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

Local Density of the Bose Glass Phase

We study the Bose-Hubbard model in the presence of on-site disorder in the canonical ensemble and conclude that the local density of the Bose glass phase behaves differently at incommensurate filling than it does at commensurate one. Scaling of the superfluid density at incommensurate filling of $\rho=1.1$ and on-site interaction $U=80t$ predicts a superfluid-Bose glass transition at disorder strength of $\Delta_c \approx 30t$. At this filling the local density distribution shows skew behavior with increasing disorder strength. Multifractal analysis also suggests a multifractal behavior resembling that of the Anderson localization. Percolation analysis points to a phase transition of percolating non-integer filled sites around the same value of disorder. Our findings support the scenario of percolating superfluid clusters enhancing Anderson localization near the superfluid-Bose glass transition. On the other hand, the behavior of the commensurate filled system is rather different. Close to the tip of the Mott lobe ($\rho=1, U=22t$) we find a Mott insulator-Bose glass transition at disorder strength of $\Delta_c \approx 16t$. An analysis of the local density distribution shows Gaussian like behavior for a wide range of disorders above and below the transition.Comment: 12 pages, 14 figure

Phase-ordering kinetics: ageing and local scale-invariance

Dynamical scaling in ageing systems, notably in phase-ordering kinetics, is well-established. New evidence in favour of Galilei-invariance in phase-ordering kinetics is reviewed.Comment: 7 pages, 1 figure,with AIP macros, based on invited talks given at the 8th Granada Seminar on Computational and Statistical Physics (7-11 February 2005) and at the Symposium `Renormalization and Scaling' at Berlin (5th of March 2005