Maor Mutzafi

Quantum Čerenkov Radiation: Spectral Cutoffs and the Role of Spin and Orbital Angular Momentum

We show that the well-known Cerenkov effect contains new phenomena arising from the quantum nature of charged particles. The Cerenkov transition amplitudes allow coupling between the charged particle and the emitted photon through their orbital angular momentum and spin, by scattering into preferred angles and polarizations. Importantly, the spectral response reveals a discontinuity immediately below a frequency cutoff that can occur in the optical region. Near this cutoff, the intensity of the conventional Cerenkov radiation (CR) is very small but still finite, while our quantum calculation predicts exactly zero intensity above the cutoff. Below that cutoff, with proper shaping of electron beams (ebeams), we predict that the traditional CR angle splits into two distinctive cones of photonic shockwaves. One of the shockwaves can move along a backward cone, otherwise considered impossible for conventional CR in ordinary matter. Our findings are observable for ebeams with realistic parameters, offering new applications including novel quantum optics sources, and opening a new realm for Cerenkov detectors involving the spin and orbital angular momentum of charged particles.

Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity

Deciphering the three-dimensional (3D) structure of complex molecules is of major importance, typically accomplished with X-ray crystallography. Unfortunately, many important molecules cannot be crystallized, hence their 3D structure is unknown. Ankylography presents an alternative, relying on scattering an ultrashort X-ray pulse off a single molecule before it disintegrates, measuring the far-field intensity on a two-dimensional surface, followed by computation. However, significant information is absent due to lower dimensionality of the measurements and the inability to measure the phase. Recent Ankylography experiments attracted much interest, but it was counter-argued that Ankylography is valid only for objects containing a small number of volume pixels. Here, we propose a sparsity-based approach to reconstruct the 3D structure of molecules. Sparsity is natural for Ankylography, because molecules can be represented compactly in stoichiometric basis. Utilizing sparsity, we surpass current limits on recoverable information by orders of magnitude, paving the way for deciphering the 3D structure of macromolecules.

Sparsity-based recovery of three-photon quantum states from two-fold correlations

Recovery of quantum states from measurements is an essential component in quantum information processing. In quantum optical systems, which naturally offer low decoherence and easy manipulation, quantum states are characterized by correlation measurements. When the states comprise more photons so as to encode more qubits, high-order correlation measurements are required. However, high-order correlations are hard to measure in experiments, as the rate of high-order coincidences decreases very fast when increasing the correlation order. This results in a poor signal-to-noise ratio. Likewise, the number of measurements required to characterize a quantum state increases exponentially with the increase in the number of qubits. Here, we use structure, present in most quantum states of interest (for quantum computing, cryptography, boson sampling, etc.), to recover the full quantum state of three photons from two-fold correlations in a single experimental setup.

Quantum state tomography with a single measurement setup

The field of quantum information relies on the crucial issue of characterizing quantum states from measurements. This is performed through a process called quantum state tomography (QST). However, QST requires a large number of measurements, each derived from a different physical observable corresponding to a different experimental setup. Changing the setup results in unwanted changes to the data, prolongs the measurement, and impairs assumptions made about noise. Here, we propose to overcome these drawbacks by performing QST with a single observable. A single observable can often be realized by a single setup, thereby considerably reducing the experimental effort. However, the information contained in a single observable is insufficient for full QST. To overcome the lack of sufficient measurements in a single observable, we increase the system dimension by adding an ancilla that couples to the information in the system and exploit the fact that the sought state is often close to a pure state. We demonstrate our approach on multiphoton states by recovering structured quantum states from a single observable in a single experimental setup.

Non-diffracting multi-electron vortex beams balancing their electron–electron interactions

The wave-like nature of electrons has been known for almost a century, but only in recent years has the ability to shape the wavefunction of EBeams (Electron-Beams) become experimentally accessible. Various EBeam wavefunctions have been demonstrated, such as vortex, self-accelerating, Bessel EBeams etc. However, none has attempted to manipulate multi-electron beams, because the repulsion between electrons rapidly alters the beam shape. Here, we show how interference effects of the quantum wavefunction describing multiple electrons can be used to exactly balance both the repulsion and diffraction-broadening. We propose non-diffracting wavepackets of multiple electrons, which can also carry orbital angular momentum. Such wavefunction shaping facilitates the use of multi-electron beams in electron microscopy with higher current without compromising on spatial resolution. Simulating the quantum evolution in three-dimensions and time, we show that imprinting such wavefunctions on electron pulses leads to shape-preserving multi-electrons ultrashort pulses. Our scheme applies to any beams of charged particles, such as protons and ion beams.Vortex electron beams are generated using single electrons but their low beam-density is a limitation in electron microscopy. Here the authors propose a scheme for the realization of non-diffracting electron beams by shaping wavepackets of multiple electrons and including electron–electron interactions.

Sparsity-based super-resolution optical fluctuation imaging

We present a new imaging technique optimizing the spatio-temporal resolution in fluorescence microscopy. This method achieves short integration time as SOFI, with high spatial resolution comparable to STORM, leading towards super-resolution imaging within living cells.

Non-linear shape preserving electron-beams

We show that shaping the initial wavefunction of a multi-electron system can lead to electron beams displaying shape-preserving propagation in spite of the inherent repulsion among electrons. This idea suggests applications in microscopy and lithography.

Sparsity based super-resolution optical imaging using correlation information

Traditionally, spatial resolution in optical imaging is limited by diffraction. Although sub-wavelength information is absent in the measurements, state-of-the-art fluorescence based localization techniques such as PALM and STORM manage to achieve spatial resolution of tens of nano-meters, but with limited temporal resolution. A more recent technique super-resolution optical fluctuation imaging (SOFI) exploits the temporal statistical behavior of uncorrelated fluorescence emissions to practically improve the spatial resolution by a factor of two over the diffraction limit, but with considerably faster image capturing. Here we propose to exploit the sparse nature of the fluorophores distribution, combined with a statistical prior of uncorrelated emissions such as in SOFI to achieve spatial resolution comparable to PALM/STORM, while retaining the temporal resolution of SOFI. We demonstrate our method on simulations and show improved results over STORM and SOFI. Our method may facilitate super-resolution imaging and capturing of intra-cellular dynamics within living cells.

Experimental demonstration of sparsity-based single-shot fluorescence imaging at sub-wavelength resolution

We present, in experiments and simulations, a novel technique facilitating subwavelength resolution in a single-shot fluorescence imaging without capturing multiple frames, thereby enabling video-rate super-resolution imaging within living cells.

Improving electron microscopy by shaping the electron beam wavefunction

We show a novel technique to enhance resolution and SNR in electron microscopes-by shaping the quantum wavefunction of electrons. Our technique overcomes fundamental limits that currently set the resolution and SNR in electron microscopy.