Optical bistability in one dimensional doped photonic crystals with spontaneously generated coherence

We investigate optical bistability in a multilayer one-dimensional photonic crystal where the central layer is doped with $\Lambda$-type three level atoms. We take into account the influence of spontaneously generated coherence when the lower atomic levels are sufficiently close to each other, in which case Kerr-type nonlinear response of the atoms is enhanced. We calculate the propagation of a probe beam in the defect mode window using numerical nonlinear transfer matrix method. We find that Rabi frequency of a control field acting on the defect layer and the detuning of the probe field from the atomic resonance can be used to control the size and contrast of the hysteresis loop and the threshold of the optical bistability. In particular we find that, at the optimal spontaneously generated coherence, three orders of magnitude lower threshold can be achieved relative to the case without the coherence.Comment: 9 pages, 7 figure

Enhancing capacity of optical information storage in a Bose-Einstein condensate

Bose-Einstein condensates (BECs) have potential to be used in attractive applications. In particular, they have been thought to be suitable for being quantum optical dynamic memories to store coherent quantum optical information. In order to assess and enhance practical value of this proposal, we have performed various realistic examinations using detailed numerical and analytical methods. Firstly, propagation of short pulses of widths in microsecond to nanosecond range through the BEC has been considered. In this part, the influence of dispersion on the temporal characteristics and on the coherent optical information storage capacity is discussed. By modeling ultra-slow short pulses in the condensate under electromagnetically induced transparency (EIT) conditions, taking into account pulse broadening, we have determined optimum optical information storage capacity. Secondly, we have investigated conditions limiting the optimum number of optical modes that can be supported by an atomic BEC. In this part, in addition to EIT, a refractive index enhancement scheme was also considered, as it allows for accommodating many numbers  of modes in the condensate. Furthermore, we have shown that multi-mode pulses, though less in number can also be realized at the cost of tolerable absorption in the case of EIT scheme. Secondly, we determine the number of optical modes supported by a wave guide in which refractive index enhancement is produced by an atomic BEC. Some analytical approximations have been made neglecting the spatial inhomogeneity. More accurate results have been obtained using a numerical model where the spatial inhomogeneity is taken into account. In the refractive index enhancement model, the predictions of (WKB) theory have been compared with those of fully numerical simulations. In this study, we investigate potential of atomic Bose-Einstein condensates as dynamic memory devices for coherent optical information processing. Specifically, the number of ultra-slow pulses that can be simultaneously present within the storage time in the condensate has been analyzed. By modeling short pulse propagation through the condensate, taking into account high-order dispersive properties, constraints on the information storage capacity has been discussed. The roles of temperature, spatial inhomogeneity, the interatomic interactions and the coupling laser on the pulse shape have been pointed out. For a restricted set of parameters, it has been found that coherent optical information storage capacity would be optimized. Coherent optical information storage capacity of an atomic Bose-Einstein condensate is examined. Theory of slow light propagation in atomic clouds is generalized to short pulse regime by taking into account group velocity dispersion. It is shown that the number of stored pulses in the condensate can be optimized for a particular coupling laser power, temperature and interatomic interaction strength. Analytical results are derived for semi-ideal model of the condensate using effective uniform density zone approximation. Detailed numerical simulations are also performed. It is found that axial density profile of the condensate protects the pulse against the group velocity dispersion. We examine the conditions determining the number of optical modes that can be supported by an atomic Bose-Einstein condensate. We show that under the conditions of refractive index enhancement via quantum coherence, it is possible to control the number of modes by means of experimentally accessible parameters including trap size, temperature, condensate number density and scattering lengths. Analytical results for the single and two-mode conditions are found. In order to slow down the group velocity we use electromagnetically induced transparency and find detuning parameter corresponding to number of modes. Results of numerical simulations are compared with analytical  calculations of the propagation constants for a parabolic-refractive index profile. Furthermore, taking into account finite radial size of the condensate, multi-mode light propagation in atomic Bose-Einstein condensate is investigated. The number of modes that can be supported by a condensate is found. Single mode condition is determined as a function of experimentally accessible parameters including trap size, temperature, condensate number density and scattering length. Quantum coherent atom-light interaction schemes are proposed for enhancing multi-mode light propagation effects. Keywords: Optical memories, Coherent optical effects, Pulse shaping, and Bose-Einstein condensate.Bose-Einstein yoğuşuk maddesini uyumlu optik bilgi işlemleri için dinamik hafıza aleti olarak araştırdık. Özellikle, yoğuşuk maddede depolama zamanı içinde çok yavaş optik darbeler  (vurumlar) analiz edildi. Yüksek dereceden dağınım özelliklerini hesaba katarak yoğuşuk maddede optik darbelerin ilerlemesini modelledik. Bu çalışmada atomik sistemin konuma bağlı olarak değişen yoğunluğu, sıcaklık ve atomik çarpışmaların şiddetine göre değişen yoğunluk profili de dikkate alındı. Yapılan analitik hesaplar ile kısa darbenin genişlemesini sıcaklığa, konuma ve atomik çarpışmalara göre analiz ettik. Bir optik darbe yoğuşuk madde içinde rezonans frekansında elektromanyetik olarak indüklenmiş saydamlık etkisi ile çok yavaş ilerletilebilir. Hızı son derece yavaş olduğundan sistem, optik bilgiyi saklama için kullanılabilir. Sınırlı parametreler için eşevreli optik bilgi hafıza kapasitesi bulundu. Ek olarak, radyal yöndeki yoğunluk profilini dikkate alan ve fiber optikte eğimli indeks fiber profili adı ile bilinen model ile  yoğuşuk maddenin kırılma indisini modelledik. Yoğunlaşmış maddenin taşıyabileceği mod sayısını analitik olarak irdeledik. Ayrıca optik vurumların Bose-Einstein yoğuşuk maddesinde ilerlemesinde üç boyutlu etkileri ve optik modların sayısındaki bağ koşulları incelendi. Kırılma indisinin arttırılması durumunda  daha çok optik modun Bose-Einstein yoğuşuk maddesinde taşınabileceğini gösterdik. Mod sayısının sıcaklığa bağlı değişimini inceledik. Kuvantum eşevrelik sayesinde, deneysel parametreleri kullanarak mod sayısının kontrol edilebileceğini gösterdik. Ayrıca tek ve çok mod koşulları analitik olarak bulundu. Analitik sonuçlar, sayısal sonuçlarla karşılaştırıldı. Anahtar Kelimeler: Optik hafıza, eşevreli optik etkiler, darbe şekli, Bose-Einstein yoğuşması

Dynamical analysis of a weakly coupled nonlinear dielectric waveguide -- surface-plasmon model as a new type of Josephson Junction

We propose that a weakly-coupled nonlinear dielectric waveguide -- surface-plasmon system can be formulated as a new type of Josephson junction. Such a system can be realized along a metal - dielectric interface where the dielectric medium hosts a nonlinear waveguide (e.g. fiber) for soliton propagation. We demonstrate that the system is in close analogy to the bosonic Josephson-Junction (BJJ) of atomic condensates at very low temperatures, yet exhibits different dynamical features. In particular, the inherently dynamic coupling parameter between soliton and surface-plasmon generates self-trapped oscillatory states at nonzero fractional populations with zero and $\pi$ time averaged phase difference. The salient features of the dynamics are presented in the phase space.Comment: 9 pages, 7 figure

Statistics of Raman-Active Excitations via Masurement of Stokes-Anti-Stokes Correlations

A general fundamental relation connecting the correlation of Stokes and anti-Stokes modes to the quantum statistical behavior of vibration and pump modes in Raman-active materials is derived. We show that under certain conditions this relation can be used to determine the equilibrium number variance of phonons.Time and temperature ranges for which such conditions can be satisfied are studied and found to be available in todays' experimental standards. Furthermore, we examine the results in the presence of multi-mode pump as well as for the coupling of pump to the many vibration modes and discuss their validity in these cases.Comment: 12 pages, 1 figure, accepted for publication in Phys.Rev.

Super-radiant light scattering from trapped Bose Einstein condensates

We propose a new formulation for atomic side mode dynamics from super-radiant light scattering of trapped atoms. A detailed analysis of the recently observed super-radiant light scattering from trapped bose gases [S. Inouye {\it et al.}, Science {\bf 285}, 571 (1999)] is presented. We find that scattered light intensity can exhibit both oscillatory and exponential growth behaviors depending on densities, pump pulse characteristics, temperatures, and geometric shapes of trapped gas samples. The total photon scattering rate as well as the accompanied matter wave amplification depends explicitly on atom number fluctuations in the condensate. Our formulation allows for natural and transparent interpretations of subtle features in the MIT data, and provides numerical simulations in good agreement with all aspects of the experimental observations.Comment: 24 pages,16 figures, submitted to Phys.Rev.