Locking Local Oscillator Phase to the Atomic Phase via Weak Measurement

We propose a new method to reduce the frequency noise of a Local Oscillator (LO) to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many measurement cycles. This scheme uses weak measurement to monitor the phase in Ramsey method and repeat the cycle without initialization of phase and we call, "atomic phase lock (APL)" in this paper. APL will achieve white phase noise as long as the noise accumulated during dead time and the decoherence are smaller than the measurement noise. A numerical simulation confirms that with APL, Allan deviation is averaged down at a maximum rate that is proportional to the inverse of total measurement time, tau^-1. In contrast, the current atomic clocks that use projection measurement suppress the noise only down to the level of white frequency, in which case Allan deviation scales as tau^-1/2. Faraday rotation is one of the possible ways to realize weak measurement for APL. We evaluate the strength of Faraday rotation with 171Yb+ ions trapped in a linear rf-trap and discuss the performance of APL. The main source of the decoherence is a spontaneous emission induced by the probe beam for Faraday rotation measurement. One can repeat the Faraday rotation measurement until the decoherence become comparable to the SNR of measurement. We estimate this number of cycles to be ~100 cycles for a realistic experimental parameter.Comment: 18 pages, 7 figures, submitted to New Journal of Physic

Complex joint probabilities as expressions of determinism in quantum mechanics

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a state-independent definition of the deterministic relation between the outcomes of different quantum measurements. In this paper, it is shown how classical reality emerges as an approximation to the fundamental laws of quantum determinism expressed by complex conditional probabilities. The quantum mechanical origin of phase spaces and trajectories is identified and implications for the interpretation of quantum measurements are considered. It is argued that the transformation laws of quantum determinism provide a fundamental description of the measurement dependence of empirical reality.Comment: 12 pages, including 1 figure, updated introduction includes references to the historical background of complex joint probabilities and to related work by Lars M. Johanse

Infrared absorption and Raman scattering on coupled plasmon--phonon modes in superlattices

We consider theoretically a superlattice formed by thin conducting layers separated spatially between insulating layers. The dispersion of two coupled phonon-plasmon modes of the system is analyzed by using Maxwell's equations, with the influence of retardation included. Both transmission for the finite plate as well as absorption for the semi-infinite superlattice in the infrared are calculated. Reflectance minima are determined by the longitudinal and transverse phonon frequencies in the insulating layers and by the density-state singularities of the coupled modes. We evaluate also the Raman cross section from the semi-infinite superlattice.Comment: 20 pages,14 figure

Iwasawa N=8 Attractors

Starting from the symplectic construction of the Lie algebra e_7(7) due to Adams, we consider an Iwasawa parametrization of the coset E_7(7)/SU(8), which is the scalar manifold of N=8, d=4 supergravity. Our approach, and the manifest off-shell symmetry of the resulting symplectic frame, is determined by a non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E_7(7). In absence of gauging, we utilize the explicit expression of the Lie algebra to study the origin of E_7(7)/SU(8) as scalar configuration of a 1/8-BPS extremal black hole attractor. In such a framework, we highlight the action of a U(1) symmetry spanning the dyonic 1/8-BPS attractors. Within a suitable supersymmetry truncation allowing for the embedding of the Reissner-Nordstrom black hole, this U(1) is interpreted as nothing but the global R-symmetry of pure N=2 supergravity. Moreover, we find that the above mentioned U(1) symmetry is broken down to a discrete subgroup Z_4, implying that all 1/8-BPS Iwasawa attractors are non-dyonic near the origin of the scalar manifold. We can trace this phenomenon back to the fact that the Cartan subalgebra of SL(8,R) used in our construction endows the symplectic frame with a manifest off-shell covariance which is smaller than SL(8,R) itself. Thus, the consistence of the Adams-Iwasawa symplectic basis with the action of the U(1) symmetry gives rise to the observed Z_4 residual non-dyonic symmetry.Comment: 1+26 page

Stabilization and Controlled Association of Inorganic Nanoparticles using Block Copolymers

We report on the structural properties of mixed aggregates made from rare-earth inorganic nanoparticles (radius 20 Angstroms) and polyelectrolyte-neutral block copolymers in aqueous solutions. Using scattering experiments and Monte Carlo simulations, we show that these mixed aggregates have a hierarchical core-shell microstructure. The core is made of densely packed nanoparticles and it is surrounded by a corona of neutral chains. This microstructure results from a process of controlled association and confers to the hybrid aggregates a remarkable colloidal stability.Comment: 14 pages, 5 figure

Weak measurement of photon polarization by back-action induced path interference

The essential feature of weak measurements on quantum systems is the reduction of measurement back-action to negligible levels. To observe the non-classical features of weak measurements, it is therefore more important to avoid additional back-action errors than it is to avoid errors in the actual measurement outcome. In this paper, it is shown how an optical weak measurement of diagonal (PM) polarization can be realized by path interference between the horizontal (H) and vertical (V) polarization components of the input beam. The measurement strength can then be controlled by rotating the H and V polarizations towards each other. This well-controlled operation effectively generates the back-action without additional decoherence, while the visibility of the interference between the two beams only limits the measurement resolution. As the experimental results confirm, we can obtain extremely high weak values, even at rather low visibilities. Our method therefore provides a realization of weak measurements that is extremely robust against experimental imperfections.Comment: 11 pages, 3 figure

All the Exact Solutions of Generalized Calogero-Sutherland Models

A collective field method is extended to obtain all the explicit solutions of the generalized Calogero-Sutherland models that are characterized by the roots of all the classical groups, including the solutions corresponding to spinor representations for $B_N$ and $D_N$ cases.Comment: Latex, 17 pages. Title and abstract slightly changed, plus minor correction