arXiv subjects

Maor Mutzafi

Publications and source records attributed to Maor Mutzafi.

5 recordsLinked to original sources

arXiv2018

SPARCOM: Sparsity Based Super-Resolution Correlation Microscopy

In traditional optical imaging systems, the spatial resolution is limited by the physics of diffraction, which acts as a low-pass filter. The information on sub-wavelength features is carried by evanescent waves, never reaching the camera, thereby posing a hard limit on resolution: the so-called diffraction limit. Modern microscopic methods enable super-resolution, by employing florescence techniques. State-of-the-art localization based fluorescence subwavelength imaging techniques such as PALM and STORM achieve sub-diffraction spatial resolution of several tens of nano-meters. However, they require tens of thousands of exposures, which limits their temporal resolution. We have recently proposed SPARCOM (sparsity based super-resolution correlation microscopy), which exploits the sparse nature of the fluorophores distribution, alongside a statistical prior of uncorrelated emissions, and showed that SPARCOM achieves spatial resolution comparable to PALM/STORM, while capturing the data hundreds of times faster. Here, we provide a detailed mathematical formulation of SPARCOM, which in turn leads to an efficient numerical implementation, suitable for large-scale problems. We further extend our method to a general framework for sparsity based super-resolution imaging, in which sparsity can be assumed in other domains such as wavelet or discrete-cosine, leading to improved reconstructions in a variety of physical settings.

physics.optics↗

arXiv2017

Quantum State Tomography with a Single Observable

Quantum information has been drawing a wealth of research in recent years, shedding light on questions at the heart of quantum mechanics, as well as advancing fields such as complexity theory, cryptography, key distribution, and chemistry. These fundamental and applied aspects of quantum information rely on a crucial issue: the ability to characterize a quantum state from measurements, 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. Unfortunately, changing the setup results in unwanted changes to the data, prolongs the measurement and impairs the assumptions that are always made about the stationarity of the 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, thus considerably reducing the experimental effort. In general, measurements of a single observable do not hold enough information to recover the quantum state. We overcome this lack of information by relying on concepts inspired by Compressed Sensing (CS), exploiting the fact that the sought state - in many applications of quantum information - is close to a pure state (and thus has low rank). Additionally, we increase the system dimension by adding an ancilla that couples to information evolving in the system, thereby providing more measurements, enabling the recovery of the original quantum state from a single-observable measurements. We demonstrate our approach on multi-photon states by recovering structured quantum states from a single observable, in a single experimental setup. We further show how this approach can be used to recover quantum states without number-resolving detectors.

quant-ph↗

arXiv2016

Non-Diffracting Electron Vortex Beams Balancing Their Electron-Electron Interactions

By introducing concepts of beam shaping into quantum mechanics, we show how interference effects of the quantum wavefunction describing multiple electrons can exactly balance the repulsion among the electrons. With proper shaping of the fermionic wavefunction, we propose non-diffracting quantum wavepackets of multiple electrons that can also carry orbital angular momentum, in the form of multi-electron non-diffracting vortex beams. The wavefunction is designed to compensate for both the repulsion between electrons and for the diffraction-broadening. This wavefunction shaping facilitates the use of electron beams of higher current in numerous applications, thereby improving the signal-to-noise-ratio in electron microscopy and related systems without compromising on the spatial resolution. Our scheme potentially applies for any beams of charged particles, such as protons, muons and ion beams.

quant-ph↗

arXiv2015

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

We show that the well-known Čerenkov Effect contains new phenomena arising from the quantum nature of charged particles. The Čerenkov transition amplitudes allow coupling between the charged particle and the emitted photon through their orbital angular momentum (OAM) 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. Specifically, with proper shaping of electron beams (ebeams), we predict that the traditional Čerenkov radiation angle splits into two distinctive cones of photonic shockwaves. One of the shockwaves can move along a backward cone, otherwise considered impossible for Čerenkov radiation in ordinary matter. Our findings are observable for ebeams with realistic parameters, offering new applications including novel quantum optics sources, and open a new realm for Čerenkov detectors involving the spin and orbital angular momentum of charged particles.

quant-ph↗

arXiv2014

Structure-Based Super-Resolution Recovery of Three-Photon Quantum States from Two-Fold Coincidences

The field of quantum information has been growing fast over the past decade. Optical quantum computation, based on the concepts of KLM and cluster states, has witnessed experimental realizations of larger and more complex systems in terms of photon number. Quantum optical systems, which offer long coherence times and easy manipulation of single qubits, allow us to probe quantum properties of the light itself and of the physical systems around it. Recently, a linear scheme for quantum computing, relying on the bosonic nature of particles, has been proposed and realized experimentally with photons. The ability to efficiently measure superpositions of quantum states consisting of several photons is essential to the characterization of such systems. In fact, the entire field of quantum information completely relies on the ability to recover quantum states from measurements. However, the characterization of quantum states requires many measurements, and often necessitates complicated measurements schemes; for example, characterizing qubits requires measurements. Here, we utilize structure, inherent to physically interesting quantum states of light, in order to reduce the complexity in the recovery of a quantum state. In particular, we devise a method enabling the recovery of three-photon quantum states from only two-fold correlation measurements in a single setting. The ability to take two-fold coincidences instead of three-fold offers the recovery of the quantum states in far less measurements and in a considerably higher SNR, because detection of two-photon events is much more likely than that of three-photon ones. The concept suggested here paves the way to further ideas on structure-based super resolution in quantum state tomography, such as recovering a quantum state in an unknown basis in a single setup and recovering the state of several photons without number resolving detectors.

quant-ph↗