Temporal and spectral hybrid interference from phase transition of Eu3+/Pr3+: YPO4 and evolution of amplifier and multiplexer

doi:10.1016/j.physleta.2021.127400

Physics Letters A

Volume 404, 19 July 2021, 127400

https://doi.org/10.1016/j.physleta.2021.127400 Get rights and content

Highlights

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The temporal and spectral oscillation originating from the interference among the FL and SPFWM signals.
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The frequency of oscillation is directly proportional to the interference.
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The self Rabi-oscillation is robust and prominent with resonant excitation when compared with off-resonant excitation.
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The interference oscillation observed in Pr³⁺: YPO₄ is significantly higher than Eu³⁺: YPO₄.

Abstract

We study the temporal and spectral oscillation originated from the interference between the fluorescence (FL) and spontaneous parametric four-wave mixing (SP-FWM) signals. The FL and SP-FWM are generated from different phases of Eu³⁺ or Pr³⁺ doped YPO₄ under the nonlinear SP-FWM process. We discuss and compare the spectral interfering oscillations and self-Rabi oscillations controlled via multiple phase transitions (hexagonal-phase and mixed-phase) of Eu³⁺: YPO₄ and Pr³⁺: YPO₄. The coexistence mechanism of interference and self-oscillations in time domain is also investigated. Further, we discuss the cross-Rabi oscillation in correlated light beams, which evolves from FL signal (having Sinc profile) to SP-FWM (having Cosine profile) in the hybrid signal regime. Based on these results, we have realized wavelength division multiplexing, and temporal amplifier with the temporal interference being controlled by the gate position, and frequency detuning. Our experimental results provide a technique to achieve higher channel equalization ratio about 85%.

Introduction

In recent decades, quantum coherence excitation and coherence transfer have been thoroughly studied in atomic gases. These processes lead to many important physical phenomena. Compared with atomic gases, atomic coherence-induced effects in solid materials are very attractive for practical applications. Rare-earth orthophosphates matrix doped with trivalent ions (like Pr³⁺: YPO₄, Eu³⁺: YPO₄) are more suitable for practical applications due to their unique physical, chemical, and structural properties. These properties make them suitable candidates for luminescent materials [1][2], which play a significant role in optical communication, optical microscopy, displaying information [3][4], and quantum optics. In Yttrium phosphate crystal YPO₄ crystal, the “atom-like” properties of the dopant can be kept, due to which the atomic coherence can be induced easily when interacting with multiple laser beams. Research on light coherent storage, all-optical routing [5], optical velocity reduction and reversible storage of double light pulses [6], enhanced four-wave mixing, all-optically controlled higher-order fluorescence (FL), has been reported in YPO₄. Such crystals have potential applications in optical devices such as transistors, routers, filters, etc. The YPO₄ crystal exists in two polymorphic forms, i.e., hexagonal (H) and tetragonal (T) [7][8]. Specifically, the hexagonal phase has a P6222 space group with a rhabdophane-type structure where Y³⁺ ions occupy a D2 point-group symmetry site [9], while the tetragonal phase has an I41/amd space group, where Y³⁺ ions occupy a D2d point-group, and two kinds of coordination bonds [10].

Interference is a well-known effect to understand the coherence and superposition in quantum physics [11][12] and it provides a solid foundation for the development of the coherence and the quantum theory of light [13]. First and second-order interference is defined [14] between two different independent sources, i.e., thermal and laser light. It was found that ghost imaging can be realized experimentally with chaotic thermal light [15][16]. Bennink et al. showed that ghost imaging technique does not require entanglement and provided an experimental demonstration with a classical source [17]. Compared to two-photon entangled sources, the disadvantage of classical light in ghost imaging is the limited visibility [18]. Dirac considered superposition comes only from the single photon in the single photon interference [19]. According to the superposition principle in Feynman's path integral theory [20], two-photon interference is not the interference between two individual photons, but the interference resulting from different Feynman paths [21]. However, in Haijun Tang's article [22], the interference between the three multi-order fluorescence (MFL) signals at room temperature is realized by nonlinear interaction. Similarly, the hybrid interference between the fluorescence (FL) and spontaneous parametric four-wave mixing (SP-FWM) signals in this article can also be realized by nonlinear interaction.

In this paper, we discuss the oscillations originated from the interference of FL and the coherent outputs from Eu³⁺/Pr³⁺: YPO₄ in both time and spectral domains of the nonlinear SP-FWM process. Interference is high when the emission of FL and coherent (Stokes ( $E_{S}$ ) and anti-Stokes (E_AS)) have equal contributions in the hybrid signal regime. We further evaluate the interference and self Rabi-oscillations coexisting in the spectral and temporal intensity of the hybrid signal regime. Spectral oscillations from different phases of Eu³⁺: YPO₄ and Pr³⁺: YPO₄ are also discussed. Such results are employed to realize the wavelength division multiplexing (WDM) of classical and coherent channels, and temporal amplifier. The cross-Rabi oscillation is found in the two-mode intensity-noise correlation of $E_{S}$ /E_AS and the hybrid FL signals. The evolution of FL profile (Sinc function) to SP-FWM profile (Cosine function) is discussed when power is changed from high to low.

Section snippets

Experimental setup and basic theory

In this experiment, the sample is held in a cryostat (CFM-102) at 77 K (due to low phonon effect, strong dressing effect) and the temperature is controlled by flowing liquid nitrogen. The sample has 5% concentration of doped Eu ${}^{3 +}/$ Pr³⁺ ions in a host YPO4 crystal. To generate the pumping field $E_{i}$ ( $ω_{i}$ , $Δ_{i}$ ), a tunable dye laser (narrow scan with a 0.04 cm⁻¹ linewidth) is pumped by an injection-locked single-mode Nd: YAG laser (Continuum Power lite DLS 9010, 10 Hz repetition rate, 5 ns pulse

Theoretical model

In a two-level system (Fig. 1(e)), by opening the laser field $E_{1}$ , the $E_{S}$ and E_AS signals are generated under the phase-matching conditions. The perturbation chains for $E_{S}$ and E_AS signals in the two-level system are $ρ_{00}^{(0)} \overset{E_{1}^{'}}{\to} ρ_{10}^{(1)} \overset{E_{s}}{\to} ρ_{00}^{(2)} \overset{E_{1}^{'}}{\to} ρ_{10 (S)}^{(3)}$ and $ρ_{00}^{(0)} \overset{E_{1}^{'}}{\to} ρ_{10}^{(1)} \overset{E_{A S}}{\to} ρ_{00}^{(2)} \overset{E_{1}^{'}}{\to} ρ_{10 (AS)}^{(3)}$ , respectively. $ρ_{10}^{(3)} = \frac{- i G_{A S} {| G_{1}^{'} |}^{2}}{(Γ_{10} + i Δ_{1}^{'}) (Γ_{00} + i Δ_{1}^{'} + {| G_{1}^{'} |}^{2} / (Γ_{00} + i Δ_{1}^{'})) Γ_{11}} = ρ_{S}^{(3)} = | ρ_{10}^{(3)} | \exp (i θ_{S})$ $ρ_{10}^{(3)} = \frac{- i G_{S} {| G_{1}^{'} |}^{2}}{(Γ_{10} + i Δ_{1}^{'}) (Γ_{00} - i Δ_{1}^{'} + {| G_{1}^{'} |}^{2} / (Γ_{00} + i Δ_{1}^{'})) Γ_{11}} = ρ_{A S}^{(3)} = | ρ_{10}^{(3)} | \exp (i θ_{A S})$

The linewidth of

Results and discussion

Fig. 2 shows the temporal comparison of oscillations obtained from mixed-phase (T + H) Eu³⁺: YPO₄. Fig. 2(a1) and 2(a2) show the temporal intensity of the hybrid signals H₁ and H₂, respectively. The output hybrid signals H₁ and H₂ are generated at a low input beam power of 1 mW. Oscillations resulted from the interference of FL and $E_{S}$ /E_AS in a hybrid signal regime is called interference oscillation, which is realized through nonlinear interaction [22]. The intensity of FL can be written as $I_{(F L)}$

Conclusion

In conclusion, we studied the oscillation generated from ${Eu}^{3 +} / \Pr^{3 +}$ : ${YPO}_{4}$ in both time and spectral domain, caused by the interference of FL and SP-FWM in hybrid signal regime. The oscillation comparison between Eu³⁺: YPO₄ and Pr³⁺: YPO₄ in spectral domain was controlled by the phase transition and the boxcar gate position. We discussed the interference and self Rabi-oscillations coexisting in temporal and spectral intensity, and also elaborated the cross-Rabi oscillation in correlated light

CRediT authorship contribution statement

^a These authors contributed equally to this work.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (2017YFA0303700, 2018YFA0307500), National Natural Science Foundation of China (61975159, 61605154, 11604256, 11804267, 11904279).

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DiscussionTemporal and spectral hybrid interference from phase transition of Eu3+/Pr3+: YPO4 and evolution of amplifier and multiplexer

Highlights

Abstract

Introduction

Section snippets

Experimental setup and basic theory

Theoretical model

Results and discussion

Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgements

Mater. Lett.

J. Lumin.

J. Alloys Compd.

Results Phys.

Observation of intermediate bands in Eu3+ doped YPO4 host: Li+ ion effect and blue to pink light emitter

AIP Adv.

Inorganic luminescent materials: 100 years of research and application

Adv. Funct. Mater.

Taking advantage of luminescent lanthanide ions

Chem. Soc. Rev.

All-optical routing by light storage in a Pr3+: Y2SiO5 crystal

Appl. Phys. Lett.

Observation of ultraslow and stored light pulses in a solid

Phys. Rev. Lett.

Mechanochemical changes of Weinschenkite-type RPO4 ⋅ 2H2O (R = Dy, Y, Er, or Yb) by grinding and thermal reactions of the ground specimens

J. Am. Ceram. Soc.