Spectral properties of a $V$-type three-level atom driven by two bichromatic fields

We theoretically investigate the spectral properties of a $V$-type three-level atom driven by two bichromatic fields with a common frequency difference. By decomposing the master equation using harmonic expansions and invoking quantum regression theorem, fluorescence and probe absorption spectra of the strong atomic transition are numerically calculated under the steady state condition. We find that both fluorescence and absorption spectra exhibit two interesting features, which are equidistant comblike structures and phase-dependent line splittings. In the comblike structures, each fluorescence peak can be made subnatural by manipulating the relative intensities of the coupling fields, while for the absorption lines only the central peak can be narrowed. Line splittings are induced by the relative phase delay between the envelopes of the amplitudes of the two bichromatic fields. Interestingly, we find that the manipulation of the relative phase delay results in the emergence of sharp subnatural dips in the absorption spectra. As a natural consequence of the subnatural absorption dips, absorption spectra in atomic vapors exhibit striking subnatural burning holes for the counterpropagating probe beam geometry.

Figure 1

A $V$-type three-level atom with excited states, $\mid 1⟩$ and $\mid 2⟩$, coupled to the common ground state, $\mid 3⟩$, by the two bichromatic fields $L_a$ and $L_b$, respectively. Frequency components of each bichromatic field are denoted by ${\omega }_a^{\pm }(={\omega }_a\pm \delta )$ and ${\omega }_b^{\pm }(={\omega }_b\pm \delta )$, respectively. Spontaneous decay rate of 1–3 and 2–3 transition are denoted by ${\Gamma }_{11}$, and ${\Gamma }_{22}$, respectively.

Figure 2

(a) Incoherent fluorescence spectrum corresponding to the 1–3 transition, with $\delta =5$, ${\Delta }_1={\Delta }_2=0$, ${\Omega }_1=1$, and $\Phi =0$. Note that the line narrowing takes place for each peak as ${\Omega }_2$ increases. (b) Probe absorption spectrum corresponding to the 1–3 transition. All parameters are the same with those for graph (a). (c) Total fluorescence intensity corresponding to the 1–3 transition, plotted as a function of ${\Omega }_2$. Solid, dashed, and dotted lines represent the total, elastic, and inelastic fluorescence intensities, respectively. All parameters are the same with those for graph (a).

Figure 3

(a) Incoherent fluorescence spectrum corresponding to the 1–3 transition, for several different values of $\Phi$, with $\delta =5$, ${\Delta }_1={\Delta }_2=0$, ${\Omega }_1=1$, and ${\Omega }_2=3$. Note the line splittings in all spectral lines. (b) Probe absorption spectrum corresponding to the 1–3 transition, for several different values of $\Phi$. All parameters are the same with those for graph (a). Note the absorption dip on the central absorption peak. (c) Probe absorption spectrum corresponding to the 1–3 transition, with $\delta =5$, $\Phi =\pi ∕15$, ${\Delta }_1={\Delta }_2=0$, ${\Omega }_1=1$, and ${\Omega }_2=3$. The FWHM of the central absorption dip is about $0.22{\Gamma }_{11}$. (d) Total fluorescence intensity corresponding to the 1–3 transition, plotted as a function of $\Phi$, with $\delta =5$, ${\Delta }_1={\Delta }_2=0$, ${\Omega }_1=1$, and ${\Omega }_2=3$. Solid, dashed, and dotted lines represent the total, elastic, and inelastic fluorescence intensities, respectively.

Figure 4

(a) Probe absorption spectrum corresponding to the 1–3 transition for the counterpropagating probe beam geometry in an atomic vapor with a Doppler-broadening taken into account. Both bichromatic fields are on resonance $({\Delta }_1={\Delta }_2=0)$, with ${\Omega }_1=1$, ${\Omega }_2=3$, $D_1=2D_2=5$, and $\Phi =\pi ∕15$. The FWHM of the central “burning hole” is about $0.25{\Gamma }_{11}$. (b) Same as (a) except that the bichromatic field $L_a$ is blue detuned $({\Delta }_1=-1)$. Note the central burning hole is shifted to the blue side.