The Study Of Coherent Control Of Lasing Without Inversion In A QuasiΛ-type Four-level Atomic System With Doppler Broadening

The study of coherent control of optical properties and optical courses is one of the mostimportant and active research front fields in international optics nowadays. The study ofcoherent control has not only an important theoretical value, but also wide applicationprospects in many fields, such as quantum optics, nonlinear optics, quantum information andphoto-communication, etc. In addition, Atomic coherence effects have multiple potentialapplications in many aspects. Among numerous phenomena of atom coherence, lasingwithout inversion (LWI) has received tremendous attention. As a new method of producinglaser, LWI can obtain laser light in spectral domains, e.g. the x-ray evenγ-ray range, whereconventional methods based on population inversion are not available or are difficult toimplement, so LWI has wide application prospects.Based on the work of the former people, we studied theoretically coherent control oflasing without inversion in a quasiΛ-type four-level atomic system Doppler broadening fromdifferent respects. This paper consists of eight chapters, and the main contents and results areillustrated as follows:In Chapter 1, we explained the significance, the history and current research state ofcoherent control and LWI, showed the research method of LWI(density matrix equations), andintroduced the effects of SGC and Doppler, which are related to LWI.In Chapter 2, the effect of spontaneously generated coherence (SGC) on the gain oflasing without inversion (LWI) is studied in an open four-level atomic system with Dopplerbroadening for both cases: co- and counter- propagating probe and driving fields. The resultsshow that: (1) In general, for a fixed SGC strength, LWI gain decreases monotonously withthe value of the Doppler broadening width increasing. Regardless of the Doppler broadeningbeing obvious or not, the LWI gain much larger than that without SGC always can be gotten by choosing suitable SGC strength, i.e. values of two factorsp1 andp 2which represent theSGC effect. (2) Varyingp1 orp 2will produce remarkable different influence on the LWIgain, and the influence is closely related to the value of the Doppler broadening width. (3) Inthe case of counter-propagating probe and driving fields, when the Doppler broadening islarge enough, gain oscillation occurs. For the same value of the Doppler broadening width,the oscillation amplitude increases with increasing values of strength of SGC. (4) The atomicexit and injection rates also can dramatically affect LWI gain. (5) The LWI gain for theco-propagating probe and driving fields is always larger than that for the counter-propagatingprobe and driving fields. (6) A much larger LWI gain in open system than that in thecorresponding closed system can be obtained.In Chapter 3, we investigate theoretically the effect of the relative phase (φ) betweenthe probe and driving fields on gain (absorption) and dispersion of the probe field in aDoppler-broadened closed quasiΛ-type four-level system with spontaneously generatedcoherence from different respects. It is shown that gain (absorption) and dispersion are verysensitive to variations in the relative phase, and changing the Doppler width also has anobvious effect on the phase-dependent gain (absorption) and dispersion. When the probe anddriving fields have the same propagation directions (copropagating), for the same Dopplerwidth, the dispersion curve withφ=αis the same as the gain(absorption) curve withφ=α+Ï€/2; however, when the probe and driving fields have opposite propagation directions(counterpropagating), the dispersion curve and gain (absorption) curve are different and thedifference becomes more considerable with an increase in Doppler width. In the co- andcounterpropagating cases, gain(absorption) and dispersion always vary periodically withvaryingφ, and the period is 2Ï€. By adjusting the value ofφ, the largest gain (absorption) anddispersion can be obtained, and a large index of refraction without absorption can be realized.Generally speaking, gain decreases with an increase in Doppler width, but by adjusting valueofφ, at some special values of Doppler width, a larger gain than that without Dopplerbroadening can be obtained. Our study also shows that gain in the copropagating case is muchlarger than that in the counterpropagating. In Chapter 4, The effect of the relative phase (φ) between the probe and driving fieldson the gain without inversion (GWI) in a Doppler broadened open quasiΛ-type four levelatomic system with spontaneously generated coherence (SGC) for both co- and counter-propagating probe and driving fields cases is studied. It is shown that: (1) GWI and the probedetuning region in which GWI exists are very sensitive to variation of the relative phase;when values of the other parameters keep unvarying, by adjusting value ofφ, the largestGWI can be obtained. (2) The Doppler width ( D ) also has dramatically modulation role onthe phase-dependent GWI. When value of D is smaller, the value ofφwhich correspondsto the largest value of GWI is aboutÏ€, when value of D is large enough, it is aboutÏ€/2. (3)GWI varies periodically withφvarying, the period is 2Ï€, but the concrete variation rule isclosely related to value of D . (4) In the co-propagating case we can obtain much larger GWIthan that in the counter-propagating case. the atomic exit rate (R₀ ) and the ratio (S) of theatomic injection rates have a considerable modulation role on the phase–dependent GWI.GWI firstly increases and then decreases withR 0increasing; in a certain value range of S,GWI increases monotonously with S increasing; by adjusting values ofR 0and S, in theopen system much larger GWI than that in the corresponding closed system can be obtained.The modulation role ofR₀and S on the phase–dependent GWI in the case with thecounter-propagating probe and driving fields is stronger than that in the co-propagating case.In Chapter 5, study influences of Doppler broadening, spontaneously generatedcoherence and other system parameters on propagation effect in a quasi lambda-typefour-level atomic system. It is shown that: When Doppler broadening is present, generallyspeaking, values of gain and intensity of lasing without inversion (i.e. the probe field) in theco-propagating probe and driving fields case are much larger than those in thecounter-propagating case; considerable larger gain and intensity of lasing without inversionthan those without Doppler broadening can be gotten by choosing appropriate values ofDoppler broadening width and spontaneously generated coherence strength. Gain andintensity of lasing without inversion increase with spontaneously generated coherencestrength increasing; when spontaneously generated coherence is present, much larger gain and intensity of lasing without inversion than those in the case without spontaneously generatedcoherence can be obtained. Choosing suitable values of the probe detuning, Rabi frequenciesof the driving and pump fields at the entrance of the medium also can remarkably enhancegain and intensity of lasing without inversion.In Chapter 6, The effect of the relative phase (φ) between the probe and driving fieldson the spatial evolution of gain of lasing without inversion (LWI, i.e. the probe field) and theintensity of the probe field in a Doppler broadened four-level atomic system withspontaneously generated coherence (SGC) for both co- and counter- propagating probe anddriving fields cases is studied. It is shown that: (1) the spatial evolution rules of gain and thefield intensity are very sensitive to value varying ofφ; Doppler broadening width ( D ) alsohas a considerable modulation role on the spatial evolution rules of gain and the field intensity.Length of propagation distance in which LWI gain existing increases monotonouslywith D increasing; Size of LWI intensity is determined by both size of LWI gain and length ofpropagation distance in which LWI gain exists. When Doppler broadening is present, themuch larger LWI gain and intensity than those without Doppler broadening can be gotten bychoosing appropriate values of D andφ. (2) When Doppler broadening is present, thepropagation directions of the probe and driving fields also have considerable effect on spatialevolutions of LWI gain and intensity. Values of LWI gain and intensity in the co-propagatingcase are much larger than those in the counter-propagating case.In Chapter 7, study influences of Doppler broadening and spontaneously generatedcoherence (SGC) on transient evolution of gain without inversion (GWI) in a quasiΛ-typefour-level atomic system. It is shown that: (1) transient evolution of gain is very sensitive tovalue varying of SGC strength,the gain maximum value(Imρ_{1 3} )maxand the steady value(Imρ_{1 3} )sincrease with SGC strength increasing; the transient and steady values of gain in thecase with SGC are much larger than those in the case without SGC. (2) When Dopplerbroadening is present, Doppler broadening width ( D ) and propagation directions of the probeand driving fields have a considerable modulation role on the transient evolution ofSGC–dependent GWI; the gain maximum value(Imρ_{1 3} )maxand the steady value(Imρ_{1 3} )s first increase and then decrease with Doppler broadening width ( D ) increasing; the value ofD which corresponds to the gain largest value(Imρ_{1 3} )Lis different from that correspondingto the largest value of steady gain(Imρ_{1 3} )sL; the value of t needed for reaching at the steadyvalue of gain, increases with D increasing; a much larger transient value of gain than thatwithout Doppler broadening can be gotten by choosing appropriate value of D ; the transientand steady values of gain in the co-propagating case are much larger than those in thecounter-propagating case respectively.In Chapter 8, The effect of the relative phase (φ) between the probe and driving fieldson transient evolution of gain of lasing without inversion (LWI, i.e. the probe field) and theintensity of the probe field in a Doppler broadened four-level atomic system withspontaneously generated coherence (SGC) for both co- and counter- propagating probe anddriving fields cases is studied. It is shown that: (1) the transient evolution rules of gain andthe probe field intensity are very sensitive to value varying ofφ; value ofφhas a smalleffect on the transient evolution rules of the driving and pump fields intensities. Dopplerbroadening width ( D ) also has a considerable modulation role on the transient evolutionrules of gain and the field intensity. For a fixed value ofφ, length of propagation distance inwhich LWI gain existing increases monotonously with D increasing; When Dopplerbroadening is present, the much larger LWI gain and intensity than those without Dopplerbroadening can be gotten by choosing appropriate values of D andφ. the gain curvesforφ=0andφ=Ï€(φ= 0.5Ï€andφ= 1.5Ï€)are symmetric with respect to Imρ_{1 3} = 0(2)Values of LWI gain and intensity in the co-propagating case are much larger than those in thecounter-propagating case.