arXiv subjects

G. Leuchs

Publications and source records attributed to G. Leuchs.

At least 19 recordsLinked to original sources

arXiv2026

Wigner negativity and stellar rank for SU(1,1) states

Quasiprobability distributions for systems endowed with SU(1,1) dynamical symmetry have received surprisingly little attention, despite the central role of this symmetry in two-photon physics, squeezed states, and nonlinear interferometry. Here, we fill this gap by constructing a full covariant family of $s$-ordered quasiprobability distributions defined on the two-sheeted hyperboloid, or equivalently, on the Poincar\'e unit disk via stereographic projection. A key result is that the Wigner function is strictly positive for all Perelomov SU(1,1) coherent states, in sharp contrast to the SU(2) case. This positivity endows Wigner negativity with an unambiguous operational meaning: any negative volume is a direct signature of genuinely quantum behavior. We further examine the stellar rank of SU(1,1) states, defined through the zeros of the Husimi $Q$-function, and show how it compares with Wigner negativity as a geometry-adapted witness of nonclassicality in this setting. We further introduce a hierarchy of generalized multipoles through a harmonic expansion of the density operator on the hyperboloid, providing a complementary framework for probing quantumness. This offers a comprehensive toolkit for characterizing and quantifying quantum resources in SU(1,1) systems.

quant-ph↗

arXiv2026

The quantum sky of Majorana stars

Majorana stars, the $2S$ spin coherent states that are orthogonal to a spin-$S$ state, offer an elegant method to visualize quantum states. This representation offers deep insights into the structure, symmetries, and entanglement properties of quantum states, bridging abstract algebraic formulations with intuitive geometrical intuition. In this paper, we briefly survey the development and applications of the Majorana constellation, exploring its relevance in modern areas of quantum information.

quant-ph↗

arXiv2024

Squeezing via self-induced transparency in mercury-filled photonic crystal fibers

We investigate the squeezing of ultrashort pulses using self-induced transparency in a mercury-filled hollow-core photonic crystal fiber. Our focus is on quadrature squeezing at low mercury vapor pressures, with atoms near resonance on the $^3{\rm D}_3 \to 6^3{\rm P}_2$ transition. We vary the atomic density, thus the gas pressure (from 2.72 to 15.7$\mu$bar), by adjusting the temperature (from 273~K to 303 ~K). Our results show that achieving squeezing at room temperature, considering both fermionic and bosonic mercury isotopes, requires ultrashort femtosecond pulses. We also determine the optimal detection length for squeezing at different pressures and temperatures.

quant-ph↗

arXiv2024

Multipoles from Majorana constellations

Majorana stars, the $2S$ spin coherent states that are orthogonal to a spin-$S$ state, offer an elegant method to visualize quantum states, disclosing their intrinsic symmetries. These states are naturally described by the corresponding multipoles. These quantities can be experimentally determined and allow for an SU(2)-invariant analysis. We investigate the relationship between Majorana constellations and state multipoles, thus providing insights into the underlying symmetries of the system. We illustrate our approach with some relevant and informative examples.

quant-ph↗

arXiv2023

Quantum squeezing via self-induced transparency in a photonic crystal fiber

We study the quantum squeezing produced in self-induced transparency in a photonic crystal fiber by performing a fully quantum simulation based on the positive $P$ representation. The amplitude squeezing depends on the area of the initial pulse: when the area is $2\pi$, there is no energy absorption and no amplitude squeezing. However, when the area is between 2$\pi$ and 3$\pi$, one observes amplitude-dependent energy absorption and a significant amount of squeezing. We also investigate the effect of damping and temperature: the results indicate that a heightened atom-pulse coupling, caused by an increase in the spontaneous emission ratio reduces the amplitude squeezing.

quant-ph↗

arXiv2023

Covariant operator bases for continuous variables

Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the basic observables, with the crucial property of behaving well under symplectic transformations. This basis is the analogue of the irreducible tensors widely used in the context of SU(2) symmetry. Given the density matrix of a state, the expansion coefficients in that basis constitute the multipoles, which describe the state in a canonically covariant form that is both concise and explicit. We use these quantities to assess properties such as quantumness or Gaussianity and to furnish direct connections between tomographic measurements and quasiprobability distribution reconstructions.

quant-ph↗

arXiv2023

Protecting quantum modes in optical fibres

Polarization-preserving fibers maintain the two polarization states of an orthogonal basis. Quantum communication, however, requires sending at least two nonorthogonal states and these cannot both be preserved. We present a new scheme that allows for using polarization encoding in a fiber not only in the discrete, but also in the continuous-variable regime. For the example of a helically twisted photonic-crystal fibre, we experimentally demonstrate that using appropriate nonorthogonal modes, the polarization-preserving fiber does not fully scramble these modes over the full Poincar\'e sphere, but that the output polarization will stay on a great circle; that is, within a one-dimensional protected subspace, which can be parametrized by a single variable. This will allow for more efficient measurements of quantum excitations in nonorthogonal modes.

quant-ph↗

arXiv2023

Sensing rotations with multiplane light conversion

We report an experiment estimating the three parameters of a general rotation. The scheme uses quantum states attaining the ultimate precision dictated by the quantum Cram\'er-Rao bound. We realize the states experimentally using the orbital angular momentum of light and implement the rotations with a multiplane light conversion setup, which allows one to perform arbitrary unitary transformations on a finite set of spatial modes. The observed performance suggests a range of potential applications in the next generation of rotation sensors.

quant-ph↗

arXiv2023

Local sampling of the SU(1,1) Wigner function

Despite the indisputable merits of the Wigner phase-space formulation, it has not been widely explored for systems with SU(1,1) symmetry, as a simple operational definition of the Wigner function has proved elusive in this case. We capitalize on the unique properties of the parity operator, to derive in a consistent way a \emph{bona fide} SU(1,1) Wigner function that faithfully parallels the structure of its continuous-variable counterpart. We propose an optical scheme, involving a squeezer and photon-number-resolving detectors, that allows for direct point-by-point sampling of that Wigner function. This provides an adequate framework to represent SU(1,1) states satisfactorily.

quant-ph↗

arXiv2023

Optimizing the generation of polarization squeezed light in nonlinear optical fibers driven by femtosecond pulses

Bright squeezed light can be generated in optical fibers utilizing the Kerr effect for ultrashort laser pulses. However, pulse propagation in a fiber is subject to nonconservative effects that deteriorate the squeezing. Here, we analyze two-mode polarization squeezing, which is SU(2)-invariant, robust against technical perturbations, and can be generated in a polarization-maintaining fiber. We perform a rigorous numerical optimization of the process and the pulse parameters using our advanced model of quantum pulse evolution in the fiber that includes various nonconservative effects and real fiber data. Numerical results are consistent with experimental results.

quant-ph↗

arXiv2022

Anticaustics in a Fabry-Perot interferometer

We address the response of a Fabry-Perot interferometer to a monochromatic point source. We calculate the anticaustics (that is, the virtual wavefronts of null path difference) resulting from the successive internal reflections occurring in the system. They turn to be a family of ellipsoids (or hyperboloids) of revolution, which allows us to reinterpret the operation of the Fabry-Perot from a geometrical point of view that facilitates comparison with other apparently disparate arrangements, such as Young's double slit.

physics.optics↗

arXiv2021

Robust quantum metrology with random Majorana constellations

Even the most classical states are still governed by quantum theory. A number of physical systems can be described by their Majorana constellations of points on the surface of a sphere, where concentrated constellations and highly symmetric distributions correspond to the least and most quantum states, respectively. If these points are chosen randomly, how quantum will the resultant state be, on average? We explore this simple conceptual question in detail, investigating the quantum properties of the resulting random states. We find these states to be far from the norm, even in the large-number-of-particles limit, where classical intuition often replaces quantum properties, making random Majorana constellations peculiar and intriguing. Moreover, we study their usefulness in the context of rotation sensing and find numerical evidence of their robustness against dephasing and particle loss. We realize these states experimentally using light's orbital angular momentum degree of freedom and implement arbitrary unitaries with a multiplane light conversion setup to demonstrate the rotation sensing. Our findings open up new possibilities for quantum-enhanced metrology.

quant-ph↗

arXiv2021

Particle trajectories, gamma-ray emission, and anomalous radiative trapping effects in magnetic dipole wave

In studies of interaction of matter with laser fields of extreme intensity there are two limiting cases of a multi-beam setup maximizing either the electric field or the magnetic field. In this work attention is paid to the optimal configuration of laser beams in the form of an m-dipole wave, which maximizes the magnetic field. We consider in such highly inhomogeneous fields the advantages and specific features of laser-matter interaction, which stem from individual particle trajectories that are strongly affected by gamma photon emission. It is shown that in this field mode qualitatively different scenarios of particle dynamics take place in comparison with the mode that maximizes the electric field. A detailed map of possible regimes of particle motion (ponderomotive trapping, normal radiative trapping, radial and axial anomalous radiative trapping), as well as angular and energy distributions of particles and gamma photons, is obtained in a wide range of laser powers up to 300 PW and reveals signatures of radiation losses experimentally detectable even with subpetawatt lasers.

physics.plasm-ph↗

arXiv2021

Dense e$^-$e$^+$ plasma formation in magnetic dipole wave: vacuum breakdown by 10-PW class lasers

When studying the interaction of matter with extreme fields using multipetawatt lasers, there are two limiting cases maximizing either the electric field or the magnetic field. Here, the main attention is paid to the optimal configuration of laser beams in the form of an m-dipole wave, which maximizes the magnetic field, and the corresponding production of pair plasma via a QED cascade using 10-PW class lasers. We show that the threshold of vacuum breakdown with respect to avalanche-like pair generation is about 10 PW. Using 3D PIC modeling in the specified fields, we go deeper into the physics of vacuum breakdown, i.e. we examined in detail the individual trajectories of particles produced in inhomogeneous electric and magnetic fields, the space-time distributions of pair densities on the avalanche stage, and the energy distributions of charged particles and gamma photons. The forming plasma structures represent concentric rings around the central magnetic axis, which can result in significant change of laser-plasma interaction in comparison with the case of an e-dipole wave.

physics.plasm-ph↗

arXiv2020

Compressively certifying quantum measurements

We introduce a reliable compressive procedure to uniquely characterize any given low-rank quantum measurement using a minimal set of probe states that is based solely on data collected from the unknown measurement itself. The procedure is most compressive when the measurement constitutes pure detection outcomes, requiring only an informationally complete number of probe states that scales linearly with the system dimension. We argue and provide numerical evidence showing that the minimal number of probe states needed is even generally below the numbers known in the closely-related classical phase-retrieval problem because of the quantum constraint. We also present affirmative results with polarization experiments that illustrate significant compressive behaviors for both two- and four-qubit detectors just by using random product probe states.

quant-ph↗

arXiv2020

Fundamental quantum limits in ellipsometry

We establish the ultimate limits that quantum theory imposes on the accuracy attainable in optical ellipsometry. We show that the standard quantum limit, as usual reached when the incident light is in a coherent state, can be surpassed with the use of appropriate squeezed states and, for tailored beams, even pushed to the ultimate Heisenberg limit.

quant-ph↗

arXiv2019

Quasiprobability currents on the sphere

We present analytic expressions for the $s$-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, exploring the appearance of the semiclassical limit in stable, unstable and tunnelling regimes.

quant-ph↗

arXiv2019

Wigner function for SU(1,1)

In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.

quant-ph↗