Classical and quantum effects in spatially modulated optical parametric oscillators

We study the effects of transverse spatial modulations in a multimode degenerate optical parametric oscillator. Intracavity photonic crystals allow us to tune the instability threshold and improve entanglement above threshold. Here we compare such results with the case in which the modulation is in the injected field profile.     

Classical and quantum mechanical aspects of time-dependent Hartree-Fock trajectories

In terms of a quantum mechanical representation based on Slater determinants, classical and quantum mechanical aspects of TDHF trajectories are investigated. The invariant integration measure of the determinantal representation is obtained in a general closed form. Phase space structures of the TDHF equation and its solutions are discussed on this basis. The formal classical structures provide a way of finding a semiclassical expression for the quantum mechanical propagator, into which the superposition principle among TDHF trajectories is incorporated. General properties of the semiclassical propagator such as the time translation/reversal symmetry, unitarity, etc., are studied. Two simple hamiltonian systems are employed as examples which exhibit analytical solutions for the propagator. To illustrate the effects of superposition of TDHF paths, a system of interacting two-level nuclei is numerically studied and a comparison with the exact result is made.     

Capture by stabilized continuum: Classical and quantum aspects

We review here the results of our investigations concerning chaotic atomic scattering in the presence of a laser field. Particular emphasis is put on the existence of classical stable resonance structures, induced by the intense laser field, which are embedded in the field-free continuum. We show that phase space structures in the vicinity of a resonance island play an important role in the chaotic scattering behavior and form the basis for a mechanism to enhance the lifetimes of the collisional partners. Quantum calculations, based on a wave packet propagation method, show that quantum solutions are strongly influenced by the classical phase space structures. More specifically, a wave packet is found to spread differently in the regular and chaotic regions; in the latter case it spreads exponentially with time until saturation occurs, defining the saturation time. We also investigate the dependence of the spreading rates in both the regular and chaotic regimes. Calculations with an ensemble of classical trajectories are also presented to further illustrate the smoothing effects of varying.     

Classical and quantum aspects of Bianchi type IX cosmological model

A detailed study of the Bianchi type IX cosmological model is done. Classical field equations are discussed with a massive scalar field. The Wheeler-DeWitt quantum equation is formed and is solved using a Born-Oppenheimer type of approximation.     

Quantum statistics of multimode parametric amplification

The effect of a multimode interaction on the squeezing attainable in parametric amplification is investigated. In the non degenerate case the maximum squeezing attainable is reduced from the single mode case, whereas in the degenerate case the squeezing is essentially unaffected by the multimode nature of the interaction.     

Classical and quantum aspects of the continuous Heisenberg chain atT=0

We review and summarize various classical and quantum aspects of the isotropic continuous Heisenberg chain with particular emphasis on the inverse scattering method and the semi-classical quantization of the action-angle representation.The present work has been supported by grants from NOR-DITA and the Danish Natural Science Research Foundation     

Classical and quantum turbulence

The reconnection of two singularities in 2D, 3D, and 4D classical and quantum turbulence is examined. Singularity reconnection plays an essential role in the dissipation of the incompressible part of kinetic energy. A reconnection condition 2(d_s+1)≥d+1 is derived, which crucially depends on the dimension d_s of the singular structure in relation to the spatial dimension d of the system. The feasibility of this condition is examined using direct numerical simulations of the Navier-Stokes and Gross-Pitaevskii equations for the classical and quantum turbulence, respectively. We observed that the condition was satisfied for d=3 and 4, in agreement with the occurrence of energy cascades in both classical and quantum turbulence in those dimensions.     

Generation and characterization of multimode quantum frequency combs

Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables, for example, in cluster state computation. We report in this Letter the first experimental evidence of a multimode nonclassical frequency comb in a femtosecond synchronously pumped optical parametric oscillator. In addition to a global reduction of its quantum intensity fluctuations, the system features quantum correlations between different parts of its frequency spectrum. This allows us to show that the frequency comb is composed of several uncorrelated eigenmodes having specific spectral shapes, two of them at least being squeezed, and to characterize their spectral shapes.     

Phonon-phonon interaction and parametric down-conversion generation in multimode optomechanical systems

We studied the process of polariton conversion in a 3-mode nonlinear optomechanical system.Compared with the standard 2-mode optomechanical system, we find a much larger conversion rate of polariton modes can be achieved under typical dissipation conditions. To obtain a transparent understanding of the relevant physical process, we show that in the large detuned case, the cavity can be eliminated adiabatically, resulting in a parametric down-conversion(PDC) interaction between two phononic polar...     

Classical spin and quantum propagation

We consider a classical Brownian motion model of diffusion in two spatial dimensions, where the Brownian particle moves on spiral paths. The classical spin does not change the propagator for the probability density for the position of the particle. However, the subdominant eigenvalues of the classical kernel are simply related to the dominant eigenvalues of the Feynman kernel for an analogous quantum system. The Feynman kernel can be extracted from the classical kernel by coupling to a spin angular momentum of the particle.     

Classical topology and quantum states

Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac’s ‘quantum mechanics’, then a quantum physicist would not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further refinements of the axiom, its C ^K - and C ^--structures) can be reconstructed using Gel’fand-Naimark theory and its extensions. Classical topology is an attribute of only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental issues concerning the role of time in quantum physics are also addressed.     

Classical and quantum Hamiltonian ratchets

We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and we derive a classical sum rule which allows one to predict the chaotic transport velocity from properties of regular phase-space components. Transport in quantum Hamiltonian ratchets arises by the same mechanism as long as uncertainty allows one to resolve the classical phase-space structure. We derive a quantum sum rule analogous to the classical one, based on the relation between quantum transport and band structure.     

Classical and quantum gravitational collapse

The quantization of a homogeneous isotropic closed Friedmann model filled with an ideal fluid is discussed within the framework of a geometrodynamical approach.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 81–86, May, 1977.The authors wish to express their deep indebtedness to B. A. Lysov and A. V. Borisov for their valuable help in the writing of this paper.     

Classical physics and quantum loops

The standard picture of the loop expansion associates a factor of variant Planck's over 2pi with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss counterexamples wherein classical effects arise from loop diagrams and display the relationship between the classical terms and the long range effects of massless particles.     

Classical versus quantum gravity

Is Einstein's metric theory of gravitation to be quantized to yield a complete and logically consistent picture of the geometry of the real world in the presence of quantized material sources? To answer this question, we give arguments that there is a consistent way to extend general relativity to small distances by incorporating further geometric quantities at the level of the connection into the theory and introducing corresponding field equations for their determination, allowing thereby the metric and the Levi-Civita connection to remain classical quantities. The dualism between matter and geometry is extended to quantized fields with the help of a Hibert bundle ? raised over a Riemann-Cartan spacetime. Quantized subnuclear matter fields (generalized quantum mechanical wave functions) are sections on ? which determine generalized bilinear currents acting as sourc currents for the bundle geometry at small distances. The established dualism between matter and the underlying bundle geometry contains general relativity as a classical part.