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Wed, 07 Mar 2001 00:00:00 +0200Wed, 07 Mar 2001 00:00:00 +0200Clifford's Legacy to Mathematics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1306
Heinz Krügerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1306Tue, 03 Jul 2001 00:00:00 +0200Hilbert Norms For Graded Algebras
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1307
Abstract: This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras included) with respect to which the multiplication is continuous. 2) Such norms cannot be chosen to be submultiplicative and equal to one on the unit of the algebra.Joachim Kupsch; Oleg G. Smolyanovpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1307Tue, 03 Jul 2001 00:00:00 +0200Equivalent of a Thouless energy in lattice QCD Dirac spectra
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1308
Abstract: Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD). In mesoscopic physics, the Thouless energy sets the universal scale for which RMT applies. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator with staggered fermions and SU_(2) lattice gauge fields. Comparing lattice data with RMT predictions we find deviations which allow us to give an estimate for this scale.M.E. Berbenni; T. Guhr; J.-Z. Ma; S. Meyer; T. Wilkepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1308Tue, 03 Jul 2001 00:00:00 +0200Beyond the Thouless energy
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1309
Abstract: The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy E_= 1 / sqrt (V), where V is the physical volume. For somewhat larger energies, the same quantities can be described by chiral perturbation theory (chPT). For most quantities there is an intermediate energy regime, roughly 1/V < E < 1/sqrt (V), where the results of RMT and chPT agree with each other. We test these predictions by constructing the connected and disconnected scalar susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3) simulations with staggered fermions for a variety of lattice sizes and coupling constants. In deriving the predictions of chPT, it is important totake into account only those symmetries which are exactly realized on the lattice.M. E. Berbenni-Bitsch; M. Göckeler; H. Hehl; S. Meyer; P.E.L. Rakow; A. Schäfer; T. Wettigpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1309Tue, 03 Jul 2001 00:00:00 +0200Random Matrix Theory, Chiral Perturbation Theory, and Lattice Data
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1310
Abstract: Recently, the chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that the deviations of lattice results from random matrix theory starting around the so-called Thouless energy can be understood in terms of chiral perturbation theory as well. Comparison of lattice data with chiral perturbation theory formulae allows us to compute the pion decay constant. We present results from a calculation for quenched SU(2) with Kogut-Susskind fermions at ß = 2.0 and 2.2.M. E. Berbenni-Bitsch; M. Göckeler; H. Hehl; S. Meyer; P.E.L. Rakow; A. Schäfer; T. Wettigpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1310Tue, 03 Jul 2001 00:00:00 +0200Random Matrix Theory and Chiral Logarithms
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1311
Abstract: Recently, the contributions of chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that a detailed comparison of random matrix theory and lattice calculations allows for a precise determination of such corrections. We estimate the relative size of the m log(m), m, and m^2 corrections to the chiral condensate for quenched SU(2).M. E. Berbenni-Bitsch; M. Göckeler; H. Hehl; S. Meyer; P.E.L. Rakow; A. Schäfer; T. Wettigpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1311Tue, 03 Jul 2001 00:00:00 +0200Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1312
Abstract: Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. We focus on the bulk of the spectrum. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three-point correlation functions.T. Guhr; J.-Z. Ma; S. Meyer; T. Wilkepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1312Tue, 03 Jul 2001 00:00:00 +0200The Roughening Transition of the 3D Ising Interface: A Monte Carlo Study
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1313
Abstract: We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite size scaling method. The particular method has recently been proposed and successfully tested for various solid on solid models. The basic idea is the matching of the renormalization-groupflow of the interface with that of the exactly solvable body centered cubic solid on solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperature K_R = 0.40754(5) is almost by two orders of magnitude more accurate than the estimate of Mon, Landau and Stauffer [9].M. Hasenbusch; S. Meyer; M. Pützpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1313Tue, 03 Jul 2001 00:00:00 +0200Influence of center-of-mass correlations on spontaneous emission and Lamb shift in dense atomic gases
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1290
Abstract: Local field effects on the rate of spontaneous emission and Lamb shift in a dense gas of atoms are discussed taking into account correlations of atomic center-of-mass coordinates. For this the exact retarded propagator in the medium is calculated in independent scattering approximation and employing a virtual-cavity model. The resulting changes of the atomic polarizability lead to modi cations of the medium response which can be of the same order of magnitude but of opposite sign than those due to local field corrections of the dielectric function derived by Morice, Castin, and Dalibard [Phys.Rev.A 51, 3896 (1995)].M. Fleischhauerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1290Mon, 02 Jul 2001 00:00:00 +0200Dark-State Polaritons in Electromagnetically Induced Transparency
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1291
Abstract: We identify form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in Electromagnetically Induced Transparency. The properties of the dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and "trapped" in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this reversible coherent-control technique are discussed.M. Fleischhauer; M. D. Lukinpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1291Mon, 02 Jul 2001 00:00:00 +0200Quantum limit of optical magnetometry in the presence of ac-Stark shifts
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1292
Abstract: We analyze systematic (classical) and fundamental (quantum) limitations of the sensitivity of optical magnetometers resulting from ac-Stark shifts. We show that incontrast to absorption-based techniques, the signal reduction associated with classical broadening can be compensated in magnetometers based on phase measurements using electromagnetically induced transparency (EIT). However due to ac-Stark associated quantum noise the signal-to-noise ratio of EIT-based magnetometers attains a maximum value at a certain laser intensity. This value is independent on the quantum statistics of the light and defines a standard quantum limit of sensitivity. We demonstrate that an EIT-based optical magnetometer in Faraday configuration is the best candidate to achieve the highest sensitivity of magnetic field detection and give a detailed analysis of such a device.M. Fleischhauer; A. B. Matsko; M.O. Scullypreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1292Mon, 02 Jul 2001 00:00:00 +0200Entanglement of Atomic Ensembles by Trapping Correlated Photon States
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1293
Abstract: We describe a general technique that allows for an ideal transfer of quantum correlations between light fields and metastable states of matter. The technique is based on trapping quantum states of photons in coherently driven atomic media, in which the group velocity is adiabatically reduced to zero. We discuss possible applications such as quantum state memories, generation of squeezed atomic states, preparation of entangled atomic ensembles and quantum information processing.M. D. Lukin; S. F. Yelin; M. Fleischhauerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1293Mon, 02 Jul 2001 00:00:00 +0200How to Trap Photons? Storing Single-Photon Quantum States in Collective Atomic Excitations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1294
Abstract: We show that it is possible to "store" quantum states of single-photon fields by mapping them onto collective meta-stable states of an optically dense, coherently driven medium inside an optical resonator. An adiabatic technique is suggested which allows to transfer non-classical correlations from traveling-wave single-photon wave-packets into atomic states and vise versa with nearly 100% efficiency. In contrast to previous approaches involving single atoms, the present technique does not require the strong coupling regime corresponding to high-Q micro-cavities. Instead, intracavity Electromagnetically Induced Transparency is used to achieve a strong coupling between the cavity mode and the atoms.M. Fleischhauer; S.F. Yelin; M. D. Lukinpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1294Mon, 02 Jul 2001 00:00:00 +0200Mirrorless oscillation based on resonantly enhanced 4-wave mixing: All-order analytic solutions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1295
Abstract: The phase transition to mirrorless oscillation in resonantly enhanced four-wave mixing in double-A systems are studied analytically for the ideal case of infinite lifetimes of ground-state coherences. The stationary susceptibilities are obtained in all orders of the generated fields and analytic solutions of the coupled nonlinear differential equations for the field amplitudes are derived and discussed.M. Fleischhauerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1295Mon, 02 Jul 2001 00:00:00 +0200Threshold and linewidth of a mirrorless parametric oscillator
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1296
Abstract: We analyze the above-threshold behavior of a mirrorless parametric oscillator based on resonantly enhanced four wave mixing in a coherently driven dense atomic vapor. It is shown that, in the ideal limit, an arbitrary small flux of pump photons is sufficient to reach the oscillator threshold. We demonstrate that due to the large group velocity delays associated with coherent media, an extremely narrow oscillator linewidth is possible, making a narrow-band source of non-classical radiation feasible.M. Fleischhauer; M.D. Lukin; A. B. Matsko; M. O. Scullypreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1296Mon, 02 Jul 2001 00:00:00 +0200Enhancement of Magneto-Optic Effects via Large Atomic Coherence
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1297
Abstract: We utilize the generation of large atomic coherence to enhance the resonant nonlinear magneto-optic effect by several orders of magnitude, thereby eliminating power broadening and improving the fundamental signal-to-noise ratio. A proof-of-principle experiment is carried out in a dense vapor of Rb atoms. Detailed numerical calculations are in good agreement with the experimental results. Applications such as optical magnetometry or the search for violations of parity and time reversal symmetry are feasible.V. A. Sautenkov; M. D. Lukin; C. J. Bednar; G. R. Welch; M. Fleischhauer; V. L. Velichansky; M. O. Scullypreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1297Mon, 02 Jul 2001 00:00:00 +0200Spontaneous emission and level shifts in absorbing disordered dielectrics and dense atomic gases: A Green's function approach
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1298
Abstract: Spontaneous emission and Lamb shift of atoms in absorbing dielectrics are discussed. A Green's-function approach is used based on the multipolar interaction Hamiltonian of a collection of atomic dipoles with the quantised radiation field. The rate of decay and level shifts are determined by the retarded Green's-function of the interacting electric displacement field, which is calculated from a Dyson equation describing multiple scattering. The positions of the atomic dipoles forming the dielectrics are assumed to be uncorrelated and a continuum approximation is used. The associated unphysical interactions between different atoms at the same location is eliminated by removing the point-interaction term from the free-space Green's-function (local field correction). For the case of an atom in a purely dispersive medium the spontaneous emission rate is altered by the well-known Lorentz local-field factor. In the presence of absorption a result different from previously suggested expressions is found and nearest-neighbour interactions are shown to be important.Michael Fleischhauerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1298Mon, 02 Jul 2001 00:00:00 +0200Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1299
Abstract: We investigate the quantum properties of fields generated by resonantly enhanced wave mixing based on atomic coherence in Raman systems. We show that such a process can be used for generation of pairs of Stokes and anti-Stokes fields with nearly perfect quantum correlations, yielding almost complete (i.e. 100%) squeezing without the use of a cavity. We discuss the extension of the wave mixing interactions into the domain of a few interacting light quanta.M. D. Lukin; A. B. Matsko; M. Fleischhauer; M. O. Scullypreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1299Mon, 02 Jul 2001 00:00:00 +0200Optical pumping in dense atomic media: Limitations due to reabsorption of spontaneously emitted photons
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1300
Abstract: Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.Michael Fleischhauerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1300Mon, 02 Jul 2001 00:00:00 +0200Coherent population transfer beyond the adiabatic limit: generalized matched pulses and higher-order trapping states
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1301
Abstract: We show that the physical mechanism of population transfer in a 3-level system with a closed loop of coherent couplings (loop-STIRAP) is not equivalent to an adiabatic rotation of the dark-state of the Hamiltonian but coresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive toolto design pulse sequences for stimulated Raman adiabatic passage (STIRAP) which give maximum population transfer also under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under certain conditions for the pulses (generalized matched pulses) there exists a higher-order trapping state, which is an exact constant of motion and analytic solutions for the atomic dynamics can be derived.M. Fleischhauer; R. Unanyan; B.W. Shore; K. Bergmannpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1301Mon, 02 Jul 2001 00:00:00 +0200Long-time dynamics of spontaneous parametric down-conversion and quantum limitations of conversion effciency
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1302
Abstract: We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motions fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schrödinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum uctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.Michael Fleischhauer; Oliver Veitspreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1302Mon, 02 Jul 2001 00:00:00 +0200Radiative atom-atom interactions in optically dense media: Quantum corrections to the Lorentz-Lorenz formula
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1303
Abstract: Generalized single-atom Maxwell-Bloch equations for optically dense media are derived taking into account non-cooperative radiative atom-atom interactions. Applying a Gaussian approximation and formally eliminating the degrees of freedom of the quantized radiation field and of all but a probe atom leads to an effective time-evolution operator for the probe atom. The mean coherent amplitude of the local field seen by the atom is shown to be given by the classical Lorentz-Lorenz relation. The second-order correlations of the field lead to terms that describe relaxation or pump processes and level shifts due to multiple scattering or reabsorption of spontaneously emitted photons. In the Markov limit a non-linear and nonlocal single-atom density matrix equation is derived. To illustrate the effects of the quantum corrections we discuss amplified spontaneous emission and radiation trapping in a dense ensemble of initially inverted two-level atoms and the effects of radiative interactions on intrinsic optical bistability in coherently driven systems.Michael Fleischhauer; Susanne F. Yelinpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1303Mon, 02 Jul 2001 00:00:00 +0200Interacting Dark Resonances: Interference Effects Induced by Coherently Altered Quantum Superpositions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1304
Abstract: We predict the possibility of sharp, high-contrast resonances in the optical response of a broad class of systems, wherein interference effects are generated by coherent perturbation or interaction of dark states. The properties of these resonances can be manipulated to design a desired atomic response.M. D. Lukin; S.F. Yelin; M. Fleischhauer; M. O. Scullypreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1304Mon, 02 Jul 2001 00:00:00 +0200Thermal Properties of Interacting Bose Fields and Imaginary-Time Stochastic Differential Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1305
Abstract: Matsubara Green's functions for interacting bosons are expressed as classical statistical averages corresponding to a linear imaginary-time stochastic differential equation. This makes direct numerical simulations applicable to the study of equilibrium quantum properties of bosons in the non-perturbative regime. To verify our results we discuss an oscillator with quartic anharmonicity as a prototype model for an interacting Bose gas. An analytic expression for the characteristic function in a thermal state is derived and a Higgs-type phase transition discussed, which occurs when the oscillator frequency becomes negative.L. I. Plimak; M. Fleischhauer; D. F. Wallspreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1305Mon, 02 Jul 2001 00:00:00 +0200Wannier-Stark Resonances in optical and semiconductor superlattices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1289
In this work, we discuss the resonance states of a quantum particle in a periodic potential plus static force. Originally this problem was formulated for a crystalline electron subject to the static electric field and is known nowadays as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and, in this sense, solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems like optical or semiconductor superlattices.Markus Glück; Andrey R. Kolovsky; Hans Jürgen Korschpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1289Fri, 08 Jun 2001 00:00:00 +0200