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We derive Loop Quantum Gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity for several schemes of quantization. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime.

CAP Virtual Congress 2021

Effective Raychaudhuri equation and black hole singularity resolution

singularity resolution

raychaudhuri equation

loop quantum gravity

black holes

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technical paper

The study of plasmonics has the potential to reshape the physics of light-matter interactions in metallic nanohybrids and their applications to nanotechnology. Metallic nanohybrids are mode metallic nanoparticles and quantum emitters such as quantum dots. Recently, there is a considerable interest to study the light-matter interaction in the nanoscale size plasmonic nanohybrids. When an external light falls on the QEs, electrons in the QEs get excited from the ground state to the excited states and electron-hole pairs are created in the QEs. Similarly, when the external light (photons) falls on the MNPs it modifies the plasmonic properties of these particles. We know that there are free electrons on the surface of the MNPs. These free electrons oscillate as the charged waves on the surface. The quantized particles of the charged wave are called plasmons. When external light photons fall on the surface of the MNPs, there is an interaction between the photons and plasmons. This interaction produces new types of quantized quasi-particles called the surface plasmon polaritons (SPPs) It interesting to note that exciton energies and SPP energies can be modified by manipulating the size and shape of the QEs. It is also found that exciton and SPP energies can also be modified by applying an external field such as external control lasers, external stress-strain fields, and magnetic fields. Here we study the light-matter interaction in plasmonic nanohybrids made of an ensemble of metallic nanoparticles and quantum emitters. The study of linear and nonlinear plasmonics has the potential to reshape the physics of light-matter interactions and their applications to nanotechnology and nanomedicine. Further, we include the effect of the dipole-dipole interaction (DDI) on the light-matter interaction in plasmonic nanohybrids. We found that the SPP field also induces dipoles in QEs and MNPs and they interact with each other via that the anomalous dipole-dipole interaction. It is shown that the anomalous DDI is many times stronger than the classical DDI. The nonlinear plasmonics such as two-photon spectroscopy and Kerr nonlinearity is also explored. Finally, we have examined that these nanohybrids can be used to fabricate the nanosensors and nano switches for the applications of nanotechnology and nanomedicine.

Light-matter Interaction in Plasmonic Nanohybrids

We study Quantum Gravity effects on the density of states in statistical mechanics and its implications for the critical temperature of a Bose Einstein Condensate and fraction of bosons in its ground state. We also study the effects of compact extra dimensions on the critical temperature and the fraction. We consider both neutral and charged bosons in the study and show that the effects may just be measurable in current and future experiments.

Test of Quantum Gravity in Statistical Mechanics

We study the response of a static Unruh-DeWitt detector outside an exotic compact object (ECO) with a variety of (partially) reflective boundary conditions in 3+1 dimensions. The horizonless ECO, whose boundary is extremely close to the would-be event horizon, acts as a black hole mimicker. We find that the response rate is notably distinct from the black hole case, even when the ECO boundary is perfectly absorbing. For a (partially) reflective ECO boundary, we find resonance structures in the response rate that depend on the different locations of the ECO boundary and those of the detector. We provide a detailed analysis in connection with the ECO's vacuum mode structure and transfer function.

Unruh-DeWitt Detector Differentiation of Black Holes and Exotic Compact Objects

Using Loop Quantum Gravity corrections one can study quantum gravity effects for a dust-gravity system, resulting in a Loop Quantum version of Oppenheimer-Snyder collapse. In this talk I will explain how this model is built up and the consequences of adding holonomy corrections to the classical theory. In particular, we see that, in the black hole formation, there is a bounce when the energy density of the dust field reaches the Planck scale and the matter starts expanding. This expansion reaches, eventually, the apparent horizon, at which point the horizon disappears and there is no longer a black hole.

Dust collapse and bounce in effective loop quantum gravity

Loop Quantum Gravity (LQG) is one proposed approach to quantize General Relativity. In previous literature LQG effects have been applied to Bianchi II spaces and here we numerically solve the resulting equations of motion using the fixed step 6th order Butcher-1 Runge-Kutta method. We also test, for a wide range of initial conditions, analytic transition rules for the Kasner exponents and show in which cases these transition rules hold.

Analyzing Loop Quantum Cosmology of Bianchi II Space with Numerical Methods

Spontaneous two-photon decay rates for the $1s2s\;^1S_0$ -- $1s^2\;^1S_0$ transition in helium and its isoelectronic sequence up to $Z$ = 10 are calculated, including the effects of finite nuclear mass. We use correlated variational wave functions in Hylleraas coordinates and pseudostate summations for intermediate states. The accuracy of previous work is improved by several orders of magnitude. Length and velocity gauge calculations agree to eight or more figures, demonstrating that the theoretical formulation correctly takes into account the three effects of (1) mass scaling, (2) mass polarization, and (3) radiation due to motion of the nucleus in the center-of-mass frame [1].

Algebraic relationships are derived and tested relating the expansion coefficients in powers of $\mu/M$, where $\mu/M$ is the ratio of the electron reduced mass to the nuclear mass. Astrophysical applications of two-photon transitions to the continuum emission around 400 $\mu$m in planetary nebulae will be briefly discussed.

[1] A. T. Bondy, D. C. Morton, and G.W.F. Drake, Phys.\ Rev.\ A {\bf 102}, 052807 (2020).

$^*$Research supported by NSERC and by SHARCNET.

Two-photon decay rates in heliumlike ions: finite nuclear mass effects$^*$

Guided by the application of loop quantum gravity (LQG) to cosmological space-times and techniques developed therein, I will present an effective framework for vacuum spherically symmetric space-times. Stationary solutions of the effective theory give an LQG corrected metric with a number of interesting properties including curvature scalars that are bounded by the Planck scale and a minimal (non-zero) mass for black hole formation. Finally, the vacuum solution we derive is only valid down to some minimum (non-zero) radial coordinate; this necessitates the inclusion of matter fields for a description of the full space-time and in particular address the question of singularity resolution.

Effective loop quantum gravity framework for vacuum spherically symmetric space-times

Resonant laser ionization spectroscopy uses multiple lasers to step-wise excite atom, therefore is a powerful tool for the study of high energy atomic structures, such as Rydberg states and autoionizing states. At the laser ion source test stand (LIS-stand) in TRIUMF, resonant laser ionization spectroscopy is used to study complex atoms. The spectroscopy results not only provide efficient laser ionization schemes for on-line laser ion source beam delivery of these elements but also the information of Rydberg and autoionizing states. This allows also to refine the energy of the ionization potential of these elements as well as extract information on some electron correlations. An overview of the off-line resonant laser ionization spectroscopy at TRIUMF will be presented.

Resonant laser ionization spectroscopy to study Rydberg and autoionizing states

The $^{137}\mathrm{Ba}^+$ ion is a promising candidate for high-fidelity quantum computing. We generate barium atoms using laser ablation of a $\mathrm{BaCl}_2$ target. The flux of neutral atoms generated by ablation is then ionized near our ion trap-center, giving us trapped ions which we can then use for quantum computing. Laser ablation loading can be used to trap ions more quickly and with less added heat load than other common loading methods. Because of the relatively low abundance of the isotope of interest, a two-step photoionization technique is used, which gives us the ability to selectively load a desired isotope. In this talk, I discuss characterization of the ablation process for our $\mathrm{BaCl}_2$ targets, including typical fluences needed, preparation and lifetimes of ablation spots, and plume temperature estimates. We demonstrate loading of single $^{137}\mathrm{Ba}^+$ ions with high selectivity compared to its 11% natural abundance.

Selective Laser Ablation Ion-Trap Loading of $^{137}\mathrm{Ba}^+$

If one wishes to understand and successfully simulate the radiation damage of biological tissue one needs to understand the fundamental ionization processes of molecules in the gas or vapour
phase first. The latter problem has been addressed in a number of studies in recent years, but experimental data have remained scarce and accurate cross-section predictions based on first-principles quantum-mechanical calculations challenging due to the complexity of the molecules of interest. There is thus a role to be played by simplified modelling - provided the models used
can be shown to work for simpler systems for which reliable theoretical and experimental data are available for comparison. 

We have recently developed one such model. It is based on the independent atom model (IAM) according to which a cross section, e.g., for electron removal from a molecule can be obtained from atomic cross sections for the same process. Instead of simply adding up the cross sections for all the atoms that make up the molecule we take geometric overlap into account, which arises when the atomic cross sections are pictured as circular disks surrounding the nuclei in the molecule. The overlapping areas are calculated using a pixel counting method (PCM) and, accordingly, we label our model IAM-PCM.

The IAM-PCM has been applied to a number of ion-impact collision problems with target systems 
ranging from relatively simple molecules, such as water and methane to complex biomolecules, 
such as the RNA and DNA nucleobases [1], and also including atomic and molecular clusters [2].
In this talk, I will explain the model, present a selection of recent results and discuss what can be learned from them. 

[1] H. J. Lüdde et al., J Phys. B 52, 195203 (2019); Phys. Rev. A 101, 062709 (2020); Atoms 8, 59 (2020).

[2] H. J. Lüdde et al., Eur. Phys. J. B 91, 99 (2018).

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Effective Raychaudhuri equation and black hole singularity resolution

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