Heating and atom loss during upward ramps of Feshbach resonance levels in Bose-Einstein condensates

The production of pairs of fast atoms leads to a pronounced loss of atoms during upward ramps of Feshbach resonance levels in dilute Bose-Einstein condensates. We provide comparative studies on the formation of these bursts of atoms containing the physical predictions of several theoretical approaches at different levels of approximation. We show that despite their very different description of the microscopic binary physics during the passage of a Feshbach resonance, all approaches lead to virtually the same prediction on the total loss of condensate atoms, provided that the ramp of the magnetic field strength is purely linear. We give the reasons for this remarkable insensitivity of the remnant condensate fraction to the microscopic physical processes and compare the theoretical predictions with recent Feshbach resonance crossing experiments on 23Na and 85Rb.Comment: 12 pages, 7 eps figures; final versio

Physical realization of coupled Hilbert-space mirrors for quantum-state engineering

Manipulation of superpositions of discrete quantum states has a mathematical counterpart in the motion of a unit-length statevector in an N-dimensional Hilbert space. Any such statevector motion can be regarded as a succession of two-dimensional rotations. But the desired statevector change can also be treated as a succession of reflections, the generalization of Householder transformations. In multidimensional Hilbert space such reflection sequences offer more efficient procedures for statevector manipulation than do sequences of rotations. We here show how such reflections can be designed for a system with two degenerate levels - a generalization of the traditional two-state atom - that allows the construction of propagators for angular momentum states. We use the Morris-Shore transformation to express the propagator in terms of Morris-Shore basis states and Cayley-Klein parameters, which allows us to connect properties of laser pulses to Hilbert-space motion. Under suitable conditions on the couplings and the common detuning, the propagators within each set of degenerate states represent products of generalized Householder reflections, with orthogonal vectors. We propose physical realizations of this novel geometrical object with resonant, near-resonant and far-off-resonant laser pulses. We give several examples of implementations in real atoms or molecules.Comment: 15 pages, 6 figure

Localization and diffusion in Ising-type quantum networks

We investigate the effect of phase randomness in Ising-type quantum networks. These networks model a large class of physical systems. They describe micro- and nanostructures or arrays of optical elements such as beam splitters (interferometers) or parameteric amplifiers. Most of these stuctures are promising candidates for quantum information processing networks. We demonstrate that such systems exhibit two very distinct types of behaviour. For certain network configurations (parameters), they show quantum localization similar to Anderson localization whereas classical stochastic behaviour is observed in other cases. We relate these findings to the standard theory of quantum localization.Comment: 12 page

Landau-Zener transitions in a linear chain

We present an exact asymptotic solution for electron transition amplitudes in an infinite linear chain driven by an external homogeneous time-dependent electric field. This solution extends the Landau-Zener theory for the case of infinite number of states in discrete spectrum. In addition to transition amplitudes we calculate an effective diffusion constant.Comment: 3 figure

Fast noise in the Landau-Zener theory

We study the influence of a fast noise on Landau-Zener transitions. We demonstrate that a fast colored noise much weaker than the conventional white noise can produce transitions itself or can change substantially the Landau-Zener transition probabilities. In the limit of fast colored or strong white noise we derive asymptotically exact formulae for transition probabilities and study the time evolution of a spin coupled to the noise and a sweeping magnetic field.Comment: 28 pages, 5 figure

Formation of Two Component Bose Condensate During the Chemical Potential Curve Crossing

In this article we study the formation of the two modes Bose-Einstein condensate and the correlation between them. We show that beyond the mean field approximation the dissociation of a molecular condensate due to the chemical potential curve crossing leads to the formation of two modes condensate. We also show that these two modes are correlated in a two mode squeezed state.Comment: 10 page

Localized states in 2D semiconductors doped with magnetic impurities in quantizing magnetic field

A theory of magnetic impurities in a 2D electron gas quantized by a strong magnetic field is formulated in terms of Friedel-Anderson theory of resonance impurity scattering. It is shown that this scattering results in an appearance of bound Landau states with zero angular moment between the Landau subbands. The resonance scattering is spin selective, and it results in a strong spin polarization of Landau states, as well as in a noticeable magnetic field dependence of the $g$ factor and the crystal field splitting of the impurity $d$ levels.Comment: 12 pages, 4 figures Submitted to Physical Review B This version is edited and updated in accordance with recent experimental dat

Classical approach in quantum physics

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom recently discovered with the help of Poincar$\acute{\mathrm{e}}$ section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treating as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormgroup symmetry, criterion of accuracy and so on are reviewed as well. In conclusion, the relation between quantum theory, classical physics and measurement is discussed.Comment: This review paper was rejected from J.Phys.A with referee's comment "The author has made many worthwhile contributions to semiclassical physics, but this article does not meet the standard for a topical review"