Relative Phase Measurements Research Articles

Quantum theory of angle and relative-phase measurement

The complementarity between time and energy, as well as between an angle and a component of angular momentum, is described at three different layers of understanding. The phenomena of super-resolution are readily apparent in the quantum phase representation which also reveals that entanglement is not required. We modify Schwinger's harmonic oscillator model of angular momentum to include the case of photons. Therein the quantum angle measurement is shown to be equivalent to the measurement of the relative phase between the two oscillators. Two reasonable ways of dealing with degeneracy are shown to correspond to: a conditional measurement which takes a snapshot in absolute time (corresponding to adding probability amplitudes); and a marginal measurement which takes an average in absolute time (corresponding to adding probabilities). The sense in which distinguishability is a "matter of how long we look" is discussed and the meaning of the general theory is illustrated by taking the two oscillators to be circularly polarized photons. It is shown that an odd number of x-polarized photons will never have an angle in correspondence with the y-axis; but an even number of x-polarized photons always can! The behavior of an x-polarized coherent state is examined and the snapshot angular distributions are seen to evolve into two counter-rotating peaks resulting in considerable correspondence with the y-axis at the time for which a classical linear polarization vector would shrink to zero length. We also demonstrate how the probability distribution of absolute time (herein a measurable quantity, rather than just a parameter) has an influence on how these snapshot angular distributions evolve into a quantum version of the polarization ellipse.

Enhancement of the accuracy of single-epoch GPS positioning for long baselines by local ionospheric modelling

Single-epoch relative GPS positioning has many advantages, especially for monitoring dynamic targets. In this technique, errors occurring in previous epochs cannot affect the position accuracy at the current epoch, but careful processing is required, and resolving carrier phase ambiguities is essential. Statistical ambiguity resolution functions have been used to determine the best values of these ambiguities. The function inputs include as a minimum the known base station position, the approximate roving antenna position, and the dual-frequency carrier phase measurements from both receivers. We investigate different solutions to find the ambiguity function inputs that achieve the highest ambiguity resolution success rate. First, we address the rover seed position. A regionally filtered undifferenced pseudorange coordinate solution proves better than a double-differenced one. Multipath errors approximately repeat themselves every sidereal day in the case of static or quasi-static antennas; applying a sidereal filter to the pseudorange-derived positions mitigates their effects. Second, we address the relative carrier phase measurements, which for medium to long baselines are significantly affected by ionospheric propagation errors imperfectly removed during differencing. In addition to the International GNSS Service ionospheric model, we generate a local pseudorange-based ionospheric correction. Applying this correction improves the quality of the phase measurements, leading to more successful ambiguity resolution. Temporally smoothing the correction by means of a Kalman filter further improves the phase measurements. For baselines in the range 60–120 km, the mean absolute deviation of single-epoch coordinates improves to 10–20 cm, from 30–50 cm in the default case.

Interlimb Coordination Patterns in People with Parkinson's Disease

Efficient human walking requires the coordinated function of both the upper and lower extremities. In healthy adults as walking speeds reach 0.8 m/s and above, the arms transition from an in-phase relationship to an out-of-phase relationship with each other. Further, arm swing synchronizes with the stride frequency of the contralateral leg. It is well documented that people with Parkinson's disease (PD) show diminished arm swing during normal walking and that this may be one factor contributing to the increased falls in this population. Yet, it is unknown whether the reduction in arm swing affects interlimb coordination patterns in this specific population. PURPOSE: To investigate the interlimb coordination patterns present in people with PD during normal walking and to compare these patterns to age matched healthy older adults walking at similar speeds. METHODS: Eighteen individuals with Parkinson's disease and nine age (± 2 years) and gait velocity (±0.1 m/s) matched healthy older adults participated. Kinematic data of overground walking trials were collected utilizing a 12 camera Vicon motion capture system (Vicon Nexus, Oxford, UK). Arm and leg coordination was quantified by determining point estimate of relative phase and covariance measures. Point estimate of relative phase was calculated as the phase difference in time of maximum shoulder flexion and maximum hip flexion divided by duration of the stride cycle. Independent samples t-tests were run to analyze between-group differences. RESULTS: Comparatively, the persons with PD showed statistical reductions in comparing hip-shoulder covariance of the affected shoulder and contralateral hip compared to the healthy controls (p=.016). The persons with PD also exhibited large differences in PERP measures in comparison to the control group. The mean PERP value for the PD group was 33° compared to 9° in the control group, however, only a statistical trend could be identified (p=.077). CONCLUSION: Evidence shows that PD causes reduction in interlimb coordination patterns. The reductions in coordination may attribute to the changes seen in gait patterns as the disease progresses and risks for falling.

Phase-Sensitive Measurements of Order Parameters for Ultracold Atoms through Two-Particle Interferometry

Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms as well as condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states of fermions that could be realized in optical lattices in the Hubbard regime. Identifying these states in experiments requires measurements of the relative phase of different components of the entangled pair wave function. We propose and discuss two schemes for such phase-sensitive measurements, based on two-particle interference revealed in atom-atom or atomic density correlations. Our schemes can also be used for relative phase measurements for nontrivial particle-hole order parameters, such as d-density wave order.

Computation of continuous relative phase and modulation of frequency of human movement

Continuous relative phase measures have been used to quantify the coordination between different body segments in several activities. Our aim in this study was to investigate how the methods traditionally used to compute the continuous phase of human rhythmic movement are affected by modulations of frequency. We compared the continuous phase computed method with the traditional method derived from the position–velocity phase plane and with the Hilbert Transform. The methods were tested using sinusoidal signals with a modulation of frequency between or within cycles. Our results showed that the continuous phase computed with the first method results in oscillations in the phase time-series not expected for a sinusoidal signal and that the continuous phase is overestimated with the Hilbert Transform. We proposed a new method that produces a correct estimation of continuous phase by using half-cycle estimations of frequency to normalize the phase planes prior to calculating phase angles. The findings of the current study have important implications for computing continuous relative phase when investigating human movement coordination.

ACL Research Retreat V

ACL Research Retreat V

Characterization of Fourier-synthesized optical waveforms from optically phase-locked femtosecond multicolor pulses

For characterization of Fourier-synthesized optical waveforms of femtosecond multicolor phase-coherent pulses, we report relative-phase measurements among Fourier components from optically phase-locked two-color mode-locked lasers. The interference of two simultaneous second-order frequency-mixing processes in a common nonlinear crystal was utilized. The relative phases among three-color components with a frequency ratio of 2omega:3omega:4omega were measured by observing the interference fringes of two simultaneous frequency-mixing outputs. The inner field structure of the synthesized waveforms can be determined except for the ambiguity of its temporal shift with respect to the synthesized envelope, which corresponds to the carrier-envelope phase slip of one of the source lasers.

ROLE OF INTER-JOINT COORDINATION IN REDUCING KINEMATIC VARIABILITY: AGE AND SIZE PREDICTION

Continuous relative phase (CRP), a variable used to quantify intersegmental coordination, is difficult to interpret if care is not taken regarding the assumptions and limitations of the measure. Specifically, CRP is often interpreted as a higher resolution form of discrete relative phase (DRP). DRP, however, yields information regarding the relative dispersion of events in oscillatory signals while CRP describes their relationship in a higher order phase-plane domain. In this paper we address issues surrounding the calculation of CRP and suggest a new interpretation based on the aforementioned methodological issues. Through the use of test signals, with known properties, it was found that the CRP information will be arbitrary if no normalization procedures are used to account for frequency differences in the component oscillators. In addition, signals with non-sinusoidal trajectories will produce patterns in CRP that are not equivalent to discrete relative phase (DRP) measures. The implications of these issues are discussed.

1/f β fluctuations in bimanual coordination: an additional challenge for modeling

We analyzed the correlation structure of discrete relative phase (DRP) series in bimanual in-phase and anti-phase coordination by associating a number of fractal methods and using discrete rather than continuous relative phase measurement. ARFIMA/ARMA modeling provided statistical evidence for the presence of long-range correlation, and the series were unambiguously characterized as 1/f (beta) noise. Diverging accounts of bimanual coordination are defended in the literature. Since the evidence for 1/f (beta) noise provides new insight into the properties of stability in coordination, it should be considered as an empirical criterion for determining which mechanisms are likely to be engaged in bimanual coordination models. We discussed some implications for studying the neural basis of coordination, and we tested the performance of three current models in accounting for 1/f (beta) noise in DRP. None of these models was proven to generate the expected correlation structure.

Bose-Einstein condensates relative phase measurements through atomic homodyne detection

The dynamics of a two-mode Bose-Einstein condensate trapped in a double-well potential results approximately in an effective Rabi oscillation regime of exchange of population between both wells for sufficiently strong overlap between the modes functions. Facing this system as a temporal atomic beam splitter we show that this regime is optimal for a nondestructive atom-number measurement allowing an atomic homodyne detection, thus yielding indirect relative phase information about one of the two-mode condensates.

The Effect of Resistance Training on Hip-Knee Continuous Relative Phase Measures during Accelerative Sprinting.

PURPOSE: The aim of the present study was to examine the hip-knee coordination patterns during accelerative sprinting following a period of resistance training (RT). METHODS: Seventeen physically active males participated in a randomized controlled study. An experimental group of 10 men completed an eight week periodized RT intervention, while a control group of 7 men did not train. Pre and post-training measures of 10 m and 20 m sprint time, maximum strength and explosive strength were recorded. The first three strides of the 20 m sprint were videoed to provide kinematic data. Phase-plane diagrams and relative phase (RP) measures of the hip and knee joints were used to assess coordination during the sprint. RESULTS: The RT intervention resulted in significant increases in measures of maximum and explosive strength (p < 0.05) immediately following the training period, but sprint times were not significantly reduced (p > 0.05). Despite significant increases in the range of motion about the knee joint during the first three strides of the sprint and significant increases in the angle of extension about the hip and knee joints at toe-off, the coordination between the joints assessed with RP measures was not significantly changed immediately following the training period. CONCLUSIONS: Eight weeks of RT resulted in substantial improvements in muscular strength. However, there were no changes in the coordination between the hip and knee joints during the accelerative sprinting performance immediately following the RT program.

Structure and mechanical properties of TiBN coatings fabricated by dc reactive sputtering technique

TiBN hard coatings were fabricated by dc reactive sputtering technique, using powders target, Ti (90 wt.%) and BN (10 wt.%), prepared by indirect reactive ball milling. The nitrogen flux was varied at 0, 5, 10, 15 and 20 sccm, respectively; while the argon flux was kept constant at 25 sccm. The effects of nitrogen flux on the structure and mechanical properties of these coatings were studied. The microstructure and phase composition of coatings were studied by means of X-ray diffraction and energy dispersive spectroscopy. The fractions of the relative phase were calculated from the chemical composition stoichiometry obtained by energy dispersive spectroscopy. X-ray diffraction and fractions of the relative phase measurements confirmed the presence of three mixtures phases, TiN, BN and TiB 2, being dominant with 64.9% for sample M1. When the nitrogen flux increased, the mechanical properties decreased. This was due to the diminishments in TiB 2 phase, to a minimum value of 25%, and the crystalline TiN phase changed completely in amorphous phase, leaving only the c-BN. The variations in nanohardness and elastic modulus values were to structural and chemical composition changes with the increase of nitrogen gas flow. The sample M1 presented the highest hardness (23.52 GPa) and strength (775.5 MPa).

Dual-task influences on retrieval from semantic memory and coordination dynamics

Bimanual 1:1 rhythmic coordination was performed while retrieving words from a specified category. The effects of divided attention (DA) on coordination were indexed by changes in mean relative phase and recurrence measures of shared activity between the two limbs. Effects of DA on memory were indexed by deficits in exemplars retrieved relative to the baseline. Shifts in relative phase were found, accompanied by a recall deficit for DA during the retrieval task. DA also reduced the degree of shared activity between left and right rhythmic motions. Our discussion focuses on DA-induced parameter changes in retrieval and coordination dynamics, as well as on the hypothesis that stability is the general factor mediating dual-task performance.

Generation of attosecond pulses in molecular nitrogen

We have generated attosecond pulse trains in an ensemble of randomly aligned nitrogen molecules. Measurements of the high-order harmonic relative phases and amplitudes allow us to reconstruct the temporal profile of the attosecond pulses. We show that in the considered spectral range, the latter is very similar to the pulse train generated in argon under the same conditions. We discuss the possible influence of the molecular structure in the generation process, and how it can induce subtle differences on the relative phases.

Mapping of angular and spatial optical intensity distributions issuing from nanostructured slits, milled into subwavelength metallic layers

We present the results of experiments in support of the composite diffracted evanescent wave (CDEW) model that describes the response of subwavelength planar structures to illumination by polarised plane-wave optical excitation. These experiments consist of four types of data: (1) angular distribution of the transmitted light as a function of quarterwave groove displacement, (2) efficiency of transmission through a subwavelength slit as a function of slit-groove distance, (3) relative phase measurements by far-field interference patterns of transmitted light as a function of slit-groove displacement, and (4) far-field spatial profile of the optical field intensity issuing from subwavelength slits flanked by periodic grooves and fabricated on a thin metallic layer. These types of structure are of interest for the manipulation of cold atoms by optical potentials near surfaces.

Encoding and Retrieval During Bimanual Rhythmic Coordination.

In 2 experiments, bimanual 1:1 rhythmic coordination was performed concurrently with encoding or retrieval of word lists. Effects of divided attention (DA) on coordination were indexed by changes in mean relative phase and recurrence measures of shared activity between the 2 limbs. Effects of DA on memory were indexed by deficits in recall relative to baseline. For DA at both encoding and retrieval, the equilibrium values of relative phase were shifted and the degree of shared activity between left and right rhythmic motions was reduced. Recall was reduced, however, only for DA at encoding. The results corroborate and extend those obtained with more conventional secondary tasks (e.g., visual reaction time), suggesting attention dissimilarities between episodic encoding and retrieval.

Variability in Head Movement during Gait Transitions

Predictions from a model of coupled oscillators, which was based on stationary interlimb coordination, were examined in locomotor intralimb coordination. The present study measured head linear and angular accelerations and coordination relationships of the head and torso, e.g., using relative phase measures, during walking and running on a treadmill. Head linear acceleration increased from walking to running and decreased from running to walking, and head pitch/torso pitch relative phase decreased from walking to running and increased from running to walking. No other measures were significantly different for either walking or running (head angular acceleration, mean head vertical displacement/head pitch relative phase, SD head vertical displacement/head pitch, and SD head pitch/torso pitch). This information will aid further understanding of the many aspects involved in locomotor coordination.

Technique of quantum-state transfer for a double-Λatomic beam

We theoretically examine the quantum-state transfer process from light to a continuous atom laser by extending the original Fleischhauer-Gong scheme [M. Fleischhauer and S. Gong, 88, 070404 (2002)] to a double-$\ensuremath{\Lambda}$ atomic system. We find that the intensity of the output matter waves is controlled by the relative phase of two coherent probe lights, which may provide an interesting method for the measurement of the initial relative phase of two independent light sources.

Limitations in the use and interpretation of continuous relative phase

Continuous relative phase (CRP), a variable used to quantify intersegmental coordination, is difficult to interpret if care is not taken regarding the assumptions and limitations of the measure. Specifically, CRP is often interpreted as a higher resolution form of discrete relative phase (DRP). DRP, however, yields information regarding the relative dispersion of events in oscillatory signals while CRP describes their relationship in a higher order phase-plane domain. In this paper we address issues surrounding the calculation of CRP and suggest a new interpretation based on the aforementioned methodological issues. Through the use of test signals, with known properties, it was found that the CRP information will be arbitrary if no normalization procedures are used to account for frequency differences in the component oscillators. In addition, signals with non-sinusoidal trajectories will produce patterns in CRP that are not equivalent to discrete relative phase (DRP) measures. The implications of these issues are discussed.

Phase Offset of Rotation-Powered X-ray Pulsars

Combing the data of all the 10 rotation-powered pulsars that have measurements of relative phase of radio and X-ray pulses, we report here the behavior of radio/X-ray phase offset. We find that the radio/X-ray offset of normal pulsars does not show the trend of increase with increasing pulsar period as the radio/gamma-ray offset exhibits. The offset of millisecond pulsars is generally much less than that of the normal pulsars. Such phenomenon should also be taken into account by the high energy models for pulsars.