Comment on Semiclassical approximations in phase space with coherent states

We present a complete derivation of the semiclassical limit of the coherent-state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial-value representation for the semiclassical propagator, based on an initial Gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed Gaussian approximation. It is very different from the Herman-Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent-state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.

A numerical method for solving optimal control problems

We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. 62, 092101 (2021)] in the classical and quantum formalisms by introducing the effect of the mass function in both kinetic and potential energies. The resulting Hamiltonian is mapped into a Morse oscillator by means of a point canonical transformation from the usual phase space (x, p) to a deformed one (xγ, Πγ). Similar to the Morse potential, the deformed oscillator presents bound trajectories in phase space corresponding to an anharmonic oscillatory motion in classical formalism and, therefore, bound states with a discrete spectrum in quantum formalism. On the other hand, open trajectories in phase space are associated with scattering states and continuous energy spectrum. Employing the factorization method, we investigate the properties of the coherent states, such as the time evolution and their uncertainties. A fast localization, classical and quantum, is reported for the coherent states due to the asymmetrical position-dependent mass. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.

Using the eigenvalue definition of binomial states we construct new intermediate number-coherent states which reduce to number and coherent states in two different limits. We reveal the connection of these intermediate states with photon-added coherent states and investigate their non-classical properties and quasi-probability distributions in detail. It is of interest to note that these new states, which interpolate between coherent states and number states, neither of which exhibit squeezing, are nevertheless squeezed states. A scheme to produce these states is proposed. We also study the interaction of these states with atomic systems in the framework of the two-photon Jaynes-Cummings model, and describe the response of the atomic system as it varies between the pure Rabi oscillation and the collapse-revival mode and investigate field observables such as photon number distribution, entropy and the Q-function.

The evolution mechanisms of electrons in isolated atoms, molecules and complex systems on a natural time-scale have long been a fundamental question in atomic and molecular physics, with significant implications for the applications of quantum materials. Over the past two decades, the development of attosecond light pulses and attosecond metrology has opened new opportunities for investigating the electronic dynamics, while also posing new challenges. Traditional detection techniques, such as time-of-flight and velocity map imaging spectrometers, can be used to study the attosecond scattering phase shifts in the photoemission and ionization processes with extremely high temporal and energy resolution. However, the limitations in multi-particle coincidence detection and three-dimensional momentum correlation limit the deeper exploration of many-body correlations and non-adiabatic ultrafast dynamics involving electron-nuclear coupling. To enable multidimensional and real-time observation of the three-dimensional momenta of both electrons and ions during photoionization, the attosecond interferometry has been integrated into electron-ion coincidence systems. In this study, we utilize an attosecond coincidence interferometer that combines an attosecond pump-infrared femtosecond probe scheme with cold target recoil ion momentum spectroscopy. The apparatus enables attosecond-time-resolved momentum imaging of all charged fragments in atomic and molecular systems, thereby providing deeper insights into the dynamics of photoionization. We also highlight the recent groundbreaking applications and advances of attosecond coincidence interferometer in studying photoionization dynamics in atoms, molecules, and more complex systems.

An algorithm for automated extraction of resonance parameters from the stabilization method

We analyze the theoretical basis of a procedure to determine an unknown normalization factor in discretized wave functions, which we have successfully used in a series of calculations of resonance widths for atomic and molecular systems. By reducing this determination to that of a suitable interpolation function for the energy eigenvalues, the problem is easily solved when atomic basis sets are chosen according to simple rules. Illustrations of our procedure are presented for atomic, molecular, and model systems; renormalized wave functions are compared with the exact ones for these model systems. The resulting method of renormalized continuum wave functions has a wide range of application in the study of long‐lived quasibound states (predissociation, autoionization, photoionization, unimolecular reactions, etc.).

In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles). This configuration space (as well as phase space) can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity) symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.

In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.

The Wigner phase operator (WPO) is identified as an operator valued measure (OVM) and its eigenstates are obtained. An operator satisfying the canonical commutation relation with the Wigner phase operator is also constructed and this establishes a Wigner distribution based operator formalism for the Wigner phase distribution. It is then argued that the WPO cannot represent a projective measurement of the phase; but is in fact to be interpreted as an operator valued measure for the phase. The non-positivity of the latter can be overcome by defining a positive operator valued measure (POVM) via a proper filter function, based on the view that phase measurements are coarse-grained in phase space, leading to the well known Q-distribution. The identification of the Q phase operator as a POVM is in good agreement with the earlier observation regarding the relation between operational phase measurement schemes and the Q-distribution. The Q phase POVM can be dilated in the sense of Gelfand–Naimark, to an operational setting of interference at a beam-splitter with another coherent state – this results in a von Neumann projector with well-defined phase in the expanded Hilbert space of the two modes.

Alveolar macrophages (AMs) play a major role in host defense against microbial infections in the lung. To perform this function, these cells must ingest and destroy pathogens, generally in phagosomes, as well as secrete a number of products that signal other immune cells to respond. Recently, we demonstrated that murine alveolar macrophages employ the cystic fibrosis transmembrane conductance regulator (CFTR) Cl(-) channel as a determinant in lysosomal acidification (Di, A., Brown, M. E., Deriy, L. V., Li, C., Szeto, F. L., Chen, Y., Huang, P., Tong, J., Naren, A. P., Bindokas, V., Palfrey, H. C., and Nelson, D. J. (2006) Nat. Cell Biol. 8, 933-944). Lysosomes and phagosomes in murine cftr(-/-) AMs failed to acidify, and the cells were deficient in bacterial killing compared with wild type controls. Cystic fibrosis is caused by mutations in CFTR and is characterized by chronic lung infections. The information about relationships between the CFTR genotype and the disease phenotype is scarce both on the organismal and cellular level. The most common disease-causing mutation, DeltaF508, is found in 70% of patients with cystic fibrosis. The mutant protein fails to fold properly and is targeted for proteosomal degradation. G551D, the second most common mutation, causes loss of function of the protein at the plasma membrane. In this study, we have investigated the impact of CFTR DeltaF508 and G551D on a set of core intracellular functions, including organellar acidification, granule secretion, and microbicidal activity in the AM. Utilizing primary AMs from wild type, cftr(-/-), as well as mutant mice, we show a tight correlation between CFTR genotype and levels of lysosomal acidification, bacterial killing, and agonist-induced secretory responses, all of which would be expected to contribute to a significant impact on microbial clearance in the lung.

Using the Wigner distribution function, we analyze the behavior on phase space of generalized coherent states associated with the Morse potential (Morse-like coherent states). Within the f-deformed oscillator formalism, such states are constructed by means of the following two definitions: (i) as deformed displacement operator coherent states and (ii) as deformed photon-added coherent states.

The time-dependent Hartree-Fock solutions of the two-level Lipkin-Meshkov-Glick model are studied by transforming the time-dependent Hartree-Fock equations into Hamilton's canonical form and analyzing the qualitative structure of the Hartree-Fock energy surface in the phase space. It is shown that as the interaction strength increases these time-dependent Hartree-Fock solutions undergo a qualitative change associated with the ground state phase transition previously studied in terms of coherent states. For twobody interactions stronger than the critical value, two types of time-dependent Hartree-Fock solutions (the "librations" and "rotations" in Hamilton's mechanics) exist simultaneously, while for weaker interactions only the rotations persist. It is also shown that the coherent states with the maximum total pseudospin value are determinants, so that time-dependent Hartree-Fock analysis is equivalent to the coherent state method.NUCLEAR STRUCTURE Lipkin-Meshkov-Glick model, TDHF, transformation of TDHF equations to Hamilton's canonical form, coherent states, ground state phase transition.

Quantum processes on phase space

The theory of the time-dependent response and autocorrelation function has been rewritten in the language of quantum-mechanical phase space and the correct method whereby semiclassical approximations may be obtained are discussed. Several new relationships occurring in Moyal's phase space are derived as a prelude to the actual study of the correlation functions.