Object Wave Function Research Articles

Universal limit on spatial quantum superpositions with massive objects due to phonons

It has been a long-standing goal to bring massive objects into a superposition of different locations in real space, not only to confirm quantum theory in new regimes, but also to explore the interface with gravity. The main challenge is usually thought to arise from forces or scattering due to environmental fields and particles that decohere the large object's wave function into a statistical mixture. We unveil a decoherence channel which cannot be eliminated by improved isolation from the environment. It originates from sound waves within the object, which are excited as part of any splitting process and carry partial information. This puts stringent constraints on future spatial superpositions of large objects. Published by the American Physical Society 2024

Synchronizing quantum and classical clocks made of quantum particles

We demonstrate that the quantum corrections to the classical arrival time for a quantum object in a potential free region of space, as computed by Galapon [Phys. Rev. A {\bf 80}, 030102(R) (2009)], can be eliminated up to a given order of $\hbar$ by choosing an appropriate position-dependent phase for the object's wavefunction. This then implies that we can make the quantum arrival time of the object as close as possible to its corresponding classical arrival time, allowing us to synchronize a classical and quantum clock which tells time using the classical and quantum arrival time of the object, respectively. We provide an example for synchronizing such a clock by making use of a quantum object with a position-dependent phase imprinted on the object's initial wavefunction with the use of an impulsive potential.

Images in quantum entanglement

A system for classifying and quantifying entanglement in spin 1/2 pure states is presented based on simple images. From the image point of view, an entangled state can be described as a linear superposition of separable object wavefunction ΨO plus a portion of its own inverse image. Bell states can be defined in this way: . Using the method of images, the three-spin 1/2 system is discussed in some detail. This system can exhibit exclusive three-particle ν123 entanglement, two-particle entanglements ν12, ν13, ν23 and/or mixtures of all four. All four image states are orthogonal both to each other and to the object wavefunction. In general, five entanglement parameters ν12, ν13, ν23, ν123 and ϕ123 are required to define the general entangled state. In addition, it is shown that there is considerable scope for encoding numbers, at least from the classical point of view but using quantum-mechanical principles. Methods are developed for their extraction. It is shown that concurrence can be used to extract even-partite, but not odd-partite information. Additional relationships are also presented which can be helpful in the decoding process. However, in general, numerical methods are mandatory. A simple roulette method for decoding is presented and discussed. But it is shown that if the encoder chooses to use transcendental numbers for the angles defining the target function (α1, β1), etc, the method rapidly turns into the Devil's roulette, requiring finer and finer angular steps.

Optical discrimination between spatial decoherence and thermalization of a massive object

We propose an optical ring interferometer to observe environment-induced spatial decoherence of massive objects. The object is held in a harmonic trap and scatters light between degenerate modes of a ring cavity. The output signal of the interferometer permits to monitor the spatial width of the object's wave function. It shows oscillations that arise from coherences between energy eigenstates and that reveal the difference between pure spatial decoherence and that coinciding with energy transfer and heating. Our method is designed to work with a wide variety of masses, ranging from the atomic scale to nano-fabricated structures. We give a thorough discussion of its experimental feasibility.

What does an observed quantum system reveal to its observer?

The evolution of a quantum system under observation becomes retarded or even impeded. We review this ``quantum Zeno effect'' in the light of the criticism that has been raised upon a previous attempt to demonstrate it, of later reexaminations of both the projection postulate and the significance of the observations, and of the results of a recent experiment on an individual cold atom. Here, the micro-state of the quantum system gets unveiled with the observation, and the effect of measurement is no longer mixed up with dephasing the object's wave function by the reactive effect of the detection. A procedure is outlined that promises to provide, by observation, an upper limit for the delay of even an exponential decay.

A Study of Electric Charging Using Low-Magnification Electron Holography

As experimentally found by low-magnification holography, both the size of the condenser aperture and the excitation of the objective lens strongly modify the object wavefunction of an electron wave. For example, the phase by electrically charged polystyrene latex spheres attached to a copper grid increases with decreasing excitation of the objective lens and/or decreasing diameter of the condenser aperture. It was also found that a smaller diameter of the condenser aperture increases the phase shift by a carbon foil or magnetic memory cells. In addition, the phase of the image wave is modified by the lateral position of the aperture, whereas different electron densities of the imaging beam have only minor influence on the detected phase shifts.

Decoherence and Wavefunction Collapse in Quantum Measurements

Examining the notion of wavefunction collapse (WFC) in quantum measurements, which came again to be in question in the recent debate on the quantum Zeno effect, we remark that WFC is realized only through decoherence among branch waves by detection, after a spectral decomposition process from an initial object wavefunction to a superposition of branch waves corresponding to relevant measurement propositions. We improve the definition of the decoherence parameter, so as to be fitted to general cases, by which we can quantitatively estimate the degree of WFC given by detectors. Finally, we briefly discuss whether two special detector models, with very huge and very small degrees of freedom, can provoke WFC.

An electron holographic study of electric charging and electric charge distributions

Some electron optical parts of a transmission electron microscope modify the object wave-function of an electron wave. As experimentally found by low-magnification holography, both the size of the condenser aperture and the excitation of the lenses between the electron gun and the biprism strongly modify the phase of the image wave. It appears that changing these parameters changes the charging–discharging equilibrium between sample, supporting foil, parts of the microscope, and the electron beam. By using a special procedure to process holograms which were acquired under different conditions of charge equilibrium it is possible to reveal the phase shifts caused by the charging effects only. These phase shifts observed for uniformly charged polymer particles are in excellent agreement with the phase shifts simulated using a simple model of charged spheres. A comparison of experimental and modeled phase images suggests that the charge is uniformly distributed inside the particles rather than on their surface. In addition, this comparison enables us to quantitatively correlate an increase in the positive charge to an increase in the mean inner potential.

Statistical Estimation in Electron Microscopy of the Object Wavefunction Under Weak Scattering Conditions Using Low-dose Illumination from Different Directions

A statistically optimal (in the Cramér-Rao sense) reconstruction of the object wavefunction is presented. The analysis is based on low-dose images of weak phase-amplitude objects obtained by using parallel beams with four specific tilts. The full statistical characterization of the result is given.

On the Theory of the Reconstruction of a Weak Phase-amplitude Object from its Images, Especially in Electron Microscopy

In this paper we study the statistical properties of the reconstructed object wavefunction of a weak phase-amplitude object from two low-dose image intensity distributions. The images are obtained by successively illuminating the object coherently by plane quasi-monochromatic waves which make different angles with the optical axis. The case is discussed for isoplanatic conditions and one lateral dimension. Explicit expressions of the mean and variance of the reconstructed wavefunction are presented in terms of the illumination dose. The low spatial frequencies which were hardly retrievable in the method based on two defocused images obtained under axial illumination are accessible in this approach.

Object Reconstruction from Micrographs. Two Dimensional Theory with Three Dimensional Outlook

In this contribution we discuss the reconstruction of an object from one or more electron micrographs. We want to derive the locations and characters of the atoms which make up the object. Unfortunately inelastic scattering and multiple elastic scattering cannot reliably be related to the object structure because of the non-locality of these processes. The most promising starting point for object structure research therefore is single elastic scattering. This is a good approximation for thin objects and tends to become better fulfilled as the energy of the incident electrons increases. In that regime the weak object approximation, which is adopted here, also becomes more reliable because the phase shift and amplitude attenuation are decreasing functions of the energy (except in the neighborhood of resonances). In this approximation there is a linear relation between the intensity in the image plane and the object wavefunction. Object reconstruction for non-weak objects has been attempted but still is in its infancy.

Alternative to Holography for Determining Phase from Image Intensity Measurements in Optics

Alternative to Holography for Determining Phase from Image Intensity Measurements in Optics

An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations

An evaluation is made of an iterative method for determining the amplitude and phase from the image intensity recorded in optical systems. The method, which requires two images recorded at different lens defocus values, is tested with simulated data subject to error arising from the photographic recording of the image. In the case of error-free data, the solution for the phase distribution appears to be indeterminate to within a constant. The results for photographic noise levels of up to 20% of the maximum image intensity reflect the small effect of error on the calculated phase distribution. The calculation of phase distributions for both symmetric and asymmetric amplitude-phase distributions shows that the use of two images, taken at defocus values differing by about 100 nm in electron optics and about 1 mm in optics (depending on the numerical aperture of the objective lens), may be used to determine the complex object wave-function in both dark-field and bright-field optics.