Efficient Grover search with Rydberg blockade

We present efficient methods to implement the quantum computing Grover search algorithm using the Rydberg blockade interaction. We show that simple pi-pulse excitation sequences between ground and Rydberg excited states readily produce the key conditional phase shift and inversion-about-the mean unitary operations for the Grover search. Multi-qubit implementation schemes suitable for different properties of the atomic interactions are identifed and the error scaling of the protocols with system size is found to be promising for immediate experimental investigation.Comment: Detailed description of algorithm for sub-register architecture. Error budget modified for Cs atomic parameters. To appear in J. Phys. B. Special Issue on Strong Rydberg interactions in ultracold atomic and molecular gase

Dynamics of vorticity

Remarks are made about the status of research on the role of vorticity in fluid dynamics and some unsolved problems of current interest are described

Dependence on Reynolds number of high-order moments of velocity derivatives in isotropic turbulence

The results of a heuristic model of the fine scale structure of homogeneous turbulence are presented. Predictions are made about the way in which flatness and skewness factors of arbitrary order depend upon the Reynolds number of the turbulence

The large-scale structure of homogeneous turbulence

A field of homogeneous turbulence generated at an initial instant by a distribution of random impulsive forces is considered. The statistical properties of the forces are assumed to be such that the integral moments of the cumulants of the force system all exist. The motion generated has the property that at the initial instant E(kappa) = Ckappa^2 + o(kappa^2) where E(k) is the energy spectrum function, k is the wave-number magnitude, and C is a positive number which is not in general zero. The corresponding forms of the velocity covariance spectral tensor and correlation tensor are determined. It is found that the terms in the velocity covariance Rij(r) are O(r^−3) for large values of the separation magnitude r. An argument based on the conservation of momentum is used to show that C is a dynamical invariant and that the forms of the velocity covariance at large separation and the spectral tensor at small wave number are likewise invariant. For isotropic turbulence, the Loitsianski integral diverges but the integral $$\int_0^{\infty} r^2R(r)dr = \frac{1}{2}\pi C$$ exists and is invariant

Approach of a vortex pair to a rigid free surface in viscous fluid

The motion in a viscous incompressible fluid of a vortex pair toward a rigid plane wall on which slip is allowed is considered. It is shown that the centroids of vorticity do not approach the wall monotonically, and there is some rebound at a rate depending upon the viscosity and initial separation of the vortices

The number of waves on unstable vortex rings

An explanation is proposed for the dependence on Reynolds number and other parameters of the number of waves which appear on vortex rings formed by pushing fluid out of a tube. It is shown that the number of waves can be sensitive to the vorticity distribution in the core of the ring. The process of ring formation is discussed and it is concluded that peaked vorticity distributions, limited by viscosity, will occur. Quantitative estimates of the number of waves are made. Agreement with observation is satisfactory

Efficient multiparticle entanglement via asymmetric Rydberg blockade

We present an efficient method for producing $N$ particle entangled states using Rydberg blockade interactions. Optical excitation of Rydberg states that interact weakly, yet have a strong coupling to a second control state is used to achieve state dependent qubit rotations in small ensembles. On the basis of quantitative calculations we predict that an N=8 Schr\"odinger cat state can be produced with a fidelity of 84% in cold Rb atoms.Comment: 3 figure