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Second-order correlation analysis of multifrequency dephasing in single-particle interferometry

A. Rembold

Published Jan 1, 2018• 0 citations
Publisher

Abstract

Single-particle interferometers became a remarkable tool in many fields of fundamental research and technical applications, such as sensor technology. Due to their high phase sensitivity, these interferometers are susceptible to dephasing which originates typically from electromagnetic fields, mechanical vibrations or temperature drifts, leading to a reduced contrast in the spatial signal. In opposition to decoherence, where the contrast is reduced due to the entanglement of the quantum state to the environment, dephasing is a collective phase shift of the interference pattern. Therefore, it can in principle be reversed after the measurement if the spatial and temporal information about the particle events in the detection plane is available. Using two-particle correlations, it is possible to reveal the properties of the unperturbed interference pattern, such as contrast and spatial periodicity, and the dephasing characteristics. In this thesis, the second-order correlation analysis of multifrequency dephasing is discussed theoretically and demonstrated experimentally. The second-order correlation theory is derived and the equations are explained in detail. Additionally, the numerical correlation function used to extract the experimental data is provided and it is explained how the discretization influences the accuracy of the obtained parameters. Using an electron biprism interferometer, the validity of our correlation analysis is verified experimentally by applying artificially an external time-varying magnetic field dephasing the temporally integrated interference pattern. It is demonstrated successfully that the parameters of the unperturbed interference pattern can be revealed even if the contrast in the spatial signal is nearly vanished. Furthermore, the characteristics of single- and multifrequency dephasing can be identified and used for the reconstruction of the unperturbed interference pattern. The applicability of our correlation analysis is also investigated by applying external mechanical vibrations in a broad frequency range to the electron biprism interferometer. Here, the amplitude spectrum of the correlation function is used together with a numerical algorithm to identify the unknown dephasing frequencies, amplitudes, and phases. In this way, the vibrational response spectrum of the biprism interferometer including the mechanical resonances could be determined. Our correlation analysis can be applied in principle in all interferometers generating a spatial interference pattern on a detector with high spatial and temporal single-particle resolution. Such detectors are available for electrons, ions, atoms, neutrons, molecules, and photons which enables the application of our method in a wide range of interferometric experiments. In fundamental research, the second-order correlation analysis can be used to distinguish between dephasing and decoherence in experiments where the contrast of the interference pattern has to be determined. This is e.g. relevant for studying the mechanisms of decoherence and testing the limits of quantum mechanical superposition. Our method can also be a useful tool in technical applications to optimize the electromagnetic shielding and vibrational damping of the interferometer by measuring its response spectra. As the correlation analysis is suitable to identify unknown dephasing frequencies and the corresponding amplitudes, it can be applied in sensor technology. At the end of this thesis, a compact sensor for the measurement of time-varying electromagnetic fields based on an electron biprism interferometer is proposed. Due to the wide application possibilities of the described correlation analysis, it is of significant relevance in various fields of single-particle interferometry.

DOI
10.15496/publikation-21126

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Single-particle interferometers became a remarkable tool in many fields of fundamental research and technical applications, such as sensor technology. Due to their high phase sensitivity, these interferometers are susceptible to dephasing which originates typically from electromagnetic fields, mechanical vibrations or temperature drifts, leading to a reduced contrast in the spatial signal. In opposition to decoherence, where the contrast is reduced due to the entanglement of the quantum state to the environment, dephasing is a collective phase shift of the interference pattern. Therefore, it can in principle be reversed after the measurement if the spatial and temporal information about the particle events in the detection plane is available. Using two-particle correlations, it is possible to reveal the properties of the unperturbed interference pattern, such as contrast and spatial periodicity, and the dephasing characteristics. In this thesis, the second-order correlation analysis of multifrequency dephasing is discussed theoretically and demonstrated experimentally. The second-order correlation theory is derived and the equations are explained in detail. Additionally, the numerical correlation function used to extract the experimental data is provided and it is explained how the discretization influences the accuracy of the obtained parameters. Using an electron biprism interferometer, the validity of our correlation analysis is verified experimentally by applying artificially an external time-varying magnetic field dephasing the temporally integrated interference pattern. It is demonstrated successfully that the parameters of the unperturbed interference pattern can be revealed even if the contrast in the spatial signal is nearly vanished. Furthermore, the characteristics of single- and multifrequency dephasing can be identified and used for the reconstruction of the unperturbed interference pattern. The applicability of our correlation analysis is also investigated by applying external mechanical vibrations in a broad frequency range to the electron biprism interferometer. Here, the amplitude spectrum of the correlation function is used together with a numerical algorithm to identify the unknown dephasing frequencies, amplitudes, and phases. In this way, the vibrational response spectrum of the biprism interferometer including the mechanical resonances could be determined. Our correlation analysis can be applied in principle in all interferometers generating a spatial interference pattern on a detector with high spatial and temporal single-particle resolution. Such detectors are available for electrons, ions, atoms, neutrons, molecules, and photons which enables the application of our method in a wide range of interferometric experiments. In fundamental research, the second-order correlation analysis can be used to distinguish between dephasing and decoherence in experiments where the contrast of the interference pattern has to be determined. This is e.g. relevant for studying the mechanisms of decoherence and testing the limits of quantum mechanical superposition. Our method can also be a useful tool in technical applications to optimize the electromagnetic shielding and vibrational damping of the interferometer by measuring its response spectra. As the correlation analysis is suitable to identify unknown dephasing frequencies and the corresponding amplitudes, it can be applied in sensor technology. At the end of this thesis, a compact sensor for the measurement of time-varying electromagnetic fields based on an electron biprism interferometer is proposed. Due to the wide application possibilities of the described correlation analysis, it is of significant relevance in various fields of single-particle interferometry.
Interferometers with single particles are susceptible for dephasing perturbations from the environment, such as electromagnetic oscillations or mechanical vibrations.On the one hand, this limits sensitive quantum phase measurements as it reduces the interference contrast in the signal.On the other hand, it enables single-particle interferometers to be used as sensitive sensors for electromagnetic and mechanical perturbations.Recently, it was demonstrated experimentally, that a secondorder correlation analysis of the spatial and temporal detection signal can decrease the electromagnetic shielding and vibrational damping requirements significantly.Thereby, the relevant matter-wave characteristics and the perturbation parameters could be extracted from the correlation analysis of a spatially 'washed-out' interference pattern and the original undisturbed interferogram could be reconstructed.This method can be applied to all interferometers that produce a spatial fringe pattern on a detector with high spatial and temporal single-particle resolution.In this article, we present and discuss in detail the used two-dimensional second-order correlation theory for multifrequency perturbations.The derivations of an explicit and approximate solution of the correlation function and corresponding amplitude spectra are provided.It is explained, how the numerical correlation function is extracted from the measurement data.Thereby, the influence of the temporal and spatial discretization step size on the extracted parameters, as contrast and perturbation amplitude, is analyzed.The influence of noise on the correlation function and corresponding amplitude spectrum is calculated and numerically cross-checked by a comparison of our theory with numerical singleparticle simulations of a perturbed interference pattern.Thereby, an optimum spatial discretization step size is determined to achieve a maximum signal-to-noise ratio, which was used in former experiments to identify the perturbation caused by the electrical network.Our method can also be applied for the analysis of broad-band frequency noise, dephasing the interference pattern.Using Gaussian distributed noise in the simulations, we demonstrate that the relevant matter-wave parameters and the applied perturbation spectrum can be revealed by our correlation analysis.
Matter-wave interferometry is a highly sensitive tool to measure small perturbations in a quantum system.This property allows the creation of precision sensors for dephasing mechanisms such as mechanical vibrations.They are a challenge for phase measurements under perturbing conditions that cannot be perfectly decoupled from the interferometer, e.g.for mobile interferometric devices or vibrations with a broad frequency range.Here, we demonstrate a method based on second-order correlation theory in combination with Fourier analysis, to use an electron interferometer as a sensor that precisely characterizes the mechanical vibration spectrum of the interferometer.Using the high spatial and temporal single-particle resolution of a delay line detector, the data allows to reveal the original contrast and spatial periodicity of the interference pattern from 'washed-out' matter-wave interferograms that have been vibrationally disturbed in the frequency region between 100 and 1000 Hz.Other than with electromagnetic dephasing, due to excitations of higher harmonics and additional frequencies induced from the environment, the parts in the setup oscillate with frequencies that can be different to the applied ones.The developed numerical search algorithm is capable to determine those unknown oscillations and corresponding amplitudes.The technique can identify vibrational dephasing and decrease damping and shielding requirements in electron, ion, neutron, atom and molecule interferometers that generate a spatial fringe pattern on the detector plane.
High-contrast matter-wave interferometry is essential in various fundamental quantum mechanical experiments as well as for technical applications. Thereby, contrast and sensitivity are typically reduced by decoherence and dephasing effects. While decoherence accounts for a general loss of quantum information in a system due to entanglement with the environment, dephasing is due to collective time-dependent external phase shifts, which can be related to temperature drifts, mechanical vibrations, and electromagnetic oscillations. In contrast to decoherence, dephasing can, in principle, be reversed. Here, we demonstrate in experiment and theory a method for the analysis and reduction of the influence of dephasing noise and perturbations consisting of several external frequencies in an electron interferometer. This technique uses the high spatial and temporal resolution of a delay-line detector to reveal and remove dephasing perturbations by second-order correlation analysis. It allows matter-wave experiments under perturbing laboratory conditions and can be applied, in principle, to electron, atom, ion, neutron, and molecule interferometers.
Remarkable progress can be observed in recent years in the controlled emission, guiding, and detection of coherent, free electrons. Those methods were applied in matter wave interferometers leading to high phase sensitivities and precise sensor technologies for dephasing influences such as mechanical vibrations or electromagnetic frequencies. However, the previous devices have been large laboratory setups. For future sensor applications or tests of the coherence properties of an electron source, small, portable interferometers are required. Here, we demonstrate a compact biprism electron interferometer that can be used for mobile applications. The design was optimized for small dimensions by beam path simulations. The interferometer has a length between the tip and the superposition plane before magnification of only 47 mm and provides electron interference patterns with a contrast up to 42.7%. The detection of two dephasing frequencies at 50 and 150 Hz was demonstrated applying second order correlation and Fourier analysis of the interference data.
Matter-wave interferometry is highly susceptible to inertial acceleration noises arising from the vibration of the experimental apparatus. There are various methods for noise suppression. In this paper, we propose leveraging the cross-correlation of multidirectional vibration noises to mitigate their dephasing effect in matter-wave interferometers. Specifically, we analyze an interferometer driven by its internal state under an external field and examine the dephasing caused by a two-dimensional random inertial force. As we will demonstrate, the coupling between the two-dimensional inertial force noise components will shift the resonance peak but not change the shape of the power spectral density. Moreover, when the noise approximately resonates with the intrinsic frequency of the test mass, we find that the standard deviation of the phase can be suppressed by a factor roughly equal to the Q factor of the noise. This technique holds significant potential for future gravity experiments utilizing quantum sensors, such as measuring gravitational acceleration and exploring quantum entanglement induced by gravity.
Matter-wave interferometry is highly susceptible to inertial acceleration noises arising from the vibration of the experimental apparatus. There are various methods for noise suppression. In this paper, we propose leveraging the cross-correlation of multi-directional vibration noises to mitigate their dephasing effect in matter-wave interferometers. Specifically, we analyse an interferometer driven by its internal state under an external field and examine the dephasing caused by a two-dimensional random inertial force. As we will demonstrate, the coupling between the two-dimensional inertial force noise components will shift the resonance peak but not change the shape of the power spectral density. Moreover, when the noise approximately resonates with the intrinsic frequency of the test mass, we find that the standard deviation of the phase can be suppressed by a factor roughly equal to the Q-factor of the noise. This technique holds significant potential for future gravity experiments utilising quantum sensors, such as measuring gravitational acceleration and exploring quantum entanglement induced by gravity.