• Acta Physica Sinica
  • Vol. 69, Issue 1, 014206-1 (2020)
Teng-Fei Meng*, Jian-Feng Tian, and Yao-Yao Zhou
DOI: 10.7498/aps.69.20191099 Cite this Article
Teng-Fei Meng, Jian-Feng Tian, Yao-Yao Zhou. Selective reflection spectrum in a quasi-lambda four-level atomic system[J]. Acta Physica Sinica, 2020, 69(1): 014206-1 Copy Citation Text show less

Abstract

Selective reflection (SR) from the interface between transparent medium and dilute vapour is caused by the atomic vapor near the interface. The sub-Doppler structure in SR is due to the deexcitation caused by the collision between atomic vapor and the wall. Beacuse the interaction region between atomic vapor and incident light is on the order of a few hundred nanometers, SR has low optical loss and high spatial resolution. The experimental device of SR is simple. Because of the above characteristics, the SR has been widely studied and applied. The nonlinear SR spectrum of quasi lambda-type four-level system at gas-solid interface is studied theoretically in this paper. By sloving the density matrix equations, the approximate analytic solution of the matrix element associated with the probe field is obtained at normal incidence when the intensity of the probe field is very weak. The effect of the Rabi frequency, the detuning of the signal field and the detuning of the coupling field on the lineshape are analyzed by numerical simulation, respectively. Three peaks and two transparent windows appear in SR spectrum when the detuning of coupling field and signal field are both zero. The middle peak is generated due to the participation of signal field, and the other two peaks are caused by the other two fields. The linewidth and the amplitude of the middle peak can be changed by varying the Rabi frequency of signal field, and the other two peaks have little effect on the Rabi frequency of signal field. The signal generated due to the participation of signal field can be transformed from peak to transparent window when the detuning value of the signal field is equal to the Rabi frequency of coupling field. When the detuning value of the signal field is not equal to the Rabi frequency of coupling field, a dispersion-like signal between reflection peak and transparent window is generated due to the participation of signal field. The position of peak and transparent window can be manipulated by controlling the detuning value of the coupling field. When the detuning value of coupling field decreases from zero, three peaks all shift to red detuning direction. When the detuning value of coupling field is blue-detuned and increases, three peaks all shift to blue detuning direction. The numerical results can be explained by using the various electric transition pathways and dressed state theory. This study is helpful in investigating quantum coherence and dynamic process of atoms at gas-solid interface.
${\rho_{21}} = {\rm e}^{-{\rm i}({\omega_{\rm p}}t-{k_{\rm p}}z)}\sigma_{21},\tag{1a}$ ()

View in Article

$ {\rho_{31}} = {\rm e}^{-{\rm i}({\omega_{\rm p}}t+{\omega_{\rm c}}t-{k_{\rm p}}z-{k_{\rm c}}z)}\sigma_{31},\tag{1b}$()

View in Article

${\rho_{41}} = {\rm e}^{-{\rm i}({\omega_{\rm p}}t+{\omega_{\rm c}}t-{\omega_{\rm s}}t-{k_{\rm p}}z-{k_{\rm c}}z+{k_{\rm s}}z)}\sigma_{41},\tag{1c}$ ()

View in Article

$ {\rho_{32}} = {\rm e}^{-{\rm i}({\omega_{\rm c}}t-{k_{\rm c}}z)}\sigma_{32},\tag{1d}$ ()

View in Article

$ {\rho_{42}} = {\rm e}^{-{\rm i}({(\omega_{\rm c}-\omega_{\rm s})}t-{(k_{\rm c}-k_{\rm s})}z)}\sigma_{42}, \tag{1e}$ ()

View in Article

$ {\rho_{43}} = {\rm e}^{{\rm i}({\omega_{\rm s}}t-{k_{\rm s}}z)}\sigma_{43}.\tag{1f}$()

View in Article

$ v_z{\frac{\rm d}{{\rm d}z}}\sigma_{11} = \frac{{\rm i}\varOmega_{\rm p}}{2}{(\sigma_{21}-\sigma_{12})} +\gamma_{21}\sigma_{22}+\gamma_{31}\sigma_{33}+\gamma_{41}\sigma_{44},\tag{2a}$ ()

View in Article

$vzddzσ22=iΩc2(σ32σ23)+iΩp2(σ12σ21)γ21σ22+γ32σ33+γ24σ44,\tag{2b}$ ()

View in Article

$vzddzσ33=iΩc2(σ32σ23)iΩs2(σ34σ43)(γ31+γ32+γ34)σ33,\tag{2c}$ ()

View in Article

$ {v_z{\frac{\rm d}{{\rm d}z}}\sigma_{44}} = -\frac{{\rm i}\varOmega_{\rm s}}{2}{(\sigma_{34}-\sigma_{43})}-(\gamma_{41}+\gamma_{24})\sigma_{44}+\gamma_{34}\sigma_{33},\tag{2d}$ ()

View in Article

$vzddzσ21=iΩp2(σ11σ22)+iΩc2σ13(iΔ~p+12γ21)σ21,\tag{2e}$ ()

View in Article

$vzddzσ31=[i(Δ~p+Δ~c)12(γ31+γ32+γ34)]σ31iΩp2σ32+iΩc2σ21+iΩs2σ41,\tag{2f}$ ()

View in Article

$vzddzσ41=[i(Δ~p+Δ~cΔ~s)+12(γ41+γ24)]σ41iΩp2σ42+iΩs2σ31,\tag{2g}$ ()

View in Article

$vzddzσ32=iΩc2(σ22σ33)iΩp2σ31+iΩs2σ42[iΔ~c+12(γ21+γ31+γ32+γ34)]σ32,\tag{2h}$ ()

View in Article

$vzddzσ42=iΩp2σ41iΩc2σ43+iΩs2σ32[i(Δ~cΔ~s)+12(γ21+γ41+γ24+γ34)]σ32,\tag{2i}$ ()

View in Article

$vzddzσ43=iΩc2σ42+iΩs2(σ33σ44)[iΔ~s+12(γ31+γ32+γ34+γ41+γ24)]σ43.\tag{2j}$ ()

View in Article

$ {\widetilde{\varDelta}_{\rm p}} = {\omega_{\rm p}}-{\omega_{21}}-{k_{\rm p}}v = \varDelta_{\rm p}-{k_{\rm p}}v_{z},\tag{3a}$ ()

View in Article

$ {\widetilde{\varDelta}_{\rm c}} = {\omega_{\rm c}}-{\omega_{32}}-{k_{\rm c}}v = \varDelta_{\rm c}-{k_{\rm c}}v_{z},\tag{3b}$ ()

View in Article

$ {\widetilde{\varDelta}_{\rm s}} = {\omega_{\rm s}}-{\omega_{34}}-{k_{\rm s}}v = \varDelta_{\rm s}-{k_{\rm s}}v_{z}.\tag{3c}$ ()

View in Article

${\widehat{\sigma}(v_z,p)} = \int_0^{+\infty}{{\rm e}^{-pz}\sigma(v_z,z){\rm d}z}. $ (4)

View in Article

$ \int_0^{+\infty}{{\rm e}^{-pz}\frac{\rm d}{{\rm d}z}\sigma{dz}} = -\sigma(z = 0)+p{\widehat{\sigma}}. $ (5)

View in Article

$ \overline{\sigma} = \lim\limits_{p\rightarrow0}{p\widehat{\sigma}({p,v_z})}. $ (6)

View in Article

$ {\hat \sigma _{21}} = \dfrac{{{\rm i}\dfrac{{{\varOmega _{\rm p}}}}{2}\dfrac{1}{p}\left( {{v_z}p + A + \dfrac{{\varOmega _{\rm s}^2}}{4}\dfrac{1}{{{v_z}p + B}}} \right)}}{{\left(\!{{v_z}p \!+\! {\rm i}{\varDelta _{\rm p}} \!+\! \dfrac{{{\gamma _{21}}}}{2}}\!\right)\left(\!{{v_z}p \!+\! A \!+\! \dfrac{{\varOmega _{\rm s}^2}}{4}\dfrac{1}{{{v_z}p \!+\! B}}}\!\right) \!+\! \dfrac{{\varOmega _{\rm c}^2}}{4}}}, $ (7)

View in Article

$ A = {\rm i}\left( {{{\widetilde \varDelta }_{\rm p}} + {{\widetilde \varDelta }_{\rm c}}} \right) - \frac{1}{2}({\gamma _{31}} + {\gamma _{32}} + {\gamma _{34}}),\tag{8a}$ ()

View in Article

$ B = {\rm i}\left( {{{\widetilde \varDelta }_{\rm p}} + {{\widetilde \varDelta }_{\rm c}} - {{\widetilde \varDelta }_{\rm s}}} \right) + \frac{1}{2}({\gamma _{41}} + {\gamma _{24}}),\tag{8b}$ ()

View in Article

${\bar \sigma _{21}} = \dfrac{{{\rm i}\dfrac{{{\varOmega _{\rm p}}}}{2}\left( {A + \dfrac{{\varOmega _{\rm s}^2}}{{4B}}} \right)}}{{\left( {{\rm i}{\varDelta _{\rm p}} + \dfrac{{{\gamma _{21}}}}{2}} \right)\left( {A + \dfrac{{\varOmega _{\rm s}^2}}{{4B}}} \right) + \dfrac{{\varOmega _{\rm c}^2}}{4}}}. $ (9)

View in Article

$ {R} = \left(\frac{n-1}{n+1}\right)^2 + \frac{4n(n-1)}{(n+1)^3}{\rm{Re}}T, $ (10)

View in Article

$ {\rm{Re}}T = {\frac{{\hbar}N{{u}}_{21}}{2{\varepsilon_0}{{E}}_1}}\phi, $ (11)

View in Article

$ {\phi} = {\phi_+}+{\phi_-}, $ (12)

View in Article

$ {\phi_+} = -{\rm{Re}}{\int_0^{+\infty}}{W(v_{z})(-2{\rm i}k_{\rm p}){\widehat{\sigma}}_{21}(-2{\rm i}k_{\rm p},v_{z})}{{\rm d}v_{z}},\tag{13a}$ ()

View in Article

$ {\phi_-}= -{\rm{Re}}{\int_{-\infty}^0}{W(v_{z}){\overline{\sigma}}_{21}(v_{z})}{{\rm d}v_{z}},\tag{13b}$ ()

View in Article

Teng-Fei Meng, Jian-Feng Tian, Yao-Yao Zhou. Selective reflection spectrum in a quasi-lambda four-level atomic system[J]. Acta Physica Sinica, 2020, 69(1): 014206-1
Download Citation