Constant Phase Shift Research Articles

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as errors can be fully characterized. For multi-qubit operations, though, this is no longer the case as in the most general case analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g.~a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum information processing.

Beating Effects in a Single Nonlinear Dynamical System in a Neighborhood of the Resonance

The exact coincidence of external excitation and basic eigen-frequency of a single degree of freedom (SDOF) nonlinear system produces stationary response with constant amplitude and phase shift. When the excitation frequency differs from the system eigen-frequency, various types of quasi-periodic response occur having a character of a beating process. The period of beating changes from infinity in the resonance point until a couple of excitation periods outside the resonance area. Theabove mentioned phenomena have been identified in many papers including authors’ contributions. Nevertheless, investigation of internal structure of a quasi-period and its dependence on the difference of excitation and eigen-frequency is still missing. Combinations of harmonic balance and small parameter methods are used for qualitative analysis of the system in mono- and multi-harmonic versions. They lead to nonlinear differential and algebraic equations serving as a basis for qualitativeanalytic estimation or numerical description of characteristics of the quasi-periodic system response. Zero, first and second level perturbation techniques are used. Appearance, stability and neighborhood of limit cycles is evaluated. Numerical phases are based on simulation processes and numerical continuation tools. Parametric evaluation and illustrating examples are presented.

Calibration of photoelastic modulator based dichrometers: maintaining constant phase across the spectrum

Photoelastic modulators can alter the polarization state of a beam of ultraviolet, visible or infrared photons by means of periodic stress-induced differences in the refractive index of a transparent material that forms the optical element of the device and is isotropic in the absence of stress. They have found widespread application in instruments that characterize or alter the polarization state of a beam in fields as diverse as astronomy, structural biology, materials science and ultraviolet lithography for the manufacture of nano-scale integrated circuits. Measurement of circular dichroism, the differential absorption of left- and right circularly polarized light, and of strain-induced birefringence of optical components are major applications. Instruments using synchrotron radiation and photoelastic modulators with CaF2 optical elements have extended circular dichroism measurements down to wavelengths of about 130 nm in the vacuum ultraviolet. Maintaining a constant phase shift between two orthogonal polarization states across a spectrum requires that the amplitude of the modulated stress be changed as a function of wavelength. For commercially available photoelastic modulators, the voltage that controls the amplitude of modulation required to produce a specified phase shift, which is a surrogate for the stress modulation amplitude, has been shown to be an approximately linear function of wavelength in the spectral region where the optical element is transparent. But, extrapolations of such straight lines cross zero voltage at a non-zero wavelength, not at zero-wavelength. For modulators with calcium fluoride and fused silica optical elements, the zero-crossing wavelength is always in the spectral region where the optical element of the modulator strongly absorbs the incident radiation, and at a wavelength less than the longest-wavelength apparent resonance deduced from experimental values of the refractive index fit to the Sellmeier equation. Using a model that relates the refractive indices of a stressed optical element to the refractive index of its unstressed state, an expression for the modulator control voltage was derived that closely fits the experimental data. This result provides a theoretical rational for the apparently linear constant-phase programming voltage, and thus provides theoretical backing for the calibration procedure frequently used for these modulators. Other factors that can influence the calibration of a photoelastic modulator, including temperature and atmospheric pressure, are discussed briefly.

Superharmonic resonances in a two-dimensional non-linear photonic-crystal nano-electro-mechanical oscillator

We investigate the non-linear mechanical dynamics of a nano-optomechanical mirror formed by a suspended membrane pierced by a photonic crystal. By applying to the mirror a periodic electrostatic force induced by interdigitated electrodes integrated below the membrane, we evidence superharmonic resonances of our nano-electro-mechanical system; the constant phase shift of the oscillator across the resonance tongues is observed on the onset of principal harmonic and subharmonic excitation regimes.

Direct and inverse problems in x-ray three-crystal triple Laue case interferometry.

We study the mechanisms of forming x-ray moiré images arising under the action of one-dimensional rows of local concentrated forces at the output surface of a triple-crystalline triple Laue case interferometer for the cases of their orientation parallel and perpendicular to the vector of diffraction. The presence of constant phase shift of one of the interfering waves in the interferometer's analyzer results in the diminishing of period, contrast, and area of deformation moiré fringes. It is shown that the area of efficient interaction of phase and deformation moirés depends on both the magnitude of the constant phase shift and the magnitude and character of arrangement of local concentrated forces in rows.

Attenuation analysis of real GPR wavelets: The equivalent amplitude spectrum (EAS)

Absorption of a Ground Penetrating Radar (GPR) pulse is a frequency dependent attenuation mechanism which causes a spectral shift on the dominant frequency of GPR data. Both energy variation of GPR amplitude spectrum and spectral shift were used for the estimation of Quality Factor (Q*) and subsequently the characterization of the subsurface material properties. The variation of the amplitude spectrum energy has been studied by Spectral Ratio (SR) method and the frequency shift by the estimation of the Frequency Centroid Shift (FCS) or the Frequency Peak Shift (FPS) methods. The FPS method is more automatic, less robust. This work aims to increase the robustness of the FPS method by fitting a part of the amplitude spectrum of GPR data with Ricker, Gaussian, Sigmoid–Gaussian or Ricker–Gaussian functions. These functions fit different parts of the spectrum of a GPR reference wavelet and the Equivalent Amplitude Spectrum (EAS) is selected, reproducing Q* values used in forward Q* modeling analysis. Then, only the peak frequencies and the time differences between the reference wavelet and the subsequent reflected wavelets are used to estimate Q*. As long as the EAS is estimated, it is used for Q* evaluation in all the GPR section, under the assumption that the selected reference wavelet is representative. De-phasing and constant phase shift, for obtaining symmetrical wavelets, proved useful in the sufficiency of the horizons picking. Synthetic, experimental and real GPR data were examined in order to demonstrate the effectiveness of the proposed methodology.

Vibration parameter estimation methods for ultrasonic measurement systems – a review

A review of vibration signal estimation techniques employed in ultrasonic vibration measurement systems is presented. The review focuses on the Doppler signal extraction methods including the theory and analysis pertaining to the background of ultrasonic vibration measurement techniques. The phase modulated received signal in the vibration measurement system involves constant phase shift because of ultrasonic path length, phase shift introduced by Doppler effect because of vibrating object and the parametric phase shift caused by interaction of high frequency ultrasonic wave and low pressure developed by vibrating object. Among the three phase shifts, the Doppler phase shift contains the vibrating signal information and the extraction of Doppler signal helps in knowing the velocity of the vibrating object, amplitude and phase of the vibration. Various techniques of Doppler phase shift retrieval are categorised based on the modulation index estimation procedures from the received ultrasonic signal. An analysis is made based on the information retrieval methods for estimation of vibration signal parameters, range of the vibration amplitude, frequency and the preferable carrier frequency for transmission. Further, the analysis also presents various applications in which ultrasonic vibration measurements system are employed successfully.

Effect of flood basalt stratigraphy on the phase of seismic waveforms recorded offshore Faroe Islands

The generation of short-period multiples between highly heterogeneous layers of basalt flows can strongly alter transmitted seismic wavefields. These layers filter and modify penetrating waves, producing apparent attenuation and phase changes in the observed waveforms. We investigated the waveform and apparent phase changes of the primary seismic signal using mainly the maximum kurtosis approach. We compared the seismic recordings from two short-offset vertical seismic profiles (VSPs) with synthetic seismograms, generated from sonic logs in the same wells, and we found that short-period multiples cause a rapid broadening of the primary arrivals and strong apparent phase changes within a short depth interval below the top of the basalt flows. Relatively large uncertainties were associated with estimating constant phase shifts of the seismic arrivals within the topmost 250 m of the basalt sequences, where complex scattering occurred. Within this interval of the Brugdan I well, a phase-only compensation of the first arrivals with a frequency-independent, combined scattering, and intrinsic attenuation operator was unfeasible. At a greater depth, we found that the phase shifts, predicted by a VSP-derived effective [Formula: see text] value, were similar to those estimated from the VSP signals using the kurtosis method. Thus, phase-only compensation with a combined scattering and intrinsic attenuation operator could work well depending on the seismic signal bandwidth and the distribution, depth, and magnitude of the impedance contrasts in the basalt sequence.

Temporal analysis of fractional revivals of molecular observables following impulsive alignment

Laser-induced impulsive alignment of symmetric linear molecules leads to time-dependent observables which are analyzed in terms of their spectral components. Signals appear as sums over positive integers $\ensuremath{\ell}$ of periodic components ${A}_{2\ensuremath{\ell}}(t)$ with periods ${\ensuremath{\tau}}_{2\ensuremath{\ell}}={(2\ensuremath{\ell}c{B}_{0})}^{\ensuremath{-}1}$, where ${B}_{0}$ is the rotational constant in wave number units. Within each period ${\ensuremath{\tau}}_{2\ensuremath{\ell}}$, four fractional revivals at times $n{\ensuremath{\tau}}_{2\ensuremath{\ell}}/4$ $(n=0,1,2,3)$ exhibit constant successive phase shifts ${(\ensuremath{-}1)}^{\ensuremath{\ell}+p}\ensuremath{\pi}/2$ depending on the even-odd parity $(p=0,1)$ of the initial rotational states. This analysis gives a comprehensive account of the so-called high-order revivals usually discussed in terms of fractional revivals within the period ${\ensuremath{\tau}}_{2}$ of the average value $\ensuremath{\langle}{cos}_{\ensuremath{\vartheta}}^{2}\ensuremath{\rangle}(t)$ of ${cos}^{2}(\ensuremath{\vartheta})$, where $\ensuremath{\vartheta}$ is the angle between the molecular axis and the alignment direction. These considerations are illustrated by experiments and numerical calculations of laser-induced impulsive alignment and tunnel ionization of ${\text{CO}}_{2}$ molecules for which calculated ionization yields of fixed-in-space molecules are available.

Correlation properties of Geodesic Acoustic Modes in the T-10 tokamak

Geodesic acoustic mode (GAM) of electrostatic potential and density fluctuations are simultaneously measured by Heavy Ion Beam Probe (HIBP) and Correlation Reflectometry (CR). The regimes with Ohmic and electron cyclotron resonance heating (ECRH) were studied (B = 2.2 T, Ip = 210 - 240 kA, ne = (2.3 - 3.7) × 1019 m-3, PEC ≤ 0.6 MW). GAMs are more pronounced during ECRH, when the typical frequencies were seen in the narrow band from 22 to 27 kHz for the main peak and 25-30 kHz for the higher frequency satellite peak. The local values of electric potential and density fluctuations show the significant coherency and constant phase shift at GAM frequency range. The existence of the long-distance (one quarter of the torus) correlations of core electric potential and density for GAM implying that GAM is a global mode, was shown for the first time in tokamaks.

Novel Multi-way Broadband Differential Phase Shifter With Uniform Reference Line Using Coupled Line Structure

Conventional passive differential phase shifters (DPSs) usually require different reference lines to realize varied differential phase shifts, this results in both complex structure and bulky size for multi-way poly-phase applications. To resolve the problem, a DPS configuration with uniform reference line is proposed. It is constructed using basic coupled lines with simplicity in both design and fabrication procedures. The delay lines of the phase shifter have a similar structure and maintain desired constant phase shift compared with the uniform reference line over a wide bandwidth. To verify the proposed configuration, a four-way DPS which is comprised of 3 delay lines and a reference line, is designed, fabricated and measured. The delay lines provide the corresponding constant phase shifts (45 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , 90 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , 135 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> compared to the reference line. Over a bandwidth of 45%, excellent performance is achieved with small insertion loss and phase deviation.

Rhythmic ganglion cell activity in bleached and blind adult mouse retinas.

In retinitis pigmentosa – a degenerative disease which often leads to incurable blindness- the loss of photoreceptors deprives the retina from a continuous excitatory input, the so-called dark current. In rodent models of this disease this deprivation leads to oscillatory electrical activity in the remaining circuitry, which is reflected in the rhythmic spiking of retinal ganglion cells (RGCs). It remained unclear, however, if the rhythmic RGC activity is attributed to circuit alterations occurring during photoreceptor degeneration or if rhythmic activity is an intrinsic property of healthy retinal circuitry which is masked by the photoreceptor’s dark current. Here we tested these hypotheses by inducing and analysing oscillatory activity in adult healthy (C57/Bl6) and blind mouse retinas (rd10 and rd1). Rhythmic RGC activity in healthy retinas was detected upon partial photoreceptor bleaching using an extracellular high-density multi-transistor-array. The mean fundamental spiking frequency in bleached retinas was 4.3 Hz; close to the RGC rhythm detected in blind rd10 mouse retinas (6.5 Hz). Crosscorrelation analysis of neighbouring wild-type and rd10 RGCs (separation distance <200 µm) reveals synchrony among homologous RGC types and a constant phase shift (∼70 msec) among heterologous cell types (ON versus OFF). The rhythmic RGC spiking in these retinas is driven by a network of presynaptic neurons. The inhibition of glutamatergic ganglion cell input or the inhibition of gap junctional coupling abolished the rhythmic pattern. In rd10 and rd1 retinas the presynaptic network leads to local field potentials, whereas in bleached retinas additional pharmacological disinhibition is required to achieve detectable field potentials. Our results demonstrate that photoreceptor bleaching unmasks oscillatory activity in healthy retinas which shares many features with the functional phenotype detected in rd10 retinas. The quantitative physiological differences advance the understanding of the degeneration process and may guide future rescue strategies.

Bifurcation study of phase oscillator systems with attractive and repulsive interaction.

We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations.

Differential RF Phase Shifter With Harmonic Suppression

For the first time, a differential phase shifter with harmonic suppression is proposed. Not only does the proposed structure provide a constant differential phase shift over a wide bandwidth, but it also has good harmonic rejection. Compared to the existing coupled-line phase shifters, the proposed stub-loaded transmission line configurations show good performance, with simplicity in both design and fabrication. Design formulas for the structure are derived using an analytical technique. Optimal design parameters for typical differential phase shifts which are independent of substrate used and operating frequency are provided to allow for a quick design procedure. To illustrate the principles, a broadband 45 ° phase shifter with harmonic suppression is designed, fabricated, and measured. It achieved excellent performance with small insertion loss, small phase deviation within the desired bandwidth, and good out-of-band rejection.

Multi-Way and Poly-Phase Aligned Feed-Forward Differential Phase Shifters

Traditional two-way passive differential phase shifters (DPSs) are comprised of a reference line and a delay line. To realize a passive multi-way poly-phase DPS, a single reference line is not possible and a cascaded network becomes necessary. This results in both a cumbersome and complex structure, with large phase error that propagates through the network. A novel phase shifter is presented here that allows multi-way and poly-phase differential phase shift using just one common reference line. This phase shifter is constructed using a newly proposed phase-shift component in all element designs, where each element maintains a constant phase shift with adjacent elements. This characteristic for DPSs offers a simple solution to multi-way poly-phase systems, such as those found in phased arrays. To validate the proposed concept, phase shifters are designed as a group of five different elements operating at 2 GHz, with each maintaining a constant phase shift (45 $^{\circ}$ , 90 $^{\circ}$ , 135 $^{\circ}$ , 180 $^{\circ}$ ) compared to a reference element. Measured results agree well with the theoretical analysis. Over a 40% bandwidth the achieved phase shifts are ${\hbox{45}}^{\circ} {\pm} {\hbox{0.9}}^{\circ},$ ${\hbox{90}}^{\circ} {\pm} {\hbox{1.5}}^{\circ},$ ${\hbox{135}}^{\circ} {\pm} {\hbox{4}}^{\circ}$ , and ${\hbox{180}}^{\circ} {\pm} {\hbox{4.2}}^{\circ}$ , while amplitude imbalances are all less than 0.25 dB.

Ramsey-comb spectroscopy: Theory and signal analysis

We recently demonstrated that the spectroscopic accuracy and resolution of optical frequency combs can be obtained from a series of Ramsey-like measurements using only two amplified frequency comb pulses at variable delays. In this work we present a comprehensive analytical framework of this Ramsey-comb method in both time and frequency domains. It is shown that as opposed to traditional forms of spectroscopy, the signal analysis can be performed purely in the time domain, based on the temporal phases of the individual Ramsey signals. We give a detailed description of the robust fitting algorithm relying solely on this phase information and discuss special features such as an insensitivity to (transition-independent) spectral line-broadening mechanisms and constant phase shifts, e.g., due to the ac Stark effect from the excitation pulses themselves. The precision and resolution of the Ramsey-comb fitting method is assessed via numerical simulations, including cases of transition-dependent broadening mechanisms and phase shifts.

Characterization of the spatiotemporal evolution of ultrashort optical pulses using FROG holography.

We propose holographically recorded frequency-resolved-optical-gating (FROG) measurement for probing the evolution of ultrashort optical pulses at multiple locations. As a proof-of-concept demonstration of our method, we record holographic FROG traces at five axial locations as we traverse through the focus of an objective lens along its axis using BaTiO(3) micro-cluster as the nonlinear medium and retrieve the amplitude and phase of the ultrashort pulse at each location. Moreover, the group delay of the pulse retrieved numerically using FROG holography is used to compute the separation between the five locations which agree well with the experimentally measured distances. This study suggests that FROG holography can be used to remove the ambiguity regarding arbitrary constant phase and arbitrary temporal shift in the retrieved pulse at each location (upto to an overall constant phase).

A Novel Unity-Gain Phase Shifter for Measuring Power System Quantities

The paper presents a novel unity-gain phase shifter. Based on the voltage control all-pass filter using an analogue multiplier along with a frequency-to-voltage converter, this approach can theoretically both provide unity-gain and maintain a predetermined phase shift constant over a wide frequency range. As no complicated calculation circuit is required, the proposed scheme can be implemented using a simple hardware circuit. Some experimental results are provided to verify the validity of the proposed scheme.

Synchronization extends the life time of the desired behavior of globally coupled systems

Synchronization occurs widely in natural and technological world, but it has not been widely used to extend the life time of the desirable behavior of the coupled systems. Here we consider the globally coupled system consisting of n units and show that the initial synchronous state extends the lifetime of desired behavior of the coupled system in the case when the excitation of one or few units is suddenly (breakdown of energy supply) or gradually (as the effect of aging and fatigue) switched off. We give evidence that for the properly chosen coupling the energy transfer from the excited units allows unexcited units to operate in the desired manner. As proof of concept, we examine the system of coupled externally excited rotating pendula. After the partial excitation switch off the initial complete synchronization of all pendula is replaced by phase synchronization with a constant phase shift between the clusters of excited and unexcited pendula. Our results show that the described extension of the system's life time occurs for the wide range of coupling parameters and is robust to the external perturbations.

Spatial quasi-phase-shifting technique for single-frame dynamic fringe analysis

Phase demodulation from carrier-frequency fringe patterns is the core of many optic measurements. We propose spatial quasi-phase-shifting technique by expressing the fringe signal in the frequency-modulated form, which requires only one frame fringe pattern for instantaneous and dynamic measurements. In an area smaller than a fringe period, there substantially exists an approximately constant phase shift between spatially adjacent sample points. The technique is capable of demodulating the phase with such intra-frame phase shifts, which makes the instantaneous and dynamic measurement possible. The technique implements demodulation within three spatially adjacent neighbors, achieving spatial localization as good as a several-point level. Both numerical simulation and experiment are presented to verify its performance.