arXiv subjects

Ebrahim Karimi

Publications and source records attributed to Ebrahim Karimi.

At least 37 records · Page 2Linked to original sources

arXiv2025

Transverse Distance Estimation with Higher-Order Hermite-Gauss modes

We explore the use of higher-order Hermite-Gauss modes for sensing optically induced transverse displacements. In the small-displacement regime, we show that projective measurements onto the two neighboring spatial modes yield optimal Fisher information, linearly scaling with the mode order $m$. We further extend the analysis to arbitrary displacement values and derive general expressions for the Fisher information, demonstrating that higher-order modes continue to outperform the fundamental Gaussian mode even at larger separations. This approach enables enhanced displacement sensitivity with only a minimal number of measurements, offering a simple and scalable alternative to conventional Spatial Mode Demultiplexing schemes. We provide a proof-of-principle experimental demonstration using spatial light modulators, showing an order-of-magnitude reduction in estimation variance when employing Hermite-Gauss modes of order $m = 8$ and $m = 17$. These results highlight the potential of structured light for ultrasensitive displacement sensing and may enable new applications in birefringence measurements with broadband or low-coherence light sources.

physics.optics↗

arXiv2025

Superoscillations and Physical Applications

This book chapter gives a selective review of physical implementations and applications of superoscillations and associated phenomena. We introduce the field by reviewing simple examples of superoscillations and showing how their existence naturally follows from the real part of the quantum mechanical weak value, which the parallel phenomena of supergrowth naturally follows from the imaginary part. Focusing on electromagnetic applications, we review the topics of superoscillation and supergrowth in speckle, creating superoscillating hot spots with patterned filters, superspectroscopic discrimination of two molecules, noise mitigation and the engineering of super behavior in point spread functions for the purpose of optical superresolution. We also cover a variety of different methods for creating superoscillatory and supergrowing functions, reviewing both mathematical and physical ways to create this class of functions, and beyond. Promising directions for future research, including superoscillations in other wave phenomena, super radar, and generalized super-phenomena in quantum physics, are outlined.

quant-ph↗

arXiv2025

Diffraction of correlated biphotons through transparent samples

Two-photon states generated through degenerate spontaneous parametric down-conversion (SPDC) can exhibit sharp correlations in the transverse spatial coordinates. This property leads to unique free-space propagation features. Here, we show that a phase object placed in the image plane of the source affects the free space propagation of the SPDC in a way that is mathematically analogous to the Fresnel diffraction of a first-order coherent source. This effect can be observed via the extraction of correlation images. We demonstrate this prediction with an experiment where the diffraction of correlated bi-photons is detected using an event-based camera. The results allow us to reconstruct the phase structure of the sample via non-interferometric phase retrieval methods. We verify that the retrieved phase patterns exhibit an enhanced contrast due to the probe two-photon nature. Our findings offer applications for non-interferometric, quantum-enhanced phase imaging.

quant-ph↗

arXiv2025

Quantum enhanced beam tracking surpassing the Heisenberg uncertainty limit

Determining a beam's full trajectory requires tracking both its position and momentum (angular) information. However, the product of position and momentum uncertainty in a simultaneous measurement of the two parameters is bound by the Heisenberg uncertainty limit (HUL). In this work, we present a proof-of-principle demonstration of a quantum-enhanced beam tracking technique, leveraging the inherent position and momentum entanglement between photons produced via spontaneous parametric down-conversion (SPDC). We show that quantum entanglement can be exploited to achieve a beam tracking accuracy beyond the HUL in a simultaneous measurement. Moreover, with existing detection technologies, it is already possible to achieve near real-time beam tracking capabilities at the single-photon level. The technique also exhibits high resilience to background influences, with negligible reduction in tracking accuracy even when subjected to a disruptive beam that is significantly brighter than SPDC.

quant-ph↗

arXiv2025

Beyond Poincaré Stresses: A Modern Quantum Field Theory Take on Hydrogen's Electromagnetic Mass

We revisit the longstanding electromagnetic mass problem from a modern quantum field theory perspective. Focusing on a system of two widely separated hydrogen atoms, one in an excited $nS$ state and the other in the ground $1S$ state, we isolate the electromagnetic contribution to the electron's total linear momentum by comparing the full energy-momentum tensor with the predictions of a point-like bound state model. Our analysis reveals that the leading perturbative correction introduces a factor $4/3$, which, along with subsequent corrections, indicates that the effective electromagnetic mass deviates from the conventional relation $E/c^2$. This discrepancy is attributed to the intrinsic nonlocality of the electromagnetic field, rather than to additional compensating mechanisms such as Poincaré stresses. We further contrast our quantum field theory results with the highly accurate predictions of the Schrödinger equation, which, despite neglecting higher-order terms, achieves an average error on the order of $10^{-5}\%$. Attempts to improve this accuracy via perturbative inclusion of the self-interaction of the electron's wave function instead increase the error, prompting a re-examination of the underlying perturbative assumptions. Our findings suggest that a non-perturbative treatment of the tree-level action may be required to fully capture the dynamics of bound states in quantum field theory.

hep-ph↗

arXiv2025

High-Dimensional Quantum Key Distribution with Qubit-like States

Quantum key distribution (QKD) protocols most often use two conjugate bases in order to verify the security of the quantum channel. In the majority of protocols, these bases are mutually unbiased to one another, which is to say they are formed from balanced superpositions of the entire set of states in the opposing basis. Here, we introduce a high-dimensional QKD protocol using qubit-like states, referred to as Fourier-qubits (or $\textit{F}$-qubits). In our scheme, each $\textit{F}$-qubit is a superposition of only two computational basis states with a relative phase that can take $d$ distinct values, where $d$ is the dimension of the computational basis. This non-mutually unbiased approach allows us to bound the information leaked to an eavesdropper, maintaining security in high-dimensional quantum systems despite the states' seemingly two-dimensional nature. By simplifying state preparation and measurement, our protocol offers a practical alternative for secure high-dimensional quantum communications. We experimentally demonstrate this protocol for a noisy high-dimensional QKD channel using the orbital angular momentum degree of freedom of light and discuss the potential benefits for encoding in other degrees of freedom.

quant-ph↗

arXiv2025

Tutorial: Hong-Ou-Mandel interference with Structured Photons

The Hong-Ou-Mandel (HOM) effect, an effective two-photon interference phenomenon, is a cornerstone of quantum optics and a key tool for linear optical quantum information processing. While the HOM effect has been extensively studied both theoretically and experimentally for various photonic quantum states, particularly in the spectral domain, detailed overviews of its behaviour for structured photons -- those with complex spatial profiles -- under arbitrary spatial mode measurement schemes are still lacking. This tutorial aims to fill this gap by providing a comprehensive theoretical analysis of the HOM effect for structured photons, including an arbitrary mode projection on quantum interference outcomes. The tutorial also provides analytical, closed-form expressions of the HOM visibility under different measurement conditions, which is a crucial contribution for its application in computational and artificial-intelligence-driven discovery of new quantum experiments exploiting the power of photons with complex spatial modes.

quant-ph↗

arXiv2025

Experimental emulator of pulse dynamics in fractional nonlinear Schrödinger equation

We present a nonlinear optical platform to emulate a nonlinear \textit{Lévy waveguide} that supports the pulse propagation governed by a generalized fractional nonlinear Schrödinger equation (FNLSE). Our approach distinguishes between intra-cavity and extra-cavity regimes, exploring the interplay between the effective fractional group-velocity dispersion (FGVD) and Kerr nonlinearity. In the intra-cavity configuration, we observe stable \textit{fractional solitons} enabled by an engineered combination of the fractional and regular dispersions in the fiber cavity. The soliton pulses exhibit their specific characteristics, \textit{viz.}, "heavy tails" and a "spectral valley" in the temporal and frequency domain, respectively, highlighting the effective nonlocality introduced by FGVD. Further investigation in the extra-cavity regime reveals the generation of spectral valleys with multiple lobes, offering potential applications to the design of high-dimensional data encoding. To elucidate the spectral valleys arising from the interplay of FGVD and nonlinearity, we have developed an innovative "force" model supported by comprehensive numerical analysis. These findings open new avenues for experimental studies of spectral-temporal dynamics in fractional nonlinear systems.

physics.optics↗

arXiv2024

Generation of the Complete Bell Basis via Hong-Ou-Mandel Interference

Optical vector modes (VMs), characterized by spatially varying polarization distributions, have become essential tools across microscopy, metrology, optical trapping, nanophotonics, and optical communications. The Hong-Ou-Mandel (HOM) effect, a fundamental two-photon interference phenomenon in quantum optics, offers significant potential to extend the applications of VMs beyond the classical regime. Here, we demonstrate the simultaneous generation of all four Bell states by exploiting the HOM interference of VMs. The resulting Bell states exhibit spatially tailored distributions that are determined by the input modes. These results represent a significant step in manipulating HOM interference within structured photons, offering promising avenues for high-dimensional quantum information processing and in particular high-dimensional quantum communication, quantum sensing, and advanced photonic technologies reliant on tailored quantum states of light.

quant-ph↗

arXiv2024

Engineering qubit dynamics in open systems with photonic synthetic lattices

The evolution of a quantum system interacting with an environment can be described as a unitary process acting on both the system and the environment. In this framework, the system's evolution can be predicted by tracing out the environmental degrees of freedom. Here, we establish a precise mapping between the global unitary dynamics and the quantum operation involving the system, wherein the system is a single qubit, and the environment is modeled as a discrete lattice space. This approach enables the implementation of arbitrary noise operations on single-polarization qubits using a minimal set of three liquid-crystal metasurfaces, whose transverse distribution of the optic axes can be patterned to reproduce the target process. We experimentally validate this method by simulating common noise processes, such as phase errors and depolarization.

quant-ph↗

arXiv2024

X-ray Phase Measurements by Time-Energy Correlated Photon Pairs

The invention of X-ray interferometers has led to advanced phase-sensing devices that are invaluable in various applications. These include the precise measurement of universal constants, e.g. the Avogadro number, of lattice parameters of perfect crystals, and phase-contrast imaging, which resolves details that standard absorption imaging cannot capture. However, the sensitivity and robustness of conventional X-ray interferometers are constrained by factors, such as fabrication precision, beam quality, and, importantly, noise originating from external sources or the sample itself. In this work, we demonstrate a novel X-ray interferometric method of phase measurement with enhanced immunity to various types of noise, by extending, for the first time, the concept of the SU(1,1) interferometer into the X-ray regime. We use a monolithic silicon perfect crystal device with two thin lamellae to generate correlated photon pairs via spontaneous parametric down-conversion (SPDC). Arrival time coincidence and sum-energy filtration allow a high-precision separation of the correlated photon pairs, which carry the phase information from orders-of-magnitude larger uncorrelated photonic noise. The novel SPDC-based interferometric method presented here is anticipated to exhibit enhanced immunity to vibrations as well as to mechanical and photonic noise, compared to conventional X-ray interferometers. Therefore, this SU(1,1) X-ray interferometer should pave the way to unprecedented precision in phase measurements, with transformative implications for a wide range of applications.

physics.optics↗

arXiv2024

Predicting atmospheric turbulence for secure quantum communications in free space

Atmospheric turbulence is the main barrier to large-scale free-space quantum communication networks. Aberrations distort optical information carriers, thus limiting or preventing the possibility of establishing a secure link between two parties. For this reason, forecasting the turbulence strength within an optical channel is highly desirable, as it allows for knowing the optimal timing to establish a secure link in advance. Here, we train a Recurrent Neural Network, TAROCCO, to predict the turbulence strength within a free-space channel. The training is based on weather and turbulence data collected over 9 months for a 5.4 km intra-city free-space link across the City of Ottawa. The implications of accurate predictions from our network are demonstrated in a simulated high-dimensional Quantum Key Distribution protocol based on orbital angular momentum states of light across different turbulence regimes. TAROCCO will be crucial in validating a free-space channel to optimally route the key exchange for secure communications in real experimental scenarios.

quant-ph↗

arXiv2024

Optimal Diffractive Focusing of Quantum Waves

Following the familiar analogy between the optical paraxial wave equation and the Schrödinger equation, we derive the optimal, real-valued wave function for focusing in one and two space dimensions without the use of any phase component. We compare and contrast the focusing parameters of the optimal waves with those of other diffractive focusing approaches, such as Fresnel zones. Moreover, we experimentally demonstrate these focusing properties on optical beams using both reflective and transmissive liquid crystal devices. Our results provide an alternative direction for focusing waves where phase elements are challenging to implement, such as for X-rays, THz radiation, and electron beams.

physics.optics↗

arXiv2024

On the Electromagnetic Mass Dilemma

We show that a charged sphere moving at a constant velocity $v$ exhibits a mass due to electromagnetic radiation, expressed as $4/(3+(v/c)^2) (E/c^2)$, where $E$ is the electromagnetic energy and $c$ the speed of light in vacuum. Our finding reconciles the longstanding mismatch between the electromagnetic mass calculated from the classical electrodynamics' $4/3 (E/c^2)$ and the relativistic theory.

physics.gen-ph↗

arXiv2024

Biphoton State Reconstruction via Phase Retrieval Methods

The complete measurement of the quantum state of two correlated photons requires reconstructing the amplitude and phase of the biphoton wavefunction. We show how, by means of spatially resolved single photon detection, one can infer the spatial structure of bi-photons generated by spontaneous parametric down conversion. In particular, a spatially resolved analysis of the second-order correlations allows us to isolate the moduli of the pump and phasematching contributions to the two-photon states. When carrying this analysis on different propagation planes, the free space propagation of pump and phasematching is observed. This result allows, in principle, to gain enough information to reconstruct also the phase of pump and phasematching, and thus the full biphoton wavefunction. We show this in different examples where the pump is shaped as a superposition of orbital angular momentum modes or as a smooth amplitude with a phase structure with no singularities. The corresponding phase structure is retrieved employing maximum likelihood or genetic algorithms. These findings have potential applications in fast, efficient quantum state characterisation that does not require any control over the source.

quant-ph↗

arXiv2024

A genetic algorithm for the response of twisted nematic liquid crystals to an applied field

When an external field is applied across a liquid-crystal cell, the twist and tilt distributions cannot be calculated analytically and must be extracted numerically. In the standard approach, the Euler-Lagrange equations are derived from the minimization of the free energy of the system and then solved via finite-difference methods, often implemented in commercial software. These tools iterate from initial solutions that are compatible with the boundary conditions, providing limited to no flexibility for customization. Here, we present a genetic algorithm that outputs fast and accurate solutions to the integral form of the equations. In our approach, the evolutionary routine is sequentially applied at each position within the bulk of the cell, thus overcoming the necessity of assuming trial solutions. The predictions of our routine strongly support the experimental observations on different instances of spatially varying twisted nematic liquid-crystal cells, patterned with different topologies on the two alignment layers.

physics.comp-ph↗

arXiv2024

Quantum process tomography of structured optical gates with convolutional neural networks

The characterization of a unitary gate is experimentally accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to reconstruct the underlying operator. The process matrix is typically extracted from maximum-likelihood estimation. Recently, optimization strategies based on evolutionary and machine-learning techniques have been proposed. Here, we investigate a deep-learning approach that allows for fast and accurate reconstructions of space-dependent SU(2) operators, only processing a minimal set of measurements. We train a convolutional neural network based on a scalable U-Net architecture to process entire experimental images in parallel. Synthetic processes are reconstructed with average fidelity above 90%. The performance of our routine is experimentally validated on complex polarization transformations. Our approach further expands the toolbox of data-driven approaches to Quantum Process Tomography and shows promise in the real-time characterization of complex optical gates.

quant-ph↗

arXiv2024

Manifestation of the Berry connection in chiral lattice systems

The Aharonov-Bohm effect is a physical phenomenon where the vector potential induces a phase shift of electron wavepackets in regions with zero magnetic fields. It is often referred to as evidence for the physical reality of the vector potential. A similar effect can be observed in solid-state systems, where the Berry connection can influence electron dynamics. Here, we show that in chiral-symmetric processes the Berry connection determines an observable effect on the mean chiral displacement of delocalized wavefunctions. This finding is supported by a photonic experiment realizing a topological quantum walk, and demonstrates a new effect that can be attributed directly to the presence of a gauge field.

cond-mat.mes-hall↗