Despite the importance of quantum interference and coherent population trapping to the theory of electromagnetically induced transparency (EIT), it is shown that the recent experiments which slow down and even stop a light pulse in a dielectric really rely on a linear, refractive index type theory. From this point of view and in considerable contrast, the experiment on degenerate self-induced transparency (SIT) done 27 years ago which slowed down an optical pulse (in principle to zero velocity) was based on an intrinsically nonlinear (soliton type) theory. In quantum mechanical terms both theories are developed at the level of expectation values only and at this level the two different theories come together in terms of the storage and retrieval of information. In the Appendix we analyse the nature of this information in terms of the quantum equations governing linear EIT and nonlinear SIT.
Despite the importance of quantum interference and coherent population trapping to the theory of electromagnetically induced transparency (EIT), it is shown that the recent experiments which slow down and even stop a light pulse in a dielectric really rely on a linear, refractive index type theory. From this point of view and in considerable contrast, the experiment on degenerate self-induced transparency (SIT) done 27 years ago which slowed down an optical pulse (in principle to zero velocity) was based on an intrinsically nonlinear (soliton type) theory. In quantum mechanical terms both theories are developed at the level of expectation values only and at this level the two different theories come together in terms of the storage and retrieval of information. In the Appendix we analyse the nature of this information in terms of the quantum equations governing linear EIT and nonlinear SIT.
Summary form only given. We compare old experimental and theoretical results for the storage and retrieval of quantum information in atomic dielectrics done on the /sup 23/Na D/sub 1/ lines and based on nonlinear degenerate self-induced transparency (SIT) with more recent experiments and theory based on linearised electromagnetically induced transparency (EIT) done on the /sup 87/Rb D/sub 1/ lines. Although the nonlinear SIT theory is very different from the recent linearised EIT theory there are remarkable conceptual similarities at the level of quantum expectation values between the two theories of quantum memory in their modes of storage and retrieval of quantum information. However it has been argued that the linearised theories have the merit of recording information on the atomic dielectric accurate to all (countable) orders of normally ordered correlation functions while this is not true for the nonlinear theories. By working from the closely related theoretical case of the quantum nonlinear dielectric formed from the condensed repulsive Bose gases we bring strong evidence to show that the quantum nonlinear SIT theories can in fact show similar levels of accuracy namely beyond expectation and to all (countable) orders of correlation functions. Up to neglect of incoherence effects the exact quantum theory of EIT is exactly solvable by methods such as the quantum inverse method or Bethe ansatz, and the 3-level /spl Lambda/ atom model of EIT induces dark quantum solitons. We explore the whole set of quantum dielectrics formed by the nonlinear and linearised EIT dielectrics interpreted as quantum memories. We explore how far it is possible in principle to store quantum information accurately for continuous wave optical inputs via a merely countable infinity of correlation functions. We hope to have evaluated quantum correlation functions of arbitrary countable order for the quantum nonlinear EIT system by exact quantum inverse methods and results for quantum memory purposes will be reported. We can already explore the complete Hilbert space for strictly (non-degenerate) resonant SIT at the level of the quantum sine-Gordon equation and quantised breathers here provide generalised qubits for quantum information purposes in which the number of breather states is in general greater than two and is bounded by an adjustable constant coupling in the nonlinearity.
We analyze the energy storage process of light propagating with slow group velocity in a sample where electromagnetically induced transparency (EIT) is created by a strong coupling field. We compare the formation of slow light in EIT and in self-induced transparency (SIT). For SIT, soliton-like propagation of light with essentially reduced group velocity takes place because of the temporary storage of an appreciable part of the pulse energy in the atoms. For EIT, no energy of the probe is stored in the atoms. This energy is transformed to the coupling field and leaves the sample with phase velocity c without absorption. Slow light is formed by a low frequency coherence induced at the input by the probe and coupling fields in a two-quantum excitation process. This coherence propagates as a “spin wave” with small group velocity, and at a large distance from the input, the coherence rules the process of the energy transformation from the coupling field to the probe, reproducing exactly the temporal profile of the probe at the input.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.
The possibility of observing a self-induced transparency (SIT) in an erbium-doped optical fiber is investigated. A general equation that includes the SIT, the group-velocity dispersion (GVD) of the fiber, and the nonlinear refractive index is discussed. It is shown that for one particular value of waveguide parameters the nonlinear index can balance the GVD, that is, the nonlinear Schr\"odinger equation (NLS), while maintaining a SIT soliton. This is called a SIT-NLS soliton. The phase change of the SIT-NLS soliton is governed solely by the NLS component, and the pulse delay due to resonance is determined solely by the SIT component when the detuning is zero. Practical parameters for silica-based fibers do not allow the coexistence of a mixed soliton state. A simple derivation of a condition for a SIT-NLS soliton is also presented. The SIT-NLS soliton is computer-run, and it is shown that a stable 2\ensuremath{\pi}/N=1 SIT-NLS soliton exists. However, high-order SIT-NLS solitons always split into multiple 2\ensuremath{\pi}/N=1 solitons. The NLS property can be preserved when Zsp\ensuremath{\ll}Labs. Finally, the NLS soliton that interacts coherently with erbium ions is studied, and the coherent pulsation that produces multiple narrow pulses is described.
The two-level atom can, for good reason, be considered the basic material structure for the study of quantum optics [1]. The two-level atom has played a fundamental role in studies of physical processes, including self-induced transparency (SIT), photon echoes, optical nutation, saturation spectroscopy, and, most recently, slow- and fast-light research. This latter field has recently been the subject of great activity, as researchers have learned how to utilize various physical processes to exert control over the velocity of propagation of light pulses through material systems [2]. This interest stems both from the intellectual intrigue in situations in which the velocity of light can be speeded up or slowed down by many orders of magnitude and the promise that such techniques might be useful for applications in fields such as telecommunications and optical computing [3‐6]. Most of the recent work in this field has made use of the process of electromagnetically induced transparency (EIT) to induce a narrow transparency region in an otherwise highly absorbing optical material [7, 8]. The rapid variation of the refractive index n associated with this transparency window then leads to a strong modification of the group velocity n g in accordance with the standard relation
This thesis presents theoretical models and results of numerical simulations describing the propagation of optical pulses through dense, thermal atomic vapours. In particular we investigate the nonlinear effects of optical solitons due to self-induced transparency (SIT) in two-level systems, optical simultons in V-type three-level systems and electromagnetically induced transparency (EIT) in Λ-type systems, including the storage and retrieval of dark-state polaritons. An investigation is made into two-photon excitation of the 5D states of rubidium in a high-intensity beam including the hyperfine structure of the relevant atomic levels. Decay from these states to the 6P manifolds is ruled out as a cause of experimentally observed fluorescence due to the amount of power broadening associated with intensities necessary to provide any significant level of population in these highly excited states. We combine the nonlinear effects of optical solitons and EIT to explain experimentally observed steepened pulses in a V-type system in a micron-length cell. We explain the behaviour as the early formation of a simulton pulse drawn from a CW probe field by a strong coupling pulse, due to coherent population trapping. We predict that in a longer cell it may be possible to facilitate propagation of matched pulses, even when the transitions in the system have different propagation coefficients, as long as decoherence from collision broadening can be controlled. The fact that weak pulses can propagate with this scheme suggests an approach to achieving transparent propagation of single or few photon pulses distinct from, but related to, both SIT and EIT.