Nonlinear quantum regime

Clever schemes have been developed to treat the Barkas-Andersen effect for light ions in an electron gas ([27,34] and others) in what is called the nonlinear quantum regime. While there is little doubt that there must be a lower velocity limit for the validity of Bohr-like stopping theory, a reliable estimate of this limit does not seem available, nor is there a demonstration of where and in what manner quantum mechanics is an indispensable feature. 

The ar tide is organized as follows. We will begin with a discussion of the various possibilities of dynamical description, clarify what is meant by nonlinear quantum dynamics , discuss its connection to nonlinear classical dynamics, and then study two experimentally relevant examples of quantum nonlinearity - (i) the existence of chaos in quantum dynamical systems far from the classical regime, and (ii) real-time quantum feedback control. 

We stress that the chaos identified here is not merely a formal result - even deep in the quantum regime, the Lyapunov exponent can be obtained from measurements on a real system. Quantum predictions of this type can be tested in the near future, e.g., in cavity QED and nanomechanics experiments (H. Mabuch et.al., 2002 2004). Experimentally, one would use the known measurement record to integrate the SME this provides the time evolution of the mean value of the position. From this fiducial trajectory, given the knowledge of the system Hamiltonian, the Lyapunov exponent can be obtained by following the procedure described above. It is important to keep in mind that these results form only a starting point for the further study of nonlinear quantum dynamics and its theoretical and experimental ramifications. 

We have thus seen that the behavior of weak quantum fields is remarkably different from that of classical fields, as in the quantum regime the nonlinear phase shift is bounded between 27t tv2(i) 2/(L Sq). This fact severely limits the usefulness of weak coherent states for QI applications. Only in the limit of weak cross-phase modulation 9 [Pg.86]

Abstract. The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured quantum systems, necessary to explain actual experimental results. The dynamics of such systems is intrinsically nonlinear even at the level of distribution functions, both classically as well as quantum mechanically. Aside from being physically more complete, this treatment reveals the existence of dynamical regimes, such as chaos, that have no counterpart in the linear case. Here, we present a short introductory review of some of these aspects, with a few illustrative results and examples. 

To summarize, we have studied the interaction of two weak quantum fields with an optically dense medium of coherently driven four-level atoms in tripod configuration. We have presented a detailed semiclassical as well as quantum analysis of the system. The main conclusion that has emerged from this study is that optically dense vapors of tripod atoms are capable of realizing a novel regime of symmetric, extremely efficient nonlinear interaction of two multimode single-photon pulses, whereby the combined state of the system acquires a large conditional phase shift that can easily exceed 1r. Thus our scheme may pave the way to photon-based quantum information applications, such as deterministic all-optical quantum computation, dense coding and teleportation [Nielsen 2000]. We have also analyzed the behavior of the multimode coherent state and shown that the restriction on the classical correspondence of the coherent states severely limits their usefulness for QI applications. 

Interesting results of the studies of the strong coupling regime of Wannier-Mott excitons in a quantum dot lattice embedded in organic medium and in dendrites and also unusual nonlinear properties of such structures can be found in the articles by Birman and coworkers (33)-(37). 

The nonlinear optical properties of semiconductor particles was first studied with commercial color filters, which contain nominally CdSxSei-x particles of 100-1000 A diameter [88]. The reported large nonlinearity attracted much interest and soon the study was extended to CdS clusters in the quantum-confined size regime (i.e., below 60 A for CdS) [89,90]. 

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