Photon-Phonon Atomic Coherence Interaction of Nonlinear Signals in Various Phase Transitions Eu3+: BiPO4

Abstract

We report photon-phonon atomic coherence (cascade- and nested-dressing) interaction from the various phase transitions of Eu³⁺: BiPO₄ crystal. Such atomic coherence spectral interaction evolves from out-of-phase fluorescence to in-phase spontaneous four-wave mixing (SFWM) by changing the time gate. The dressing dip switch and three dressing dips of SFWM result from the strong photon-phonon destructive cross- and self-interaction for the hexagonal phase, respectively. More phonon dressing results in the destructive interaction, while less phonon dressing results in the constructive interaction of the atomic coherences. The experimental measurements of the photon-phonon interaction agree with the theoretical simulations. Based on our results, we proposed a model for an optical transistor (as an amplifier and switch).

Keywords: atomic coherence; phonon/photon dressing; spectral interaction; spontaneous four-wave mixing.

Figure 1

(a) Experimental setup, (b) Shows photon and phonon four-dressing energy level. (c) Shows energy levels of Eu³⁺:BiPO₄ for transition ⁷F₁→⁵D₀. (d) The schematic diagram of proposed optical transistor as an amplifier and switch.

Figure 2

(a1) The total signal intensity of $|{\rho }_{F1}^{(2)}{|}^2+|{\rho }_{F2}^{(2)}{|}^2$ (hot curve), (a2) the interaction item $2|{\rho }_{F1}^{(2)}||{\rho }_{F2}^{(2)}|\cos (\theta )$ versus $\Delta$ (purple curve), (a3) $|{\rho }_{sum}^{(2)}{|}^2$ (green curve), (a4) $|{\rho }_{F1}^{(2)}{|}^2$ (blue curve), (a5)$|{\rho }_{F2}^{(2)}{|}^2$ (black curve). Figure 2b: The parameters are $G_1=2.3$ THz, $G_2=6.1$ THz. (b1) ${\theta }_F$ (hot curve), (b2) ${\theta }_1$ (black curve), (b3) ${\theta }_2$ (blue curve) versus $\Delta$. Evolution of ${\theta }_F$, the constructive and the destructive interaction versus $\Delta$. Figure 2b: The destructive or constructive interaction is studied in this system [23].

Figure 3

(a,c) show self- and cross- interaction of FL observed from Eu³⁺ doped BiPO₄ [molar ratio (6:1)] at different E₁ wavelengths (567.4 nm, 584.4 nm, 587.4 nm, 589.4 nm, 612.4 nm) and E₂ scanned from 567.4 nm to 607.4 nm at PMT1 (far detector position) and PMT2 (near detector position), respectively. (b,d) show self- and cross- interaction of FL at different E₂ wavelengths (567.4 nm, 587.4 nm, 588 nm, 588.4 nm, 602.4 nm) and E₁ scanned from 567.4 nm to 612.4 nm. (e–h) show spectral signal intensity for (1:1) sample, which is same condition as (a–d). The time gate = 1 μs.

Figure 4

(a1–a5,b1–b5) show SFWM cross-interaction observed from Eu³⁺ doped BiPO₄ [molar ratio (7:1)] at different narrowband laser E₂ (567.4 nm, 587.4 nm, 588 nm, 588.4 nm, 602.4 nm) while broadband laser E₁ is scanned from 572.4 nm to 612.4 nm at different broadband laser E₁ wavelengths (567.4 nm, 584.4 nm, 587.4 nm, 596.4 nm, 612.4 nm) and narrowband laser E₂ is scanned from 567.4 nm to 607.4 nm at 300 K, respectively, at PMT1. The time gates are 5 μs and 20 μs, respectively, gate width = 400 ns. (c,d) show SFWM cross-interaction for the (20:1) sample at the time gate = 10 μs and 20 μs, respectively. The other experimental condition is the same as (a,b), respectively, at PMT1.

Figure 5

(a,c) show SFWM cross- interaction observed from Eu³⁺ doped in molar ratio (6:1) BiPO₄ at different E₁ wavelengths (567.4 nm, 584.4 nm, 588.4 nm, 596.4 nm, 612.4 nm) and E₂ scanned from 567.4 nm to 607.4 nm at PMT1 and PMT2 at 300 K, respectively. (b,d) show SFWM cross- interaction at different E₂ wavelengths (567.4 nm, 587.4 nm, 588 nm, 588.4 nm, 602.4 nm) and E₁ scanned from 567.4 nm to 612.4 nm at PMT1 and PMT2 in 300 K, respectively. (e,f) show SFWM cross-interaction at 77 K. The other experimental conditions are the same as (a,c), respectively. Time gate = 500 μs. (g1–g5) show the simulation result corresponding to (b1–b5). (h1–h5) show the simulation result corresponding to Figure 3(g1–g5) and Figure 7(e1–e5).

Figure 6

(a,b) show FL cross-interaction observed from the output signals of Eu³⁺ doped in molar ratio (0.5:1) BiPO₄ at different E₂ wavelengths (567.4 nm, 587.4 nm, 588 nm, 588.4 nm, 602.4 nm) and E₁ scanned from 572.4 nm to 612.4 nm at 300 K, at PMT1 and PMT2, respectively. The time gate is 10 μs. (c,d) show SFWM cross-interaction at 77 K at the time gate = 800 μs, respectively. The other experimental condition is the same as (a,b).

Figure 7

(a,b) show FL cross-interaction observed from Eu³⁺ doped in molar ratio (0.5:1) BiPO₄ at different E₁ wavelengths (577.4 nm, 584.4 nm, 587.7 nm, 592.4 nm, 612.4 nm) and E₂ scanned from 567.4 nm to 607.4 nm at PMT1 and PMT2, respectively, at the near time gate (1 μs). (c,d) show hybrid cross-interaction at the middle time gates (100 μs). (e,f) show SFWM cross-interaction at the far time gate (500 μs). The other experimental condition is the same as (a,b), respectively.