Coherently Generated And Dynamically Controlled Photonic Band Gaps And Stationary Tight Pulses In Cold Atoms

In this thesis for doctorate that consists of four parts, we study dynamicallight signals in three-level or four-level cold atomic systems, dynamically inducedphotonic and stationary light pulses (SLPs).I. Comparison of steady and transient optical responses between afour-level Tripod system and a three-level Lambda systemWe study and compare the steady and transient optical responses of afour-level system and a three-level system, which are dressed by two and threelaser fields, respectively. In the three-level system, a transmissivity window (areflectivity platform) may be induced on the probe resonance by a traveling-wave(standing-wave) coupling field. In the four-level system, both transmissivitywindow and reflectivity platform are remarkably modified when a traveling-wavedriving field is applied on two-photon resonance with the probe, but change littlewhen the traveling-wave driving field is largely two-photon detuned. This impliesthat the four-level system can be safely treated as a three-level one in certainfrequency regions of interest. Transient behaviors of atomic coherence on theprobe resonance are also examined in both three-level and four-level systems tofurther confirm this conclusion.It is worth noting that an electromagnetically induced transparency (EIT)window of high transmissivity and a platform of high reflectivity may besimultaneously generated on the probe resonance by a TW driving and an SWcoupling, respectively, when they have quite similar Rabi frequencies but verydifferent detunings. Dynamic manipulation of the transmissivity window and the reflectivity platform may be exploited to devise a novel all-optical light routing orconfinement scheme. Our new findings are beneficial to achieve a novelall-optical routing scheme by simultaneously creating a transmissivity windowand a reflectivity platform on a single resonance, and may also be used to simplifytheoretical treatments in the situations where numerical calculations arecomplicated and intractable in the presence of at least one standing-wave field.II. Steady optical spectra and light propagation dynamics in cold atomicsamples with homogeneous or inhomogeneous densitiesWe have calculated steady optical spectra and light propagation dynamics inthree samples of cold atoms with either homogeneous or inhomogeneous densityfunctions. These samples are assumed to be driven into the EIT regime by a weakprobe and a strong coupling in theΛconfiguration. When the coupling is a TWfield, the transmissivity spectra characterized by typical EIT windows are exactlyidentical for the three samples with the same amounts of cold atoms but verydifferent spatial inhomogeneity while the reflectivity spectra are not necessary tobe taken into account. Consequently, an incident pulse with its most carrierfrequencies fallen into the overlapped EIT windows will go through the threesamples with the same time delay while suffering little energy loss and profiledeformation. The spatial inhomogeneity of cold atomic samples becomes ratherimportant when the coupling is a SW field instead. That is, both transmissivityand reflectivity spectra may change dramatically if the spatial inhomogeneity of asample is increased or decreased. In particular, the dynamically induced PBG forthe homogeneous sample looks much wider than those for the twoinhomogeneous samples. As a result, an incident pulse perfectly reflected by thehomogeneous sample is seen to split into a partially reflected one and a partiallytransmitted one when impinging upon the two inhomogeneous samples.Qualitative analyses have been given in terms of constructive (destructive) interference between the BW (FW) probe photons scattered by an atomic gratinggenerated by the SW coupling. These findings should be helpful to amendrelevant theoretical results attained without considering the spatial inhomogeneityof real atomic samples coherently driven by one or more SW fields.III. Efficient generation of robust stationary light signals in a double-ΛsystemWe have studied the light propagation and evolution dynamics in a sample ofcold87Rb atoms driven into the four-level double-Λconfiguration. By modulatingRabi frequenciesΩ_c+andΩ_c- of two counter-propagating control fields, wedemonstrate several dynamic processes where an FW signal field is stored into awave packet of spin coherence, transformed into SLPs via resonant four-wavemixing, and released from the sample exit or entrance. We consider, in particular,two specific situations where the double-Λsystem either has a symmetricstructure or has an asymmetric structure. In both structures, a FW signal field anda BW signal field are simultaneously generated and tightly coupled in the middlestage because they originate from a common wave-packet of spin coherence. Thetwo signal fields are stationary only when they experience a balanced competitionin their struggle to travel in the opposite directions, which correspond toΩ_{c +} =Ω _c- in the symmetric structure butΩ_{c +}≠Ω (c-) in the asymmetric structure.We also can modulate phases of the two counter-propagating control fields in themiddle stage to manipulate phases of the signal field finally released from thesample exit or entrance. In particular, the signal field released from the sampleentrance is reversed in profile as compared to the incident signal field or the signalfield released from the sample exit. Note that SLPs generated in the double-Λsystem don't suffer fast decay and diffusion as in theΛsystem and thereforeallows a longer time for implementing light information processing. That is, thedouble-Λsystem has the advantage of high efficiency and high fidelity as far as robust SLPs generation is concerned. The dynamic processes of efficientgeneration and control of SLPs may be exploited to devise novel photonic devicesfor manipulating classical or quantum light fields such as signal repeaters,reflectors, and converters.IV. Dynamic generation of dual-channel stationary light signals in adouble-tripod systemWe have proposed and studied the dual-channel light propagation andevolution dynamics in a sample of cold87Rb atoms driven into the double-tripodconfiguration. By modulating Rabi frequencies of two counter-propagatingcontrol fields in time, we demonstrate several dynamic processes where twoseparate FW signal fields are stored into two wave packets of spin coherence,transformed into two pairs of SLPs via resonant four-wave mixing, and releasedfrom the sample exit or entrance in two mutually independent light channels,respectively. We first consider, in particular, two specific situations where twoFW signal fields with the same group velocity in medium are inputted at the sameor different time. In both situations, the dual-channel signal fields are stored intotwo wave packets of spin coherence and transformed into the form of SLPs at thesame time because only a pair of control fields couple this system. The signalfields in two channels can be released simultaneously from the same surface ofthe sample (i.e., both FW signal fields from the sample exit or both BW signalfields from the sample entrance) in the first situation but at different time fromeither the same (i.e., both FW signal fields from the sample exit or both BWsignal fields from the sample entrance) or different (i.e., a FW signal field fromthe sample exit and a BW signal field from the sample entrance) surfaces of thesample in the second situation. By modulating the population decay rates or theinitial population distribution of the sample, we also can manipulate the groupvelocities of signal fields in each channel to control the dual-channel light propagation and evolution dynamics. It has shown that, if the group velocities oftwo signal fields are tuned to be different in medium, the signal fields in twochannels can be released at different time from either the same or differentsurfaces of the sample. Finally, we have compared the released signal fields afterthe two EIT-based light memory processes via spin-wave excitations and SLPs,respectively. The SLPs may suffer a little space-dependent diffusion but maintainoptical components. The dynamic processes of efficient generation and control ofdual-channel SLPs may be exploited to synchronous multitasking classical orquantum information processing, and novel photonic devices for manipulatingclassical or quantum fields such as signal repeaters, convertors and reflectors.