Accumulated Phase Difference Research Articles

High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions

Numerical simulations of 15 orbits of an equal-mass binary black hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasi-circular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first $\sim 15$ cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, {\em generic} time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6--7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly ($<1%$ amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.

Optical control of the quantum-state distribution of vibrational wave packets using trains of phase-locked pulses

An intuitive scheme for controlling the quantum state composition of one-coordinate molecular wave packets is developed. The accumulated phase difference between the various components of the molecular wave packet is determined, and then a sequence of phase-locked optical pulses is employed to selectively enhance or depopulate specific vibrational states, or sets of vibrational states. The quantum state composition of the resulting wave packet, and the efficiency of the control scheme, is determined by calculating the multi-pulse response of the time-dependent vibrational state populations.

Analytical design of X-couplers

Symmetric X-couplers are analyzed using the supermode approach. Constraints for lossless propagation are presented. A simple analytic approximation for the total accumulated phase difference of the supermodes is found that enables the calculation of the coupling ratio of arbitrary symmetric X-couplers. Good agreement is found between results obtained with the proposed method and data calculated using a beam-propagation method. The impact of several design parameters on the coupling ratio is discussed. Due to the simplicity of the structure, X-couplers are well suited for being realized by direct light-writing techniques.

Optical control of the rotational angular momentum of a molecular Rydberg wave packet.

An intuitive scheme for controlling the rotational quantum state of a Rydberg molecule is demonstrated experimentally. We determine the accumulated phase difference between the various components of a molecular electron wave packet, and then employ a sequence of phase-locked optical pulses to selectively enhance or depopulate specific rotational states. The angular momentum composition of the resulting wave packet, and the efficiency of the control scheme, is determined by calculating the multipulse response of the time-dependent Rydberg populations.

A simple, fast and accurate method of designing directional couplers by evaluating the phase difference of local supermodes

The local supermode formalism and a three-dimensional beam propagation method (BPM) are combined in designing directional couplers. The accumulated phase difference of the two local supermodes in the input or output region is evaluated quickly with the assistance of the BPM. The design method is simple, fast and accurate. A comparison of the present method with some other design methods is given. The design results are verified both numerically and experimentally.

Wave-function recombination instability in cold-atom interferometers

Cold-atom interferometers use guiding potentials that split the wave function of the Bose-Einstein condensate and then recombine it. We present a theoretical analysis of the wave-function recombination instability that is due to the weak nonlinearity of the condensate. It is most pronounced when the accumulated phase difference between the arms of the interferometer is close to an odd multiple of $\ensuremath{\pi}$ and consists in exponential amplification of the weak ground state mode by the strong first excited mode. The instability exists for both trapped-atom and beam interferometers.

Generating Consistent Motion Transition via Decoupled Framespace Interpolation

The framespace interpolation algorithm abstracts motion sequences as 1D signals, and interpolates between them to create higher dimension signals, with weights drawn from a user specified curve in a bounded region. We reformulate the algorithm to achieve motion‐state based transition via dynamic warping of framespaces and automatic transition timing via framespace frequency interpolation. Basis motions displaying diverse coordination configurations between upper and lower body‐halves, cannot be consistently corresponded at a macro level. We address this problem here, through decoupled blending of these halves to achieve true consistency, and eliminate accumulated phase differences via cosine phase warp functions. This generalization enables interpolation of motions with diverse coordinations between the upper and lower bodies.

Compensation of nonlinear self-focusing in high-power lasers

We report on experimental results and the numerical modeling of the compensation of nonlinear self-focusing effects occurring in a high-power Nd:glass laser system at intensities above 1 GW/cm/sup 2/. A GaAs wafer with a negative nonlinear refractive index was used for the cancellation of the accumulated phase difference along the beam direction in a nonlinear medium (B integral). A numerical model is developed to calculate the behavior of the experimental setup.

Measurements of Relative Phase in Two-Component Bose-Einstein Condensates

We have measured the relative phase of two Bose-Einstein condensates (BEC) using a time-domain separated-oscillatory-field condensate interferometer. A single two-photon coupling pulse prepares the double condensate system with a well-defined relative phase; at a later time, a second pulse reads out the phase difference accumulated between the two condensates. We find that the accumulated phase difference reproduces from realization to realization of the experiment, even after the individual components have spatially separated and their relative center-of-mass motion has damped.

A novel optical current transducer for power systems

Abstract An optical current transducer (OCT) has been developed for high voltage applications based on the Faraday effect with a bulk glass sensing element. It utilises a novel dual-loop optical path with no accumulated phase difference in which the light is sent back along nearly the same path in the reverse direction by means of a specially-designed quadruple-reflection prism. The sensitivity of the OCT is nearly twice that of the former single-loop OCT due to the non-reciprocity of the Faraday effect; whereas the effects of birefringence and temperature are virtually eliminated by virtue of their reciprocity. The operating results show that the OCT functions satisfactorily, with an error of less than ±0.2% at room temperature for currents up to 800 A. There was negligible temperature dependency over a temperature range from −15 to +40°C.

On the detection of mutual perturbations as proof of planets around PSR1257+12

Unambiguous detection of the consequences of mutual perturbations of the hypothesized planets about the pulsar PSR1257+12 would be unassailable proof of their existence. Nearly all of the residuals in the times of arrival (TOA) of the pulses after subtraction of the TOA predicted from the best fit constant period model are accounted for by including the effects of two orbiting planets with constant orbital parameters. The nature and magnitude of additional residuals in the TOA due to the gravitational interactions between the planets are determined by numerically calculating the TOA residuals for the orbital motion including the perturbations and subtracting the TOA residuals from analytic expressions of the orbital motion with orbital parameters fixed at averaged values. The TOA residual differences so obtained oscillate with periods comparable to the orbital periods with the oscillations varying in amplitude as a function of epoch within any given observational period. The signature of the perturbations is thus a quasiperiodic modulation of the residual differences obtained after removal of the effects of the orbital motion with best fit, constant orbital parameters. The amplitudes of this modulation reach about 10μsec for observational periods exceeding 1000 days for the minimum planetary masses with sini = 1, and they increase as 1 / sini for 1 / sini < 5, wherei is the inclination of the orbit plane to that of the sky. Greater accumulated phase differences between the effects of perturbed and unperturbed orbital motions are available in the times of zero values in the observed and predicted TOA residuals and these comprise a second signature of the perturbations. The perturbation signatures should become detectable as the observation interval approaches 1000 days.

Computational study of the locking of electronic angular momentum in diatomic quasimolecules

A numerical study is performed for the locking of an electronic angular momentum j=1 to the molecular axis during a collision of two atoms interacting via a potential proportional to an inverse power of the interatomic distance, R. Limitations to the notion of the locking radius and slipping probability are discussed in connection with the steepness of the interaction governed by the exponent n. Numerical calculations confirm the authors' earlier analytical result: the optimal criterion for determination of the locking radius is a condition for the accumulated phase difference between two molecular states. Analytical expressions are suggested for the locking angle and the slipping probability. The implication of the locking approximation for calculation of the quasiclassical scattering matrix is discussed.