arXiv subjects

Thomas B. Bahder

Publications and source records attributed to Thomas B. Bahder.

At least 19 recordsLinked to original sources

arXiv2025

The Entropic Skin: Spatial Entanglement from the QCD Confinement Boundary

Recent investigations into High-Energy QCD have identified entanglement entropy as a crucial observable, linking parton distributions to the structure of the quantum vacuum. While momentum-space entanglement has been extensively studied in Deep Inelastic Scattering (DIS), the spatial realization of this entanglement in confined systems remains an open question. In this Letter, we demonstrate that the confining boundary of the MIT Bag Model acts as an ``Entropic Skin,'' generating maximal Spin-Position entanglement. We calculate the local reduced density matrix for the confined quark and show that the linear boundary condition, $i γ^μn_μψ= ψ$, acts as an entangling gate. The surface entropy density reaches a geometric invariant of $\approx 0.918$ bits ($92\%$ of the qubit limit), independent of the bag radius. We discuss the implications of this result for Chiral Symmetry breaking and propose that this boundary entropy is the precursor to the pion cloud in effective field theories.

hep-ph↗

arXiv2025

Photons in a Spherical Cavity

The iconic problem of photon modes in a spherical cavity has been discussed in the literature; however, conflicting results have been reported \cite{Heitler,Davydov_QuantumMechanics}. For this reason, the solution of this problem is worked out in detail here, starting with the Maxwell equations and applying boundary conditions at the surface of the bounding perfect conductor. Contrary to the treatments in the literature \cite{Heitler,Davydov_QuantumMechanics}, the allowed frequencies for photons in the sphere are given by two different conditions, one for electric and one for magnetic multipole photons. After establishing the modes and their allowed frequencies, we write down the second-quantized vector potential in the spherical geometry. Based on these spherical modes, bipartite photon entanglement is investigated showing that there are in-principle 40 different types of entangled photon states. Finally, we include some appendices about photon plane-wave and spherical-wave helicity states, helicity spherical harmonic vectors, and rotation of the helicity states and 3-d vectors using the Wigner $D$-matrix.

quant-ph↗

arXiv2015

Energy-Momentum Tensor for the Electromagnetic Field in a Dielectric

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Here we investigate the energy and momentum in a closed system composed of a propagating electromagnetic field and a negligibly reflecting dielectric. The Gordon momentum is easily identified as the total momentum by the fact that it is, by virtue of being invariant in time, conserved. We construct continuity equations for the energy and the Gordon momentum and use the continuity equations to construct an array that has the properties of a traceless, diagonally symmetric energy-momentum tensor. Then the century-old Abraham-Minkowski momentum controversy can be viewed as a consequence of attempting to construct an energy-momentum tensor from continuity equations that contain densities that correspond to nonconserved quantities.

physics.optics↗

arXiv2015

Electromagnetic Energy, Momentum, and Angular Momentum in an Inhomogeneous Linear Dielectric

In a previous work, Optics Communications 284 (2011) 2460--2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy--momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy--momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.

physics.optics↗

arXiv2014

Transfer of Spatial Reference Frame Using Singlet States and Classical Communication

A simple protocol is described for transferring spatial direction from Alice to Bob (two spatially separated observers) up to inversion. The two observers are assumed to share quantum singlet states and classical communication. The protocol assumes that Alice and Bob have complete free will (measurement independence) and is based on maximizing the Shannon mutual information between Alice and Bob's measurement outcomes. Repeated use of this protocol for each spatial axis of Alice allows transfer of a complete 3-dimensional reference frame, up to inversion of each of the axes. The technological complexity of this protocol is similar to that needed for BB84 quantum key distribution, and hence is much simpler to implement than recently proposed schemes for transmission of reference frames. A second protocol based on a Bayesian formalism is also presented.

quant-ph↗

arXiv2012

Interaction of Diatomic Molecules with Photon Angular Momentum

The interaction of a diatomic molecule with photons carrying well-defined angular momentum and parity is investigated to determine whether photon absorption can induce molecular rotational transitions between states having angular momentum $ΔJ >1$. A transformation from laboratory coordinates to coordinates with origin at the center-of-mass of the nuclei is used to obtain the interaction between the photons and the molecule's center-of-mass, electronic, and rotational degrees of freedom. For molecules making transitions between rotational levels, there is a small parameter, $ k a \ll 1 $, where $k$ is the photon wave vector and $a$ is the size of the molecule, which enters into the $Ej$ and $Mj$ photon absorption probabilities. For electric photons having arbitrary angular momentum $j \hbar$, the probability of absorbing an $E(j+1)$ photon divided by the probability of absorbing an $Ej$ photon, scales as $ (k a)^2 /(2 j+1)^2$. The probability of absorbing an $Mj$ photon, divided by the probability of absorbing and $Ej$ photon scales according to the same factor.

physics.atom-ph↗

arXiv2011

Resonant Behavior of an Augmented Railgun

We consider a lumped circuit model of an augmented electromagnetic railgun that consists of a gun circuit and an augmentation circuit that is inductively coupled to the gun circuit. The gun circuit is driven by a d.c. voltage generator, and the augmentation circuit is driven by an a.c. voltage generator. Using sample parameters, we numerically solve the three non-linear dynamical equations that describe this system. We find that there is a resonant behavior in the armature kinetic energy as a function of the frequency of the voltage generator in the augmentation circuit. This resonant behavior may be exploited to increase armature kinetic energy. Alternatively, if the presence of the kinetic energy resonance is not taken into account, parameters may be chosen that result in less than optimal kinetic energy and efficiency.

physics.class-ph↗

arXiv2011

Inductively Coupled Augmented Railgun

We derive the non-linear dynamical equations for an augmented electromagnetic railgun, whose augmentation circuit is inductively coupled to the gun circuit. We solve these differential equations numerically using example parameter values. We find a complicated interaction between the augmentation circuit, gun circuit, and mechanical degrees of freedom, leading to a complicated optimization problem. For certain values of parameters, we find that an augmented electromagnetic railgun has an armature kinetic energy that is 42% larger than the same railgun with no augmentation circuit. Optimizing the parameters may lead to further increase in performance.

physics.class-ph↗

arXiv2011

Fidelity of Physical Measurements

The fidelity (Shannon mutual information between measurements and physical quantities) is proposed as a quantitative measure of the quality of physical measurements. The fidelity does not depend on the true value of unknown physical quantities (as does the Fisher information) and it allows for the role of prior information in the measurement process. The fidelity is general enough to allow a natural comparison of the quality of classical and quantum measurements. As an example, the fidelity is used to compare the quality of measurements made by a classical and a quantum Mach-Zehnder interferometer.

quant-ph↗

arXiv2011

Phase Estimation with Non-Unitary Interferometers: Information as a Metric

Determining the phase in one arm of a quantum interferometer is discussed taking into account the three non-ideal aspects in real experiments: non-deterministic state preparation, non-unitary state evolution due to losses during state propagation, and imperfect state detection. A general expression is written for the probability of a measurement outcome taking into account these three non-ideal aspects. As an example of applying the formalism, the classical Fisher information and fidelity (Shannon mutual information between phase and measurements) are computed for few-photon Fock and N00N states input into a lossy Mach-Zehnder interferometer. These three non-ideal aspects lead to qualitative differences in phase estimation, such as a decrease in fidelity and Fisher information that depends on the true value of the phase.

quant-ph↗

arXiv2011

Upper Bound on Fidelity of Classical Sagnac Gyroscope

Numerous quantum mechanical schemes have been proposed that are intended to improve the sensitivity to rotation provided by the classical Sagnac effect in gyroscopes. A general metric is needed that can compare the performance of the new quantum systems with the classical systems. The fidelity (Shannon mutual information between the measurement and the rotation rate) is proposed as a metric that is capable of this comparison. A theoretical upper bound is derived for the fidelity of an ideal classical Sagnac gyroscope. This upper bound for the classical Sagnac gyroscope should be used as a benchmark to compare the performance of proposed enhanced classical and quantum rotation sensors. In fact, the fidelity is general enough to compare the quality of two different apparatuses (two different experiments) that attempt to measure the same quantity.

quant-ph↗

arXiv2010

Tradeoff between Efficiency and Melting for a High-Performance Electromagnetic Rail Gun

We estimate the temperature distribution in the rails of an electromagnetic rail gun (EMG) due to the confinement of the current in a narrow surface layer resulting from the skin effect. In order to obtain analytic results, we assume a simple geometry for the rails, an electromagnetic skin effect boundary edge that propagates with the accelerating armature, and a current carrying channel controlled by magnetic field diffusion into the rails. We compute the temperature distribution in the rails at the time that the armature leaves the rails. For the range of exit velocities, from 1500 m/s to 5000 m/s, we find the highest temperatures are near the gun breech. After a single gun firing, the temperature reaches the melting temperature of the metal rails in a layer of finite thickness near the surface of the rails, for rails made of copper or tantalum. We plot the thickness of the melt layer as a function of position along the rails. In all cases, the thickness of the melt layer increases with gun velocity, making damage to the gun rails more likely at higher velocity. We also calculate the efficiency of the EMG as a function of gun velocity and find that the efficiency increases with increasing velocity, but only if the length of the gun is sufficiently long. The thickness of the melted layer also decreases with increasing rail length. Therefore, there is a tradeoff: for rails of sufficient length, the gun efficiency increases with increasing velocity but the melted layer thickness in the rails also increases.

physics.class-ph↗

arXiv2008

Spin-polarized collision of deuterium and tritium: Relativistic Kinematics

We investigate the relativistic kinematics of the spin-polarized collision of deuterium incident on tritium, producing ${}^4$He and a neutron. Within the context of special relativity, we apply the conservation of four momentum and the conservation of intrinsic spin, which leads to a system of ten equations. We impose initial conditions such that the deuterium is moving along the x-axis, the tritium is stationary at the origin of coordinates, and the classical spin vector of the deuterium (spin magnitude = 1) is along the +z-axis, while the classical spin vector for tritium (spin magnitude = 1/2) is along the $-$z-axis. We expand the ten conservation equations to second order in velocities and we solve them for the velocity components of the neutron, its unit-spin-orientation vector, and the velocity components of the ${}^4$He nucleus, as a function of the incident deuterium energy. We find that this analytic solution agrees closely with the numerical solution of the ten (unexpanded) equations. For a given energy of deuterium, we find that there are two solutions, each solution having a unique velocity for the emitted neutron and helium nucleus. The two solutions are related to each other by reflection in the plane perpendicular to the deuterium spin and containing the initial deuterium velocity vector.

nucl-th↗

arXiv2007

Fishing for Eavesdroppers

A method is given to detect the presence of eavesdroppers when a noisy message is sent to a privileged receiver. A proof of the effectiveness if this method is demonstrated, and a comparison is made to other quantum cryptographic tasks.

quant-ph↗

arXiv2007

Phase Sensitivity of a Mach-Zehnder Quantum Sensor

We investigate the dependence of the fidelity of a Mach-Zehnder quantum interferometer on the prior information about the phase, for Fock state input and for maximally entangled (N00N) state input. For no prior information, the fidelity for Fock state input is greater than for N00N state input. In the limit of a narrow distribution describing the prior information, we find that both Fock and N00N state inputs lead to nearly equal fidelity.

quant-ph↗

arXiv2006

Sending Sensitive Messages in Quantum Packages

A communication protocol is introduced that allows the receiver of a message to place an a posteriori bound on the amount of information that an eavesdropper could have obtained during transmission of that message. This quantum cryptographic protocol is distinct from quantum key distribution. The quantum states and measurements required by this protocol are simple enough that it can be implemented using existing technology.

quant-ph↗

arXiv2006

Fidelity of Quantum Interferometers

For a generic interferometer, the conditional probability density distribution, $p(ϕ|m)$, for the phase $ϕ$ given measurement outcome $m$, will generally have multiple peaks. Therefore, the phase sensitivity of an interferometer cannot be adequately characterized by the standard deviation, such as $Δϕ\sim 1/\sqrt{N}$ (the standard limit), or $Δϕ\sim 1/N$ (the Heisenberg limit). We propose an alternative measure of phase sensitivity--the fidelity of an interferometer--defined as the Shannon mutual information between the phase shift $ϕ$\ and the measurement outcomes $m$. As an example application of interferometer fidelity, we consider a generic optical Mach-Zehnder interferometer, used as a sensor of a classical field. We find the surprising result that an entangled {\it N00N} state input leads to a lower fidelity than a Fock state input, for the same photon number.

quant-ph↗

arXiv2004

Quantum Positioning System

A quantum positioning system (QPS) is proposed that can provide a user with all four of his space-time coordinates. The user must carry a corner cube reflector, a good clock, and have a two-way classical channel of communication with the origin of the reference frame. Four pairs of entangled photons (biphotons) are sent through four interferometers: three interferometers are used to determine the user's spatial position, and an additional interferometer is used to synchronize the user's clock to coordinate time in the reference frame. The spatial positioning part of the QPS is similar to a classical time-of-arrival (TOA) system, however, a classical TOA system (such as GPS) must have synchronized clocks that keep coordinate time and therefore the clocks must have long-term stability, whereas in the QPS only a photon coincidence counter is needed and the clocks need only have short-term stability. Several scenarios are considered for a QPS: one is a terrestrial system and another is a space-based-system composed of low-Earth orbit (LEO) satellites. Calculations indicate that for a space-based system, neglecting atmospheric effects, a position accuracy below the 1 cm-level is possible for much of the region near the Earth. The QPS may be used as a primary system to define a global 4-dimensional reference frame.

quant-ph↗