Quantum delocalization in photon-pair generation

The generation of correlated photon pairs is a key to the production of entangled quantum states, which have a variety of applications within the area of quantum information. In spontaneous parametric down-conversion—the primary method of generating correlated photon pairs—the associated photon annihilation and creation events are generally thought of as being colocated: The correlated pair of photons is localized with regards to the pump photon and its positional origin. A detailed quantum electrodynamical analysis highlights a mechanism exhibiting the possibility of a delocalized origin for paired output photons: The spatial extent of the region from which the pair is generated can be much larger than previously thought. The theory of both localized and nonlocalized degenerate down-conversion is presented, followed by a quantitative analysis using discrete-volume computational methods. The results may have significant implications for quantum information and imaging applications, and the design of nonlinear optical metamaterials

Signatures of exciton coupling in paired nanoemitters

An exciton formed by the delocalized electronic excitation of paired nanoemitters is interpreted in terms of the electromagnetic emission of the pair and their mutual coupling with a photodetector. A formulation directly tailored for fluorescence detection is identified, giving results which are strongly dependent on geometry and selection rules. Signature symmetric and antisymmetric combinations are analyzed and their distinctive features identified

Dynamics of a two-mode Bose-Einstein condensate beyond mean-field theory

We study the dynamics of a two-mode Bose-Einstein condensate in the vicinity of a mean-field dynamical instability. Convergence to mean-field theory (MFT), with increasing total number of particles $N$, is shown to be logarithmically slow. Using a density matrix formalism rather than the conventional wavefunction methods, we derive an improved set of equations of motion for the mean-field plus the fluctuations, which goes beyond MFT and provides accurate predictions for the leading quantum corrections and the quantum break time. We show that the leading quantum corrections appear as decoherence of the reduced single-particle quantum state; we also compare this phenomenon to the effects of thermal noise. Using the rapid dephasing near an instability, we propose a method for the direct measurement of scattering lengths.Comment: 17 pages, 9 figures, Phys. Rev. A 64, 0136XX (2001

Quasi-continuous atom laser in the presence of gravity

We analyse the extraction of a coherent atomic beam from a trapped Bose-Einstein condensate using a rf transition to a non-trapping state at T=0 K. Our quantum treatment fully takes gravity into account but neglects all interactions in the free falling beam. We obtain an analytical expression of the output rate and of the wave function of the extracted beam, i.e. the output mode of the ``atom laser''. Our model reproduces satisfactorily experimental data without any adjustable parameter.Comment: 4 pages, 2 figure

Barrier effects on the collective excitations of split Bose-Einstein condensates

We investigate the collective excitations of a single-species Bose gas at T=0 in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider onedimensional potentials consisting of two harmonic wells separated a distance 2 z_0, since they essentially contain all the barrier effects that one may visualize in the 3D situation. We find, within a hydrodynamic approximation, that regardless the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighbouring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results of exactly solving the time-dependent Gross-Pitaevskii equation. We analyze as well the characteristics of the spatial pattern of excitations of threedimensional boson systems according to the amount of splitting of the condensate.Comment: RevTeX, 12 pages, 13 ps figure

Effects of interatomic collisions on atom laser outcoupling

We present a computational approach to the outcoupling in a simple one-dimensional atom laser model, the objective being to circumvent mathematical difficulties arising from the breakdown of the Born and Markov approximations. The approach relies on the discretization of the continuum representing the reservoir of output modes, which allows the treatment of arbitrary forms of outcoupling as well as the incorporation of non-linear terms in the Hamiltonian, associated with interatomic collisions. By considering a single-mode trapped condensate, we study the influence of elastic collisions between trapped and free atoms on the quasi steady-state population of the trap, as well as the energy distribution and the coherence of the outcoupled atoms.Comment: 25 pages, 11 figures, to appear in J. Phys.

Macroscopic superpositions of Bose-Einstein condensates

We consider two dilute gas Bose-Einstein condensates with opposite velocities from which a monochromatic light field detuned far from the resonance of the optical transition is coherently scattered. In the thermodynamic limit, when the relative fluctuations of the atom number difference between the two condensates vanish, the relative phase between the Bose-Einstein condensates may be established in a superposition state by detections of spontaneously scattered photons, even though the condensates have initially well-defined atom numbers. For a finite system, stochastic simulations show that the measurements of the scattered photons lead to a randomly drifting relative phase and drive the condensates into entangled superpositions of number states. This is because according to Bose-Einstein statistics the scattering to an already occupied state is enhanced.Comment: 18 pages, RevTex, 5 postscript figures, 1 MacBinary eps-figur

Quantum vs Classical Integrability in Ruijsenaars-Schneider Systems

The relationship (resemblance and/or contrast) between quantum and classical integrability in Ruijsenaars-Schneider systems, which are one parameter deformation of Calogero-Moser systems, is addressed. Many remarkable properties of classical Calogero and Sutherland systems (based on any root system) at equilibrium are reported in a previous paper (Corrigan-Sasaki). For example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair matrices at equilibrium are all "integer valued". In this paper we report that similar features and results hold for the Ruijsenaars-Schneider type of integrable systems based on the classical root systems.Comment: LaTeX2e with amsfonts 15 pages, no figure

Atom laser coherence and its control via feedback

We present a quantum-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical expressions in various regimes. The decay of this function is characterized by the coherence time, or its reciprocal, the linewidth. A crucial contributor to the linewidth is the collisional interaction of the atoms. We find four distinct regimes for the linewidth with increasing interaction strength. These range from the standard laser linewidth, through quadratic and linear regimes, to another constant regime due to quantum revivals of the coherence function. The laser output is only coherent (Bose degenerate) up to the linear regime. However, we show that application of a quantum nondemolition measurement and feedback scheme will increase, by many orders of magnitude, the range of interaction strengths for which it remains coherent.Comment: 15 pages, 6 figures, revtex

Subcortical amyloid load is associated with shape and volume in cognitively normal individuals

Amyloid-beta (Aβ) deposition is one of the main hallmarks of Alzheimer’s disease. The study assessed the associations between cortical and subcortical 11C-Pittsburgh Compound B retention, namely in the hippocampus, amygdala, putamen, caudate, pallidum, and thalamus, and subcortical morphology in cognitively normal individuals. We recruited 104 cognitive normal individuals who underwent extensive neuropsychological assessment, PiB-positron emission tomography (PET) scan and 3-tesla magnetic resonance imaging (MRI) acquisition of T1-weighted images. Global, cortical, and subcortical regional PiB retention values were derived from each scan and subcortical morphology analyses were performed to investigate vertex-wise local surface and global volumes, including the hippocampal subfields volumes. We found that subcortical regional Aβ was associated with the surface of the hippocampus, thalamus, and pallidum, with changes being due to volume and shape. Hippocampal Aβ was marginally associated with volume of the whole hippocampus as well as with the CA1 subfield, subiculum, and molecular layer. Participants showing higher subcortical Aβ also showed worse cognitive performance and smaller hippocampal volumes. In contrast, global and cortical PiB uptake did not associate with any subcortical metrics. This study shows that subcortical Aβ is associated with subcortical surface morphology in cognitively normal individuals. This study highlights the importance of quantifying subcortical regional PiB retention values in these individuals