I n 1998, laser pulses were slowed [1] in a Bose-Einstein condensate (BEe) [2] ofsodium to only 17 m/s, more than seven orders of magnitude lower than the speed of light in vacuum. Associated with the dramatic reduction factor for the light speed was a spatial compression of the pulses by the same large factor. A light pulse, which was more than 1 km long in vacuum, was compressed to a size of -50 flm, and at that point was completely contained within the condensate [1]. This allowed the light-slowing experiments to be brought to their ultimate extreme [3]: in the summer of 2000, light pulses were completely stopped, stored, and subsequently revived in an atomic medium, with millisecond storage times [4]. The initial ultra-slow light experiments spurred a flurry of slow light investigations, and slow or partially stopped light has now been observed in limited geometries in warm rubidium vapours [5-7], liquid-nitrogen cooled crystals [8], and recently in room temperature crystals [9]. Here, we begin with a discussion ofultra-slow and stopped light. We describe how cold atoms and Bose-Einstein condensates have been manipulated to generate media with extreme optical properties. While the initial experiments concentrated on the light propagation, we have recently begun a number of investigations of the effects that slow light has on the medium in which it propagates. Effects are profound because both the velocity and length scales associated with propagating light pulses have been brought down to match the characteristic velocity and length scales of the medium. With the most recent extension, the light roadblock [10], we have compressed light pulses to a length ofonly 2 f!ill. Here, we describe the use of ultra-compressed light pulses to probe superfluidity and the creation of quantized vortices in BEes through formation of'superfluid shock. waves'. We also present the observation of an ultra-slow-light-based, pulsed atom laser. Furthermore, we demonstrate the use of slow and stopped light for manipulation of optical information, in particular in Bose-Einstein condensates that allow for phase coherent processing of three-dimensional, compressed patterns of stored optical information.
I n 1998, laser pulses were slowed [1] in a Bose-Einstein condensate (BEe) [2] ofsodium to only 17 m/s, more than seven orders of magnitude lower than the speed of light in vacuum. Associated with the dramatic reduction factor for the light speed was a spatial compression of the pulses by the same large factor. A light pulse, which was more than 1 km long in vacuum, was compressed to a size of -50 flm, and at that point was completely contained within the condensate [1]. This allowed the light-slowing experiments to be brought to their ultimate extreme [3]: in the summer of 2000, light pulses were completely stopped, stored, and subsequently revived in an atomic medium, with millisecond storage times [4]. The initial ultra-slow light experiments spurred a flurry of slow light investigations, and slow or partially stopped light has now been observed in limited geometries in warm rubidium vapours [5-7], liquid-nitrogen cooled crystals [8], and recently in room temperature crystals [9]. Here, we begin with a discussion ofultra-slow and stopped light. We describe how cold atoms and Bose-Einstein condensates have been manipulated to generate media with extreme optical properties. While the initial experiments concentrated on the light propagation, we have recently begun a number of investigations of the effects that slow light has on the medium in which it propagates. Effects are profound because both the velocity and length scales associated with propagating light pulses have been brought down to match the characteristic velocity and length scales of the medium. With the most recent extension, the light roadblock [10], we have compressed light pulses to a length ofonly 2 f!ill. Here, we describe the use of ultra-compressed light pulses to probe superfluidity and the creation of quantized vortices in BEes through formation of'superfluid shock. waves'. We also present the observation of an ultra-slow-light-based, pulsed atom laser. Furthermore, we demonstrate the use of slow and stopped light for manipulation of optical information, in particular in Bose-Einstein condensates that allow for phase coherent processing of three-dimensional, compressed patterns of stored optical information.
In the framework of the nonlinear Λ model, propagation of solitons was analysed in atomic vapours and Bose-Einstein condensates. The complicated nonlinear interplay between fast and slow-light solitons in a Λ-type medium was shown to facilitate control of its optical transparency and formation of optical gates. An exact analytical description was given for the deceleration, stopping and revival of slow-light solitons in the experimentally relevant non-adiabatic regime. A stopping slow-light soliton imprints a localized immobile polarization pattern in the medium, which, as explicitly demonstrated here, can be used as a bit of readable optical memory. The whole process can be controlled with the background field and an auxiliary laser field. The latter regulates the signal velocity, while the slow-light soliton can be stopped by switching off the former. The location and shape of the imprinted memory bit were also determined. With few assumptions characteristic of slow light, the Λ model was reduced to a simpler nonlinear model that also describes two-dimensional dilatonic gravity. Exact solutions could now be derived also in the presence of relaxation. Spontaneous decay of the upper atomic level was found to be strongly suppressed, and the spatial form of the decelerating slow-light soliton was preserved, even if the optical relaxation time was much shorter than the typical time scale of the soliton. The effective relaxation coefficient of the slow-light soliton was significantly smaller than that of an arbitrary optical pulse. Such features are obviously of great importance when this kind of system is applied, in practice, to information processing. A number of experimentally observable properties of the solutions reported were found to be in good agreement with recent experimental results, and a few suggestions are also made for future experiments.
Earlier this year, Lene Hau (Rowland Institute for Science and Harvard University) and her coworkers captured the media spotlight with their announcement of having slowed the speed of light pulses through a Bose—Einstein condensate to a mere 17 m/s, down by a factor of nearly 20 million from light's speed in vacuum. (See Physics Today, April 1999, page 9.) Marian Scully and his colleagues at Texas A&M University, the National Institute for Standards and Technology in Boulder, Colorado, and the Harvard-Smithsonian Center for Astrophysics have recently reported comparable results using an ensemble of rubidium atoms that, at a temperature of 360 K, are a billion times hotter than Hau's sodium atoms. And Dmitry Budker's group at the University of California, Berkeley has seen even slower speeds in rubidium at room temperature. Accompanying the slow speeds are extremely nonlinear optical properties, as well.
We theoretically explore coherent information transfer between ultraslow light pulses and Bose-Einstein condensates (BEC's) and find that storing light pulses in BEC's allows the coherent condensate dynamics to process optical information. We consider BEC's of alkali atoms with a $\ensuremath{\Lambda}$ energy level configuration. In this configuration, one laser (the coupling field) can cause a pulse of a second pulsed laser (the probe field) to propagate with little attenuation (electromagnetically induced transparency) at a very slow group velocity $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ and be spatially compressed to lengths smaller than the BEC. These pulses can be fully stopped and later revived by switching the coupling field off and on. Here we develop a formalism, applicable in both the weak- and strong-probe regimes, to analyze such experiments and establish several results: (1) We show that the switching can be performed on time scales much faster than the adiabatic time scale for electromagnetically induced transparancy even in the strong-probe regime. We also study the behavior of the system changes when this time scale is faster than the excited state lifetime. (2) Stopped light pulses write their phase and amplitude information onto spatially dependent atomic wave functions, resulting in coherent two-component BEC dynamics during long storage times. We investigate examples relevant to 87Rb experimental parameters and see a variety of novel dynamics occur, including interference fringes, gentle breathing excitations, and two-component solitons, depending on the relative scattering lengths of the atomic states used and the probe to coupling intensity ratio. We find that the dynamics when the levels $\ensuremath{\mid}F=1,{M}_{F}=\ensuremath{-}1⟩$ and $\ensuremath{\mid}F=2,{M}_{F}=+1⟩$ are used could be well suited to designing controlled processing of the information input on the probe. (3) Switching the coupling field on after the dynamics writes the evolved BEC wave functions density and phase features onto a revived probe pulse, which then propagates out. We establish equations linking the BEC wave function to the resulting output probe pulses in both the strong- and weak-probe regimes. We then identify sources of deviations from these equations due to absorption and distortion of the pulses. These deviations result in imperfect fidelity of the information transfer from the atoms to the light fields and we calculate this fidelity for Gaussian-shaped features in the BEC wave functions. In the weak-probe case, we find that the fidelity is affected both by absorption of very-small-length-scale features and absorption of features occupying regions near the condensate edge. We discuss how to optimize the fidelity using these considerations. In the strong-probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BEC's, squeezed light generation, and quantum information are anticipated.
Slow and superluminal group velocities can be observed in any material that has large normal or anomalous dispersion. While this fact has been known for more than a century, recent experiments have shown that the dispersion can be very large without dramatically deforming a pulse. As a result, the significance and nature of pulse velocity is being reevaluated. In this review, we discuss some of the current techniques used for generating ultra-slow, superluminal, and even stopped light. While ultra-slow and superluminal group velocities have been observed in complicated systems, from an applications point of view it is highly desirable to do have this done in a solid that can operate at room temperature. We describe how coherent population oscillations can produce ultra-slow and superluminal light under these conditions.
The group velocity at which light pulses propagate through a dispersive material system is very different from the vacuum speed of light c, One refers to light as being "slow" for v g << c (Boyd & Gauthier, 2009) or "fast" for v g > c or v g <0 (Stenner et al, 2003 ).For v g <0, the pulse envelope appears to travel backward in the material (Gehring et al, 2006), and hence it is sometimes referred to as "backward light."The subject of slow light has caused keen interest in the past decade or more, and it is possible to control the group velocity of light pulses in the dispersive materials.Interest in slow and fast light dates back to the early days of the 20th century.Sommerfeld and Brillouin (Sommerfeld & Brillouin, 1960) were intrigued by the fact that theory predicts that v g can exceed c, which leads to apparent inconsistencies with Einstein's special theory of relativity.Experimental investigations of extreme propagation velocities were performed soon after the invention of the laser (Faxvog and et al, 1970).In 1999, Harris's group research work greatly stimulated researchers' interests, which showed that light could be slowed down to 17m/s.The result was obtained in ultra cold atom clouds with the use of electromagnetically induced transparency (EIT), which induces transparency in a material while allowing it to retain strong linear and nonlinear optical properties (Hau et al, 1999).Slow light can also be obtained through the use of the optical response of hot atomic vapors (Philips et al, 2001).These early research works require hard conditions and the slow light cannot operate in room temperature.Recently, researchers found ways to realize slow light operating in room temperature and solid-state materials, which are more suited for many practical applications, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.In this chapter, we describe some of the physical mechanisms that can be used to induce slow and fast light effects in room-temperature solids (Bigelow et al, 2003) and some of the exotic propagation effects that can thereby be observed.We also survey some applications of slow and fast light within the fields of quantum electronics and photonics. Fundamentals of slow and fast lightSlow and fast light refer to the group velocity of a light wave.The group velocity is the velocity most closely related to the velocity at which the peak of a light pulse moves through an optical dispersive material (Milonni, 2005), and is given by the standard result www.intechopen.comRecent Progress in Optical Fiber Research 82where n is the refractive (phase) index and ω is the angular frequency of the carrier wave of the light field.One refers to light as being slow light for v g << c, fast light for for v g > c, and backwards light for v g <0 or v g is negative.Extreme values of the group velocity invariably rely on the dominance of the second contribution to the group index of Equation ( 1).This contribution of course results from the frequency dependence of the refractive index, and for this reason extreme values of the group velocity are usually associated with the resonant or near-resonant response of material systems.According to this theory, slow light is expected in the wings of an absorption line and fast light is expected near line center, and the spatial dispersion, that is, the non-locality in space of the medium response, is another mechanism that can lead to slow light, as has been predicted (Kocharovskaya et al,2001) and observed (Strekalov et al, 2001).We catalogue the main methods to realize slow light in room temperature solid, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.We will describe CPO and SBS slow light in more details.