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arXiv:1502.06731 · Optics Letters

Noisy metamolecule: strong narrowing of fluorescence line

E. S. Andrianov, N. M. Chtchelkatchev, Александр Александрович Пухов

Published Jul 22, 2015• 4 citations
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Abstract

We consider a metamolecule consisting of a bosonic mode correlated with a two-level system (TLS): it can be, for example, a plasmonic mode interacting with a quantum dot. We focus on the parameter range where all the correlations are strong and of the same order. The interaction between the bosonic mode is correlated with the TLS, external coherent drive, and dissipation. Quantum Monte Carlo simulations show that the fluorescence of this system at dissipation is larger than the driving amplitude and shows a strong (by the order of magnitude) narrowing of its spectral line. This effect may be related to kind of a quantum stochastic resonance. We show that the fluorescence corresponds to the finite domain over the coherent drive with sharp, low threshold, and that the Wigner function splits.

DOI
10.1364/ol.40.003536

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We comment on the recent Letter by Andrianov et al. [Opt. Lett.40, 3536 (2015)OPLEDP0146-959210.1364/OL.40.003536], in which they study a strongly dissipative driven bosonic mode strongly coupled to a two-level system using the quantum Monte Carlo simulations. We recalculate their quantities via sparse numerical solvers and find that their results for larger drives are incorrect, most likely due to insufficient Monte Carlo sampling in the presence of an emergent long time scale. These findings call for a corrected interpretation of the physical behavior of the studied model.

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We consider a metamolecule consisting of a bosonic mode correlated with a two-level system (TLS): it can be, for example, a plasmonic mode interacting with a quantum dot. We focus on the parameter range where all the correlations are strong and of the same order. The interaction between the bosonic mode is correlated with the TLS, external coherent drive, and dissipation. Quantum Monte Carlo simulations show that the fluorescence of this system at dissipation is larger than the driving amplitude and shows a strong (by the order of magnitude) narrowing of its spectral line. This effect may be related to kind of a quantum stochastic resonance. We show that the fluorescence corresponds to the finite domain over the coherent drive with sharp, low threshold, and that the Wigner function splits.
We comment on the recent Letter by Andrianov et al. [Opt. Lett.40, 3536 (2015)OPLEDP0146-959210.1364/OL.40.003536], in which they study a strongly dissipative driven bosonic mode strongly coupled to a two-level system using the quantum Monte Carlo simulations. We recalculate their quantities via sparse numerical solvers and find that their results for larger drives are incorrect, most likely due to insufficient Monte Carlo sampling in the presence of an emergent long time scale. These findings call for a corrected interpretation of the physical behavior of the studied model.
We reply on the comment [Opt. Lett.41, 5821 (2016)10.1364/OL.41.005821OPLEDP0146-9592] regarding our Letter [Opt. Lett.40, 3536 (2015)OPLEDP0146-959210.1364/OL.40.003536], where a dissipative driven bosonic mode strongly coupled to a two-level system is studied. We show that the authors of the comment erroneously claim that the Monte Carlo simulation is insufficient. More important is the basic statement of the comment about the vanishing width of the spectral line. This means that the plasmon spectral line vanishes at a large external field. The authors of the comment do not distinguish the averages of the observables from the quasi-averages that are quite different in multistable systems where ergodicity is challenged.
We consider the interaction of a two-level atom inside an optical parametric oscillator. In the weak-driving-field limit, we essentially have an atom-cavity system driven by the occasional pair of correlated photons, or weakly squeezed light. We find that we may have holes, or dips, in the spectrum of the fluorescent and transmitted light. This occurs even in the strong-coupling limit when we find holes in the vacuum-Rabi doublet. Also, spectra with a subnatural linewidth may occur. These effects disappear for larger driving fields, unlike the spectral narrowing obtained in resonance fluorescence in a squeezed vacuum; here it is important that the squeezing parameter N tends to zero so that the system interacts with only one correlated pair of photons at a time. We show that a previous explanation for spectral narrowing and spectral holes for incoherent scattering is not applicable in the present case, and propose an alternative explanation. We attribute these anomalous effects to quantum interference in the two-photon scattering of the system.
We explore the role of quantum fluctuations in the strong-coupling limit of the dissipative Jaynes–Cummings oscillator driven on resonance. For weak excitation, we derive analytical expressions for the spectrum and the intensity correlation function for the photons scattered by the two-state atom coupled to the coherently driven cavity mode. We do so by writing down a birth–death process adding the higher orders in the excitation strength needed to go beyond the pure-state factorization, following the method introduced in Carmichael (2008). Our results for the first and second-order correlation functions are complemented by the numerical investigation of the waiting-time distribution for the photon emissions directed sideways, and the comparison with ordinary resonance fluorescence. To close out our discussion, we increase the driving field amplitude and approach the critical point organizing a second-order dissipative quantum phase transition by depicting the excitation pathways in the intracavity field distribution for a finite system size.
The authors apply the recently developed theory of multiplicative stochastic correlation functions with Markovian random jumps to the problem of resonance fluorescence from a two-level atom in a strong laser field. The finite bandwidth of a single-mode laser or the appearance of distinct lines in a multimode laser is considered to be brought about by a random mode-switching process. The two-time dipole correlation functions, which determine the spectral distribution of the fluorescence and the temporal correlations between the emitted photons are averaged exactly over the stochastics of the driving field. The authors' explicit expressions only involve single-time averages, which can be easily evaluated for a given probability distribution. These results generalise and modify earlier results. The authors obtain closed expressions, rather than implicit differential equations, which can handle the continuous case as well, and take into account the initial correlations, which always arise when the laser coherence time is finite. They illustrate the dependence on the stochastics of the laser model by comparing the multimode description with the phase-diffusion process and the Lorentz wave, which all give rise to the same laser profile, but to a different fluorescence spectrum.
The resonance fluorescence of a two-level atom driven by a coherent laser field and damped by a finite bandwidth squeezed vacuum is analysed. We extend the Yeoman and Barnett technique to a non-zero detuning of the driving field from the atomic resonance and discuss the role of squeezing bandwidth and the detuning in the level shifts, widths and intensities of the spectral lines. The approach is valid for arbitrary values of the Rabi frequency and detuning but for the squeezing bandwidths larger than the natural line-width in order to satisfy the Markoff approximation. The narrowing of the spectral lines is interpreted in terms of the quadrature-noise spectrum. We find that, depending on the Rabi frequency, detuning and the squeezing phase, different factors contribute to the line narrowing. For a strong resonant driving field there is no squeezing in the emitted field and the fluorescence spectrum exactly reveals the noise spectrum. In this case the narrowing of the spectral lines arises from the noise reduction in the input squeezed vacuum. For a weak or detuned driving field the fluorescence exhibits a large squeezing and, as a consequence, the spectral lines have narrowed linewidths. Moreover, the fluorescence spectrum can be asymmetric about the central frequency despite the symmetrical distribution of the noise. The asymmetry arises from the absorption of photons by the squeezed vacuum which reduces the spontaneous emission. For an appropriate choice of the detuning some of the spectral lines can vanish despite that there is no population trapping. Again this process can be interpreted as arising from the absorption of photons by the squeezed vacuum. When the absorption is large it may compensate the spontaneous emission resulting in the vanishing of the fluorescence lines.