Cascade superfluorescence in Er:YLF

Open Access

Cascade superfluorescence in Er:YLF

F. Chiossi, C. Braggio, A. Khanbekyan, G. Carugno, A. Ortolan, G. Ruoso, R. Calabrese, A. Di Lieto, L. Tomassetti, and M. Tonelli

Phys. Rev. Research 3, 013138 – Published 12 February 2021

Abstract

We report the analysis of paired photon pulses arising from two cascading transitions in continuously pumped erbium-doped ${YLiF}_{4}$ 1% and 0.01% crystals at 1.6 K. The dependence of the pulse peak intensity on the squared number of involved erbium ions, between $10^{11}$ and $10^{13}$ , definitely identifies the cooperative nature of the two pulsed emissions, that are generated by the subsequent, spontaneous formation of coherent states. The observed fluctuations of the time interval between the paired pulses and, most importantly, its correlation with the second pulse duration demonstrate that the erbium ions coherence is indeed seeded by quantum fluctuations.

Received 13 September 2020
Accepted 2 December 2020

DOI:https://doi.org/10.1103/PhysRevResearch.3.013138

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Light-matter interaction Nonlinear optics

Atomic, Molecular & Optical

Authors & Affiliations

F. Chiossi ^1,*, C. Braggio¹, A. Khanbekyan ², G. Carugno¹, A. Ortolan ³, G. Ruoso ³, R. Calabrese², A. Di Lieto^4,5, L. Tomassetti ², and M. Tonelli^4,5

¹Dipartimento di Fisica e Astronomia, University of Padova and INFN of Padova, I-35131 Padova, Italy
²Dip. di Fisica e Scienze della Terra, University of Ferrara and INFN of Ferrara, I-44122, Ferrara, Italy
³INFN, Laboratori Nazionali di Legnaro, I-35020 Legnaro, Italy
⁴Dip. di Fisica, University of Pisa, I-56127, Pisa, Italy
⁵NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy

^*federico.chiossi@unipd.it

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Issue

Vol. 3, Iss. 1 — February - April 2021

Subject Areas

Optics

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Images

Figure 1
(a) General energy level and pumping schemes for the studies of cascade and yoked superfluorescence in gaseous systems. The two coherent emissions in CSF evolve independently and the SF pulses are temporally separated. This is not the case in yoked SF, where the second $3 \to 0$ transition is induced by the combination of the two coherences $0 \to 2$ and $2 \to 3$ . (b) Energy level scheme of erbium ions in YLF. The blue arrow indicates the cw laser excitation, the black wavy line the multiphonon relaxation, and the two red arrow the cascading superfluorescent transitions. The measured lifetime of the long-lived levels is also reported.
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Figure 2
Spectrum of the forward emission recorded at a FTIR interferometer (Bruker, Equinox55) equipped with an InAs photodiode. The CSF emissions at 6516.7 ${cm}^{- 1}$ (1534.5 nm) and 3678.8 ${cm}^{- 1}$ (2718.3 nm) are identified. In the inset, the SF intensity at 1534 nm measured with a germanium sensor is plotted as a function of the absorbed laser power, proportional to the inverted population density in the Er:YLF 0.01% crystal. Above the pumping threshold, data are fitted by a quadratic function (black line).
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Figure 3
(Bottom) Representative paired pulses recorded with a InAs detector (black line). Each pulse profile is fitted with the function $f (t) = P {sech}^{2} ((t - t_{a}) / 2 τ_{R})$ (violet and red line) centered at time $t_{a}$ , with maximum value $P$ . (Top) Pictorial representation of cascade superfluorescence in ${Er}^{3 +}$ . Starting from uncorrelated excited ions (blue spheres) in $\underset{11 / 2}{{}^{4}I} (0)$ level, atomic coherence (yellow spheres) develops between the latter and the $^{4} I_{13 / 2} (1)$ level, achieving its maximal degree at the peak of the 2718-nm pulse. These ions then quickly thermalize to the long-lived $\underset{13 / 2}{{}^{4}I} (0)$ level, where coherence is spontaneously established again, seeding SF emission to $\underset{15 / 2}{{}^{4}I} (1)$ at 1534 nm.
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Figure 4
$R_{p}$ vs $\bar{N}$ and $τ_{R}$ vs $R_{p}$ (inset) best-fit parameters of the 1.5- $μ m$ pulses emitted by Er:YLF doped at 1%. The laser power and beam diameter at the crystal are 400 mW and 66 $μ m$ , respectively. The black lines are the results of the fitting procedure with the functions in Eqs. (1) and (2).
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Figure 5
(a) $τ_{R}$ vs ${\bar{τ}}_{d}$ for Er:YLF 0.01% (C1) and Er:YLF 1% (C2) crystals with pump laser wavelength $λ_{r} = 808.9921$ nm ( $370575.3 GHz$ ) or $λ_{q} = 808.9964$ nm ( $370573.3 GHz$ ), and $Φ_{2} = 130 μ m$ or $Φ_{1} = 66 μ m$ beam waist. For the sake of clarity, only the linear fits corresponding to the Er:YLF 1% data sets are drawn. (b) Comparison of absorption spectra of Er:YLF 1% (black line, saturated) and Er:YLF 0.01% (purple line, magnified by a factor 20) centered at 370575.3 GHz. The sidebands at approximately $\pm 3$ GHz are attributed to hyperfine transitions of the $^{167} {Er}^{3 +}$ isotope. Colored circles are referred to the data sets in panel (a). (c) Correlation between the area of the first and second pulses for the red data set. Uncalibrated units are used for both axis. $R$ denotes the correlation coefficient.
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Figure 6
Observed ${\bar{τ}}_{d}$ probability distribution (orange histogram) for Er:YLF 1% with pump laser wavelength $λ_{r} = 808.9921 nm$ and waist $Φ_{1} = 66 μ m$ . The same distribution for 25 ns $< τ_{R} <$ 30 ns is shown in black. In the inset, we report the ${\bar{τ}}_{d}$ distribution for Er:YLF 0.01% with $λ_{r} = 808.9921 nm$ and $Φ_{2} = 130 μ m$ .
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