arXiv subjects

Kelvin Titimbo

Publications and source records attributed to Kelvin Titimbo.

7 recordsLinked to original sources

arXiv2024

Quantum mechanical modeling of the multi-stage Stern$\unicode{x2013}$Gerlach experiment conducted by Frisch and Segrè

The multi-stage Stern$\unicode{x2013}$Gerlach experiment conducted by Frisch and Segrè includes two cascaded quantum measurements with a nonadiabatic flipper in between. The Frisch and Segrè experiment has been modeled analytically by Majorana without the nuclear effect and subsequently revised by Rabi with the hyperfine interaction. However, the theoretical predictions do not match the experimental observation accurately. Here, we numerically solve the standard quantum mechanical model, via the von Neumann equation, including the hyperfine interaction for the time evolution of the spin. Thus far, the coefficients of determination from the standard quantum mechanical model without using free parameters are still low, indicating a mismatch between the theory and the experiment. Non-standard variants that improve the match are explored for discussion.

quant-ph↗

arXiv2024

Simulation of atom trajectories in the original Stern-Gerlach experiment

Following a comprehensive analysis of the historical literature, we model the geometry of the Stern$\unicode{x2013}$Gerlach experiment to numerically calculate the magnetic field using the finite-element method. Using this calculated field and Monte Carlo methods, the atomic translational dynamics are simulated to produce the well-known quantized end-pattern with matching dimensions. The finite-element method used provides the most accurate description of the Stern$\unicode{x2013}$Gerlach magnetic field and end-pattern in the literature, matching the historically reported values and figures.

physics.comp-ph↗

arXiv2023

Numerical modeling of the multi-stage Stern$\unicode{x2013}$Gerlach experiment by Frisch and Segrè using co-quantum dynamics via the Bloch equation

We numerically study the spin flip in the Frisch$\unicode{x2013}$Segrè experiment, the first multi-stage Stern$\unicode{x2013}$Gerlach experiment, within the context of the novel co-quantum dynamics theory. We model the middle stage responsible for spin rotation by sampling the atoms with the Monte Carlo method and solving the dynamics of the electron and nuclear magnetic moments numerically according to the Bloch equation. Our results show that, without using any fitting parameters, the co-quantum dynamics closely reproduces the experimental observation reported by Frisch and Segrè in 1933, which has so far lacked theoretical predictions.

quant-ph↗

arXiv2023

Numerical modeling of the multi-stage Stern$\unicode{x2013}$Gerlach experiment by Frisch and Segrè using co-quantum dynamics via the Schrödinger equation

We use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern$\unicode{x2013}$Gerlach (SG) experiment conducted by R. Frisch and E. Segrè. This experiment consists of two Stern$\unicode{x2013}$Gerlach apparatuses separated by an inner rotation chamber that varies the fraction of spin flip. To this day, quantum mechanical treatments inadequately predict the Frisch$\unicode{x2013}$Segrè experiment. Here, we account for electron-nuclear interactions according to CQD and solve the associated Schrödinger equation. Our simulation outcome agrees with the Frisch$\unicode{x2013}$Segrè experimental observation and supports CQD as a potential model for electron spin evolution and collapse.

quant-ph↗

arXiv2020

Distinguishing quantum features in classical propagation

The strictly classical propagation of an initial Wigner function, referred to as TWA or LSC-IVR, is considered to provide approximate averages, despite not being a true Wigner function: it does not represent a positive operator. We here show that its symplectic Fourier transform, the truncated chord approximation (TCA), coincides with the full semiclassical approximation to the evolved quantum characteristic function (or chord function) in a narrow neighbourhood of the origin of the dual chord phase space. Surprisingly, this small region accounts for purely quantum features, such as blind spots and local wave function correlations, as well as the expectation of observables with a close classical correspondence. Direct numerical comparison of the TCA with exact quantum results verifies the semiclassical predictions for an initial coherent state evolving under the Kerr Hamiltonian. The resulting clear criterion for any further features, which may be estimated by classical propagation, is that, within the chord representation, they are concentrated near the origin.

quant-ph↗

arXiv2016

Photon number statistics uncover the fluctuations in non-equilibrium lattice dynamics

Fluctuations of the atomic positions are at the core of a large class of unusual material properties ranging from quantum para-electricity to high temperature superconductivity. Their measurement in solids is the subject of an intense scientific debate focused on seeking a methodology capable of establishing a direct link between the variance of the atomic displacements and experimentally measurable observables. Here we address this issue by means of non-equilibrium optical experiments performed in shot-noise limited regime. The variance of the time dependent atomic positions and momenta is directly mapped into the quantum fluctuations of the photon number of the scattered probing light. A fully quantum description of the non-linear interaction between photonic and phononic fields is benchmarked by unveiling the squeezing of thermal phonons in $α$-quartz.

quant-ph↗

arXiv2014

Pulsed homodyne Gaussian quantum tomography with low detection efficiency

Pulsed homodyne quantum tomography usually requires a high detection efficiency limiting its applicability in quantum optics. Here, it is shown that the presence of low detection efficiency ($<50\%$) does not prevent the tomographic reconstruction of quantum states of light, specifically, of Gaussian type. This result is obtained by applying the so-called "minimax" adaptive reconstruction of the Wigner function to pulsed homodyne detection. In particular, we prove, by both numerical and real experiments, that an effective discrimination of different Gaussian quantum states can be achieved. Our finding paves the way to a more extensive use of quantum tomographic methods, even in physical situations in which high detection efficiency is unattainable.

physics.optics↗