast and continuous-wave excitation have been extensively studied, the time-dynamics of finite pulses bear interesting phenomena. In this paper, we explore the nonlinear optical probe signals of a two-level system excited with a laser pulse of finite duration. In addition to the prominent Mollow peaks, the probe spectra feature several smaller peaks for certain time delays. Similar features have been recently observed for resonance fluorescence signals [arxiv:2305.15827 (2023)]. We discuss that the emergent phenomena can be explained by a combination of Mollow triplet physics and perturbed free induction decay effects, providing an insightful understanding of the underlying physics.
The coherent interaction between a two-level system and electromagnetic fields serves as a foundation for fundamental quantum physics and modern photonic quantum technology. A profound example is resonance fluorescence, where the non-classical photon emission appears in the form of a Mollow-triplet when a two-level system is continuously driven by a resonant laser. Pushing resonance fluorescence from a static to dynamic regime by using short optical pulses generates on-demand emissions of highly coherent single photons. Further increasing the driving strength in the dynamical regime enables the pursuit of exotic non-classical light emission in photon number superposition, photon number entanglement, and photon bundle states. However, the long-sought-after spectrum beyond the Mollow-triplet, a characteristic of dynamic resonance fluorescence under strong driving strength, has not been observed yet. Here we report the direct observation and systematic investigations of dynamic resonance fluorescence spectra beyond the Mollow-triplet in a solid-state cavity quantum electrodynamic system. The dynamic resonance fluorescence spectra with up to five pairs of side peaks, excitation detuning induced spectral asymmetry, and cavity filtering effect are observed and quantitatively modeled by a full quantum model with phonon scattering included. Time-resolved measurements further reveal that the multiple side peaks originate from interference of the emission associated with different temporal positions of the excitation pulses. Our work facilitates the generation of a variety of exotic quantum states of light with dynamic driving of two-level systems.
Abstract The coherent interaction between a two-level system and electromagnetic fields serves as a foundation for fundamental quantum physics and modern photonic quantum technology. A profound example is resonance fluorescence, where the non-classical photon emission appears in the form of a Mollow-triplet when a two-level system is continuously driven by a resonant laser. Pushing resonance fluorescence from a static to dynamic regime by using short optical pulses generates on-demand emissions of highly coherent single photons. Further increasing the driving strength in the dynamical regime enables the pursuit of exotic non-classical light emission in photon number superposition, photon number entanglement, and photon bundle states. However, the long-sought-after spectrum beyond the Mollow-triplet, a characteristic of dynamic resonance fluorescence under strong driving strength, has not been observed yet. Here we report the direct observation and systematic investigations of dynamic resonance fluorescence spectra beyond the Mollow-triplet in a solid-state cavity quantum electrodynamic system. The dynamic resonance fluorescence spectra with up to five pairs of side peaks, excitation detuning induced spectral asymmetry, and cavity filtering effect are observed and quantitatively modeled by a full quantum model with phonon scattering included. Time-resolved measurements further reveal that the multiple side peaks originate from interference of the emission associated with different temporal positions of the excitation pulses. Our work facilitates the generation of a variety of exotic quantum states of light with dynamic driving of two-level systems.
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.
We study the time-resolved fluorescence spectrum in two-level systems interacting with an incident coherent field, both in the weak and intermediate coupling regimes. For a single two-level system in the intermediate-coupling case, as time flows, the spectrum develops distinct features that are not captured by a semiclassical treatment of the incident field. Specifically, for a field on resonance with the atomic transition energy, the usual Mollow spectrum is replaced by a four-peak structure, and for a frequency that is half of the atomic transition energy, the time-dependent spectrum develops a second-harmonic peak with a superimposed Mollow triplet. In the long-time limit, our description recovers results previously found in the literature. After analyzing why a different behavior is observed in the quantum and classical dynamics, the reason for the occurrence of a second-harmonic signal in a two-level system is explained via a symmetry analysis of the total (electron and photon) system and in terms of a three-level system operating in limiting regimes. We find an increased second-harmonic signal in an array of two-level systems, suggesting a superradiance-like enhancement for multiple two-level systems in cavity setups. Finally, initial explorative results are presented for two-level model atoms entering and exiting a cavity, which hint at an interesting interplay between cavity-photon screening and atomic dynamics effects.
We study transients in resonantly coupled three-level systems. Two of the levels are coupled by intense two-photon pumping, and the third one provides a probing level. Adiabatically eliminated levels appear in effective system parameters. Experimentally, this model is applicable, e.g., in resonantly enhanced parametric and harmonic generation in atomic vapors. A distinguishing feature in the system is the appearance of ac Stark shifts in the probe spectra when pumping at the two-photon resonance. The nutation signal is shown to give information on the effective two-photon Rabi frequency and on the decay rate of the dipole-forbidden two-photon coherence. Free-induction decay is strongly dominated by population-induced effects; Raman-like peaks introduced by Stark shifts may show large instantaneous gain. Gaussian pump pulses are investigated to investigate effects arising from the temporal sweeping of the two-photon Rabi flipping and the modulation of the Stark shifts. The results also provide relevant information on the gain dynamics of coherently pumped lasers.