Electromagnetically Induced Transparency, Four-wave Mixing Gain And Two-color Photonic Bandgaps In Coherent Atoms

In this thesis for doctorate that consists of three parts. Firstly, we investigatethe steady optical response of a coherently driven five-level cold atomic system inthree different situations. It is worth stressing that, in the case where the last twocoupling fields have large nonzero detunings, a super narrow absorption line oflinewidth~50KHz appears between the two transparency windows. Base onelectromagnetically induced transparency (EIT), we realize the probe gain withoutpopulation inversion in the condition of resonant four-wave mixing (FWM) in acoherently driven four level double-Λ atomic system. In this system, we study thegain spectra with considering spontaneously generated coherence (SGC) in further,this can be shown in the second part. In the third part, we trapped double-Λ atomsinside a one-dimensional (1D) optical lattice to study the dynamically tunabletwo-color photonic bandgaps (PBGs) via balanced FWM.I. Absorption and dispersion control in a five-level M-type atomic systemWe have calculated the steady optical response of a five-level atomic systemdriven into the M configuration by examining its absorption and dispersionspectra in three different situations. In the case where all three coupling fieldshave zero detuning, we find only one narrow and deep EIT window at the proberesonance accompanied by a very steep normal dispersion. Turning off the lastcoupling field, we can reduce the five-level M system into a four-level N systemand then observe a third absorption line completely destroying the EIT window.To recover the EIT window, we just need to reduce a four-level N system into a three-level A system by turning off the second coupling field. In the case where the last two coupling fields have nonzero detunings, a third absorption line arises beside the EIT window yet without introducing more absorption therein. Simultaneously, a new absorption dip is found on the other side of the third absorption line. It is worth stressing that the new absorption line will become extremely narrow and the new absorption dip will be as deep as the EIT window when the last two coupling fields are far detuned from the relevant transitions. In fact, the M-type system reduces into a four level quasi-A system. In contrast, the relevant experiment is much easier to be implemented in a five level atomic system. In addition, we can examine how a shallow absorption dip gradually turns into a deep EIT window just by controlling the detunings of the two laser fields in the M system. In the case where all three coupling fields are detuned to different extents, we cannot find deep EIT windows, narrow absorption lines, and steep dispersion curves in the probe absorption and dispersion spectra.Ⅱ. Probe gain via four-wave mixing based on spontaneously generated coherenceWe have studied in detail the probe gain without population inversion in a coherently driven double-A configuration with two closely lying lower levels, in the presence of two probe and two coherent pumping fields, which can form a resonant FWM system. Our numerical results are obtained in the case of△P2=△p1=△c1=△c2=△or△P2=-△p1,△c1=△c2,which can satisfy the balanced optical gain. Meanwhile, as a result of the two near-degenerate lower levels, that the SGC effect must be considered. Comparing with the probe gain realized in previous single A-type system with an incoherent pump, we have made a vast improvement. At first, the two probe lights are amplified due to the resonant FWM instead of applying an incoherent pumping. Our numerical calculations show that greatly enhanced amplitude of the probe gain spectral line can be obtained in the present of SGC effect, and the linewidth of each probe gain spectrum becomes more and more narrow (can reach to10KHz) with the reduced Rabi-frequency of coherent pumping fields, it is a great advantage to the former works. In addition, the probe gain is sensitive to the relative phase between the two fields which can modulate the gain spectrum periodically, while influenced by the phase between dipole elements (θ). We find that, when θ=π/4the maximum value of the probe gain appears at Φ=2kπ, then θ=3π/4the maximum value of the probe gain appears atΦ=(2k+1)π, it is to say that the gain spectra can be modulated by the common actions of0and Φ.Ⅲ. Dynamically controlled two-color photonic bandgaps via balanced four-wave mixing in one-dimensional cold atomic latticeWe study the steady-state optical response of the ID atomic lattices with a Gaussian density distribution in each period and exhibiting a double-A configuration for all atoms. As we have known, that photonic crystal is an artificial material of PBG which can allow light of certain frequencies to transmit. Besides, the dynamically tunable PBG can be realized in a spatially homogeneous medium on the application of a standing-wave (SW) driving field which can modulate the refractive index periodically. In our regime, the refractive index is depending on the modulation of atomic density distribution in periodicity, thus the travelling-wave (TW) fields can be used as driving fields instead of SW fields. We find that well developed PBGs are attained in two spectral regions (narrow resonant or wide detuned) on a pair of probe transitions as manifested by high platforms of probe reflectivities (up to97%) and reduced densities of photonic states (down to0.02). The narrow resonant PBG is generated within an EIT window while the wide detuned PBG is far from probe resonance so that no large absorption blocks their development. Both narrow resonant and wide detuned PBGs are two-color in fact in that each one opens up, simultaneously, for two probe fields highly correlated via the balanced FWM interaction.It is worth to stress that a pair of two-color PBGs are attained in a specific symmetric driving scheme and can be easily tuned in position and width bycontrolling the geometric Bragg detunings, the coupling Rabi frequencies, and theatomic density distribution. One obvious advantage of multi-color PBGs (easilygot by extending the present work) is that they allow the synchronous nonlinearmanipulation of a few light signals at one network node, e.g., to deviseswitching/routing devices and optical diodes efficient even at the single-photonlevel.