Tracy S. Clement

Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum

We have created heralded coherent-state superpositions (CSSs) by subtracting up to three photons from a pulse of squeezed vacuum light. To produce such CSSs at a sufficient rate, we used our high-efficiency photon-number-resolving transition edge sensor to detect the subtracted photons. This experiment is enabled by and utilizes the full photon-number-resolving capabilities of this detector. The CSS produced by three-photon subtraction had a mean-photon number of 2.75{sub -0.24}{sup +0.06} and a fidelity of 0.59{sub -0.14}{sup +0.04} with an ideal CSS. This confirms that subtracting more photons results in higher-amplitude CSSs.

Calibration of sampling oscilloscopes with high-speed photodiodes

We calibrate the magnitude and phase response of equivalent-time sampling oscilloscopes to 110 GHz. We use a photodiode that has been calibrated with our electrooptic sampling system as a reference input pulse source to the sampling oscilloscope. We account for the impedance of the oscilloscope and the reference photodiode and correct for electrical reflections and distortions due to impedance mismatch. We also correct for time-base imperfections such as drift, time-base distortion, and jitter. We have performed a rigorous uncertainty analysis, which includes a Monte Carlo simulation of time-domain error sources combined with error sources from the deconvolution of the photodiode pulse, from the mismatch correction, and from the jitter correction

Amplitude and Phase Measurements of Femtosecond Pulse Splitting in Nonlinear Dispersive Media

Frequency-resolved optical gating is used to characterize the propagation of intense femtosecond pulses in a nonlinear, dispersive medium. The combined effects of diffraction, normal dispersion, and cubic nonlinearity lead to pulse splitting. The role of the phase of the input pulse is studied. The results are compared with the predictions of a three-dimensional nonlinear Schrödinger equation.

Covariance-based uncertainty analysis of the NIST electrooptic sampling system

We develop a covariance matrix describing the uncertainty of mismatch-corrected measurements performed on the National Institute of Standards and Technologys electrooptic sampling system. This formulation offers a general way of describing the uncertainties of the measurement system in both the temporal and frequency domains. We illustrate the utility of the approach with several examples, including determining the uncertainty in the temporal voltage generated by the photodiode

Calibrating electro-optic sampling systems

We apply frequency-domain impedance mismatch corrections to a temporal electro-optic sampling system and use it to characterize the magnitude and phase response of a photoreceiver that is physically far removed from the point where the voltage waveforms are measured. We identify and evaluate additional sources of measurement uncertainty.

Estimating the Magnitude and Phase Response of a 50 GHz Sampling Oscilloscope Using the "Nose-to-Nose" Method

We describe estimation of the magnitude and phase response of a sampling oscilloscope with 50 GHz bandwidth using the nose-to-nose method. The measurements are corrected for the non-ideal properties of the oscilloscope and calibration apparatus, including mismatch and time-base distortion, drift, and jitter. The mean and standard deviation of repeated measurements of an ensemble of three oscilloscope samplers are reported, along with attempts to verify the magnitude calibration using a swept sine-wave method.

Traceable Waveform Calibration With a Covariance-Based Uncertainty Analysis

We describe a method for calibrating the voltage that a step-like pulse generator produces at a load at every time point in the measured waveform. The calibration includes an equivalent-circuit model of the generator that can be used to determine how the generator behaves when it is connected to arbitrary loads. The generator is calibrated with an equivalent-time sampling oscilloscope and is traceable to fundamental physics via the electro-optic sampling system at the National Institute of Standards and Technology. The calibration includes a covariance-based uncertainty analysis that provides the uncertainty at each time in the waveform vector and the correlations between the uncertainties at the different times. From the calibrated waveform vector and its covariance matrix, we calculate pulse parameters and their uncertainties. We compare our method with a more traditional parameter-based uncertainty analysis.

Calibrated 200-GHz waveform measurement

We develop a method for mismatch-correcting temporal waveforms measured with a high-speed electrooptic sampling system to 200 GHz. The new calibration determines a complete equivalent-circuit model describing the source in both the time and frequency domains with uncertainties, and accounts for all impedances and multiple reflections in the measurement system.

Comb-Generator Characterization

We characterize a 50-GHz comb generator with a sampling oscilloscope. With careful control of the input power, input harmonics, and comb generator temperature, we measure the output spectrum with a standard uncertainty of 0.1 dB and 0.5deg. We correct the measurements for time-base distortion, impedance mismatch, an inline attenuator, and the complex frequency response of the oscilloscopes sampler. We also report on the stability of the comb-generator spectrum and the effects of the recorded time windows, drive levels, and temperature. These results provide general guidelines for practioners of high-speed measurements and a benchmark for future inter-laboratory comparisons of harmonic phase-reference calibrations.

Adaptive characterization of jitter noise in sampled high-speed signals

We estimate the root-mean-square (RMS) value of timing jitter noise in simulated signals similar to measured high-speed sampled signals. The simulated signals are contaminated by additive noise, timing jitter noise, and time shift errors. Before estimating the RMS value of the jitter noise, we align the signals (unless there are no time shift errors) based on estimates of the relative shifts from cross-correlation analysis. We compute the mean and sample variance of the aligned signals based on repeated measurements at each time sample. We estimate the derivative of the noise-free signal based, in part, on a regression spline fit to the average of the aligned signals. Our initial estimate of the RMS value of the jitter noise depends on estimated derivatives and sample variances at time samples where the magnitude of the estimated derivative exceeds a selected threshold. This initial estimate is generally biased. Using a parametric bootstrap approach, we adaptively adjust this initial estimate of the RMS value of the jitter noise based on an estimate of this bias. We apply our method to real data collected at NIST. We study how results depend on the derivative threshold.