arXiv subjects

Adi Pick

Publications and source records attributed to Adi Pick.

At least 19 recordsLinked to original sources

arXiv2026

Efficient Hamiltonian Engineering for Adiabatic MIS Algorithms

We present a hybrid adiabatic algorithm for maximum independent set (MIS) using Rydberg atom arrays. We engineer local controls that preferentially excite atoms with few neighbors, which represent graph nodes with small degrees. Numerical simulations show that the designed pulses accelerate convergence to the MIS state and suppress population in trap states. We obtain higher success probabilities than traditional global controls and a $25\%$ reduction in fidelity decay rate as problem hardness increases.

quant-ph↗

arXiv2025

Gradient-free pulse optimization for adiabatic control in open few-body quantum systems

We present a robust pulse optimization method for adiabatic population transfer and adiabatic quantum computation. The approach relies on identifying control pulses that keep the evolving quantum system close to its instantaneous ground state. By combining advanced gradient-free optimization tools with specialized cost functions for adiabatic control, it achieves both efficiency and robustness. To demonstrate its generality, we apply the method to three examples involving both atomic and superconducting qubits. We test different optimization cost functions and discretization bases, showing that the approach outperforms ensemble optimization. Finally, to verify its performance on real quantum hardware, we implement digitized adiabatic qubit control using the optimized pulses on the IBM Quantum cloud.

quant-ph↗

arXiv2025

Correlation-induced phase shifts and time delays in resonance enhanced high harmonic generation from Cr+

We investigate resonance-enhanced high harmonic generation (rHHG) in Cr+ by comparing a 1D shape-resonant model, time-dependent density functional theory (TDDFT), and independent particle approximation (IPA) simulations. Previous studies linked rHHG to the 3p -> 3d giant resonance, suggesting a modified four-step model where recolliding electrons are first captured in the autoionizing state before recombining into the ground state, potentially leading to an emission delay associated with the resonance lifetime. While both the 1D-model and TDDFT reproduce experimental spectra, TDDFT reveals that rHHG counterintuitively originates from spin-down 3p states, while spin-up 3d electrons negligibly contribute. The IPA fails to reproduce rHHG, highlighting the significance of electron correlations. Furthermore, TDDFT revealed a correlation induced ~480 attosecond time delay, accompanied by a strong phase shift across the resonance, potentially explaining earlier RABBIT measurements. Our work sheds light on long-standing open questions in rHHG and should advance novel ultrafast spectroscopies of electron correlations and resonances.

physics.atom-ph↗

arXiv2023

Inertial geometric quantum logic gates

We present rapid and robust protocols for STIRAP and quantum logic gates. Our gates are based on geometric phases acquired by instantaneous eigenstates of a slowly accelerating inertial Hamiltonian. To begin, we establish the criteria for inertial evolution and subsequently engineer pulse shapes that fulfill these conditions. These tailored pulses are then used to optimize geometric logic gates. We analyze a realization of our protocols with $^{87}$Rb atoms, resulting in gate fidelity that approaches the current state-of-the-art, with marked improvements in robustness.

quant-ph↗

arXiv2022

Unveiling the Enhancement of Spontaneous Emission at Exceptional Points

Exceptional points (EPs), singularities of non-Hermitian physics where complex spectral resonances degenerate, are one of the most exotic features of nonequilibrium open systems with unique properties. For instance, the emission rate of quantum emitters placed near resonators with EPs is enhanced (compared to the free-space emission rate) by a factor that scales quadratically with the resonance quality factor. Here, we verify the theory of spontaneous emission at EPs by measuring photoluminescence from photonic-crystal slabs that are embedded with a high-quantum-yield active material. While our experimental results verify the theoretically predicted enhancement, it also highlights the practical limitations on the enhancement due to material loss. Our designed structures can be used in applications that require enhanced and controlled emission, such as quantum sensing and imaging.

physics.optics↗

arXiv2020

Boosting photonic quantum computation with moderate nonlinearity

Photonic measurement-based quantum computation (MBQC) is a promising route towards fault-tolerant universal quantum computing. A central challenge in this effort is the huge overhead in the resources required for the construction of large photonic clusters using probabilistic linear-optics gates. Although strong single-photon nonlinearity ideally enables deterministic construction of such clusters, it is challenging to realise in a scalable way. Here we explore the prospects of using moderate nonlinearity (with conditional phase shifts smaller than $\pi$) to boost photonic quantum computing and significantly reduce its resources overhead. The key element in our scheme is a nonlinear router that preferentially directs photonic wavepackets to different output ports depending on their intensity. As a relevant example, we analyze the nonlinearity provided by Rydberg blockade in atomic ensembles, in which the trade-off between the nonlinearity and the accompanying loss is well understood. We present protocols for efficient Bell measurement and GHZ-state preparation -- both key elements in the construction of cluster states, as well as for the CNOT gate and quantum factorization. Given the large number of entangling operations involved in fault-tolerant MBQC, the increase in success probability provided by our protocols already at moderate nonlinearity can result in a dramatic reduction in the required resources.

quant-ph↗

arXiv2019

Robust mode conversion in NV centers using exceptional points

We show that microwave-driven NV centers can function as topological mode switches by utilizing a special degeneracy called an exceptional point (EP). By tuning the intensities and frequencies of the driving fields, we find an EP---where two normal modes of the system coalesce---and, then, use it to simulate the dynamics and demonstrate topological and non-reciprocal mode switching. By comparing density matrices of the input and output states, we find that the quantum correlations decrease by three orders of magnitude at room temperature, and discuss ways for improving this result. This work extends the theory of topological mode switches (originally derived for pure states) to mixed states and is, therefore, applicable to general open quantum systems. Our theory enables exploring new phenomena (e.g., high-order EPs in low-dimensional systems) and presents a crucial step towards incorporating topological mode switches in quantum-information applications.

quant-ph↗

arXiv2018

Ab-initio Theory of Photoionization via Resonances

We present an \emph{ab-initio} approach for computing the photoionization spectrum near autoionization resonances in multi-electron systems. While traditional (Hermitian) theories typically require computing the continuum states, which are difficult to obtain with high accuracy, our non-Hermitian approach requires only discrete bound and metastable states, which are accurately computed with advanced quantum chemistry tools. We derive a simple formula for the absorption lineshape near Fano resonances, which relates the asymmetry of the spectral peaks to the phase of the complex transition dipole moment. Additionally, we present a formula for the ionization spectrum of laser-driven targets and relate the `Autler-Townes' splitting of spectral lines to the existence of exceptional points in the Hamiltonian. We apply our formulas to compute the autoionization spectrum of helium, but our theory is also applicable for non-trivial multi-electron atoms and molecules.

physics.optics↗

arXiv2018

Ab-initio theory of quantum fluctuations and relaxation oscillations in multimode lasers

We present an \emph{ab-initio} semi-analytical solution for the noise spectrum of complex-cavity micro-structured lasers, including central Lorentzian peaks at the multimode lasing frequencies and additional sidepeaks due to relaxation-oscillation (RO) dynamics. In~Ref.~1, we computed the central-peak linewidths by solving generalized laser rate equations, which we derived from the Maxwell--Bloch equations by invoking the fluctuation--dissipation theorem to relate the noise correlations to the steady-state lasing properties; Here, we generalize this approach and obtain the entire laser spectrum, focusing on the RO sidepeaks. Our formulation treats inhomogeneity, cavity openness, nonlinearity, and multimode effects accurately. We find a number of new effects, including new multimode RO sidepeaks and three generalized $\alpha$ factors. Last, we apply our formulas to compute the noise spectrum of single- and multimode photonic-crystal lasers.

physics.optics↗

arXiv2018

Optical absorption in atoms and molecules near laser-induced exceptional points

We present a non-Hermitian theory of atomic and molecular absorption, which enables computing the absorption spectrum of multi-electron atoms and molecules without using any fitting parameters. We propose a method for optically inducing exceptional points in atomic systems, and show that slight changes in the laser parameters may lead to dramatic changes in the absorption lineshape. We demonstrate these predictions for helium using exact ab-initio electronic-structure data. Finally, we derive a simple formula for the Fano asymmetry factor and evaluate it for a model xenon atom.

physics.chem-ph↗

arXiv2018

The effect of polarization on the propagation distance of leaky guided modes

We show that transverse-magnetic (TM) leaky modes can propagate further than transverse electric (TE) modes in real-index dielectric waveguides. We compute the density of states and find that while the TE spectrum contains only overlapping resonances, the TM spectrum typically contains several isolated peaks. By transforming the TM equation into a Schr\"{o}dinger-type equation, we show that these isolated peaks arise due to $\delta$-function barriers at the core-cladding interface. Our theory is useful for a range of applications, including filtering TM modes from initially unpolarized light and transferring information between distant waveguides.

physics.optics↗

arXiv2017

Enhanced nonlinear frequency conversion and Purcell enhancement at exceptional points

We derive analytical formulas quantifying radiative emission from subwavelength emitters embedded in triply resonant nonlinear $\chi^{(2)}$ cavities supporting exceptional points (EP) made of dark and leaky modes. We show that the up-converted radiation rate in such a system can be greatly enhanced---by up to two orders of magnitude---compared to typical Purcell factors achievable in non-degenerate cavities, for both monochromatic and broadband emitters. We provide a proof-of-concept demonstration by studying an inverse-designed 2D photonic-crystal slab that supports an EP formed out of a Dirac cone at the emission frequency and a phase-matched, leaky-mode resonance at the second harmonic frequency.

physics.optics↗

arXiv2017

Scalable computation of Jordan chains

We present an algorithm to compute the Jordan chain of a nearly defective matrix with a $2\times2$ Jordan block. The algorithm is based on an inverse-iteration procedure and only needs information about the invariant subspace corresponding to the Jordan chain, making it suitable for use with large matrices arising in applications, in contrast with existing algorithms which rely on an SVD. The algorithm produces the eigenvector and Jordan vector with $O(\varepsilon)$ error, with $\varepsilon$ being the distance of the given matrix to an exactly defective matrix. As an example, we demonstrate the use of this algorithm in a problem arising from electromagnetism, in which the matrix has size $212^2\times 212^2$. An extension of this algorithm is also presented which can achieve higher order convergence [$O(\varepsilon^2)$] when the matrix derivative is known.

math.NA↗

arXiv2016

Symmetry, stability, and computation of degenerate lasing modes

We present a general method to obtain the stable lasing solutions for the steady-state ab-initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2d). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2d rotational symmetry groups. Our method uses a combination of semi-analytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell--Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its "chiral" intensity pattern, which arises from spontaneous symmetry-breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy.

physics.optics↗

arXiv2016

Inverse design of third-order Dirac exceptional points in photonic crystals

We propose a novel inverse-design method that enables brute-force discovery of photonic crystal (PhC) structures with complex spectral degeneracies. As a proof of principle, we demonstrate PhCs exhibiting third-order Dirac points formed by the \emph{accidental} degeneracy of modes of monopolar, dipolar, and quadrupolar nature. We show that under suitable conditions, these modes can coalesce and form a third-order exceptional point (EP3), leading to diverging Petermann factors. We show that the spontaneous emission (SE) rate of emitters at such EP3s, related to the local density of states, can be enhanced by a factor of 8 in purely lossy (passive) structures, with larger enhancements $\sim \sqrt{n^3}$ possible at exceptional points of higher order $n$ or in materials with gain.

physics.optics↗

arXiv2016

General Theory of Spontaneous Emission Near Exceptional Points

We present a general theory of spontaneous emission at exceptional points (EPs)---exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light--matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding $400\times$) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, EPs are associated with non-Lorentzian emission curves, leading to enhancements that scale polynomially with the resonance quality factor.

physics.optics↗

arXiv2015

Giant frequency-selective near-field energy transfer in active--passive structures

We apply a fluctuation electrodynamics framework in combination with semianalytical (dipolar) approximations to study amplified spontaneous energy transfer (ASET) between active and passive bodies. We consider near-field energy transfer between semi-infinite planar media and spherical structures (dimers and lattices) subject to gain, and show that the combination of loss compensation and near-field enhancement (achieved by the proximity, enhanced interactions, and tuning of subwavelength resonances) in these structures can result in orders of magnitude ASET enhancements below the lasing threshold. We examine various possible geometric configurations, including realistic materials, and describe optimal conditions for enhancing ASET, showing that the latter depends sensitively on both geometry and gain, enabling efficient and tunable gain-assisted energy extraction from structured surfaces.

cond-mat.mes-hall↗

arXiv2015

Amplified and directional spontaneous emission from arbitrary composite bodies: self-consistent treatment of Purcell effect below threshold

We study amplified spontaneous emission (ASE) from wavelength-scale composite bodies--complicated arrangements of active and passive media--demonstrating highly directional and tunable radiation patterns, depending strongly on pump conditions, materials, and object shapes. For instance, we show that under large enough gain, $\mathcal{PT}$ symmetric dielectric spheres radiate mostly along either active or passive regions, depending on the gain distribution. Our predictions are based on a recently proposed fluctuating volume--current (FVC) formulation of electromagnetic radiation that can handle inhomogeneities in the dielectric and fluctuation statistics of active media, e.g. arising from the presence of non-uniform pump or material properties, which we exploit to demonstrate an approach to modelling ASE in regimes where Purcell effect (PE) has a significant impact on the gain, leading to spatial dispersion and/or changes in power requirements. The nonlinear feedback of PE on the active medium, captured by the Maxwell--Bloch equations but often ignored in linear formulations of ASE, is introduced into our linear framework by a self-consistent renormalization of the (dressed) gain parameters, requiring the solution of a large system of nonlinear equations involving many linear scattering calculations.

cond-mat.mes-hall↗