The Phase Dependent Properties Of The Probe Gain And Absorption In A Four Level System With A Closed Interaction Contour

(College of Physics, Jilin University, Changchun, 130023) In this paper, we mainly discuss the phase dependent properties of theprobe transition by quantum interference in a four-level atomic system. Mythesis is consisted of two parts:I: The phase dependent double electromagnetically induced transparency in a four-level atomic system with a closed interaction contour As shown in Fig. 1, we propose a novel four-level atomic system with a Fig. 1 the four level system with a closed interaction contourclosed interaction contour to realize the double electromagnetically inducedtransparency [double-EIT]. Transitions |1 >?| 3 > and | 2 >?| 3 > arerespectively coupled by two strong coupling laser fields ?1 and ?2 ,microwave laser field ?m is applied to the transition | 2 >?| 3 > . Thus,under the effects of microwave laser field ?m and two strong coupling laserfields ?1 and ?2 , the upper level and two middle levels form a closedinteraction. The transition | 4 >?| 3 > driven by the weak probe laser field?p is outside of the closed interaction contour. Fig. 2 The probe absorption efficient Im(χ ) vs the probe detuning δ p for different values of the phase Φ is illustrated As shown in Fig. 2, in such a system the total closed interaction phaseΦ plays an important role in the probe absorption properties: under theconditions of ?1 = ?2 = ?m and δ 1= δ2 = δm = 0 , not only the frequencyintervals of double-EIT but also the numbers of the transparency windows canbe affected by the total closed interaction phase Φ. In numerical analysis, wefind that Φ=0 and Φ=π/2 are two specific points: in the case of Φ=0, thephenomenon of double-EIT is degenerated into one transparency window, butwhen Φ=π/2 we can observe the phenomenon of double-EIT with the samefrequency interval. Also under two specific conditions Φ=0 and Φ=π/2, weanalyzed the dependence of the phenomenon of double-EIT on the strengthsof applied laser fields. When Φ=π/2, the effects of the strengths of appliedlaser fields on the phenomenon of double-EIT are just alike but the case isdifferent when Φ=0. In a conclusion, we can observe the phenomenon ofdouble-EIT with various frequency intervals by varying the phase and thestrengths of applied laser fields in the model under study.II:: The gain properties in a four-level atomic system with a closedinteraction contour As shown in Fig. 3, the atomic model we considered here is about thesame with the one in Fig. 1, the only difference is that an incoherent pumping Λ Fig. 3 the four level system with a closed interaction contourΛ is applied to the transition |4 >|3>. In this model, bymodifying the value of the incoherent pumping Λ, we can observetwo distinct phenomena: the symmetric light amplification and the gainequalization, which can be seen in Fig. 4. As shown by the dashed curve, Fig. 4 The gain coefficient Im(χ) vs the probe detuningδ for different p values of incoherent pumping Λ is demonstrated.with a small incoherent pumping Λ=0.2?=2, we can observe thesymmetric light amplification with three large gain peaks and thefrequency interval of the gain peaks is proportional to the Rabi frequencyof the coherent laser fields. With the increase of incoherent pumping Λ thesymmetric light amplification still exists but the value of gain peaksdecreases as shown by the dotted curve. When the incoherent pumpingincreases to a value Λ=2.4?=24 (the solid curve), we find that thesymmetric light amplification with three gain peaks degenerates into onewith an approximate gain equalization in a large frequency region except avery small peak at the gain center. It is well known that a good gainequalization is required in optical communication, so we need to eliminatethe peak at the gain center though it is small.