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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.

CAP Virtual Congress 2021

Analyzing Loop Quantum Cosmology of Bianchi II Space with Numerical Methods

bianchi ii

kasner

bounce

numerical

loop quantum gravity

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technical paper

We investigate the effect of coupling between translational and internal degrees of freedom of composite quantum particles on their localization in a random potential. We show that entanglement between the two degrees of freedom weakens localization due to the upper bound imposed on the inverse participation ratio by purity of a quantum state. We perform numerical calculations for a two-particle system bound by a harmonic force in a 1D disordered lattice and a rigid rotor in a 2D disordered lattice. We illustrate that the coupling has a dramatic effect on localization properties, even with a small number of internal states participating in quantum dynamics.

arXiv:2011.06279

Localization of composite quantum particles in a random potential

Scalar-tensor gravity can be described as general relativity plus an effective imperfect fluid corresponding to the scalar field degree of freedom of this class of theories. A symmetry of electrovacuum Brans-Dicke gravity translates into a symmetry of the corresponding effective fluid. We present the formalism and an application to an anomaly in the limit of Brans-Dicke theory to Einstein gravity. 

[Based on V. Faraoni & J. Côté, Phys. Rev. D 98, 084019 (2018); Phys. Rev. D 99, 064013 (2019)]

Scalar-tensor gravity as an imperfect fluid, with applications

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 model an atomic Bose-Einstein condensate (BEC) near an instability, looking for universal features. Instabilities are often associated with bifurcations where the classical field theory provided here by the Gross-Pitaevskii equation predicts that two or more solutions appear or disappear. Simple examples of such a situation can be realized in a BEC in a double well potential or in a BEC rotating in a ring trap. We analyze this problem using both Bogoliubov theory and exact diagonalization. The former describes elementary excitations which display complex frequencies near the bifurcation. We make connections to the description of bifurcations using catastrophe theory but modified to include field quantization.

Quantum bifurcations in a Bose-Einstein condensate

In recent years, multi-species trapped-ion systems have been investigated for the benefits they provide in quantum information processing experiments, such as sympathetic cooling and combining long coherence time of one species with ease of optical manipulation of the other. However, a large mass-imbalance between the ions result in decoupling of their motion in the collective vibrational (phonon) modes that are used to mediate entanglement between ion-qubits. We theoretically and numerically investigate a scheme that introduces far off-resonant optical tweezers, tightly focused laser beams on individual ions, of controllable strength in a conventional Paul (RF and DC) trap. The tweezers enable site-dependent control over the trapping strength and manipulation of the phonon mode structure (eigenfrequencies or eigenvectors) of the trapped-ion system. The tweezers provide local control over the effective mass of the ion and hence minimize the motional decoupling. We demonstrate an algorithm to program the optical tweezer array to achieve a target set of phonon modes. Our work paves the way for high efficiency sympathetic cooling and fast quantum gates in multi-species trapped-ion systems.

We acknowledge support from TQT (CFREF), the University of Waterloo, NSERC Discovery and NFRF grants, and Govt. of Ontario.

Manipulation of phonon modes in a trapped-ion system by optical tweezers

One of the cornerstones of Quantum Mechanics (QM), Heisenberg’s Uncertainty Principle (HUP), establishes that it is not possible to simultaneously measure with arbitrary precision both the position and the momentum of a quantum system. This principle, however, does not prevent one from measuring with infinite precision the system’s position. However, theories of Quantum Gravity, aiming to bridge between General Relativity and QM, predict the existence of a minimal observable length - a minimal uncertainty on the position generally of the order of the Planck length. This prediction results therefore in a contradiction with HUP, requiring a modification of the principle. This need gave rise to the Generalized Uncertainty Principle (GUP). In this talk, I will show how the GUP can change known aspects of standard QM, leading to ways to test Quantum Gravity.

Quantum Gravity Phenomenology from the Generalized Uncertainty Principle

Cooling atomic gases to ultracold temperatures revolutionized the field of atomic physics, connecting with and impacting many other areas in physics. Recent advances in producing ultracold molecules suggest similarly dramatic discoveries are on the horizon. I will review the physics of ultracold molecules, including our work bringing a new class of molecules to ultracold temperatures. Chemistry at these temperatures has a very different character than at room temperature. I will describe two striking effects: Spin-dependent reactivity and molecular Feshbach resonances.

Ultracold chemistry with triplet molecules

Over the past decade, significant progress has been made in the commercialization of quantum sensors based on ultra-cold atoms and matter-wave interferometry. Nowadays, the first absolute quantum gravimeters have reached the market and there is even a cold-atom machine on the International Space Station. Matter-wave interferometers utilize the wave nature of atoms and their interaction with laser light to create interference between different quantum-mechanical states. Compared to an optical interferometer, the roles of matter and light are reversed: light is used as the "optic" to split, reflect, and recombine matter-waves. The resulting interference contains precise information about the atom's motion, such as its acceleration, as well as the electro-magnetic fields that permeate its environment. These atom interferometers can be designed as extremely sensitive instruments and have already led to breakthroughs in time-keeping, gravimetry, and tests of fundamental physics. In this talk, I will give an overview of laser-cooling and matter-wave interferometry and its applications as a versatile tool, for example, to test Einstein's Equivalence Principle, map the Earth's gravitational field, or aid future navigation systems.

Quantum Sensing with Matter-Wave Interferometers

One of the most famous tidbits of received wisdom about quantum mechanics is that “you can’t ask” which path a photon took in an interferometer once it reaches the screen, or in general, that only questions about the specific things you finally measure are well-posed at all. Much work over the past decades has aimed to chip away at this blanket renunciation, and investigate “quantum retrodiction.” Particularly in light of modern experiments in which we can trap and control individual quantum systems for an extended time, and quantum information protocols which rely on “postselection,” these become more and more timely issues.

All the same, the principal experiment I wish to tell you about addresses a century-old controversy: that of the tunneling time. Since the 1930s, and more heatedly since the 1980s, the question of how long a particle spends in a classically forbidden region on those occasions when quantum uncertainty permits it to appear on the far side has been a subject of debate. Using Bose-condensed Rubidium atoms cooled down below a billionth of a degree above absolute zero, we have now measured just how long they spend inside an optical beam which acts as a “tunnel barrier” for them. I will describe these ongoing experiments, as well as proposals we are now refining to study exactly how long it would take to “collapse” an atom to be in the barrier.

I will also say a few words about a more recent experiment, which looks back at the common picture that when light slows down in glass, or a cloud of atoms, it is because the photons “get virtually absorbed” before being sent back along their way. It turns out that although it is possible to measure “the average time a photon spends as an atomic excitation,” there seems to be no prior work which directly addresses this, especially in the resonant situation. We carry out an experiment that lets us distinguish between the time spent by transmitted photons and by photons which are eventually absorbed, asking the question “how much time are atoms caused to spend in the excited state by photons which are not absorbed?”

Quantum archæology: how much time does an atom spend tunneling through a beam of light, and how much time do photons spend “trapped” in atoms?

Many of previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. 

In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.

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Analyzing Loop Quantum Cosmology of Bianchi II Space with Numerical Methods

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