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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.

CAP Virtual Congress 2021

Quantum Gravity Phenomenology from the Generalized Uncertainty Principle

minimal length

generalized uncertainty principle

quantum gravity phenomenology

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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

A crucial challenge in engineering modern, integrated systems is to produce robust designs. However, quantifying the robustness of a design is less straightforward than quantifying the robustness of products. For products, in particular engineering materials, intuitive, plain language terms of strong versus weak and brittle versus ductile take on precise, quantitative meaning in terms of stress–strain relationships. Here, we show that a “systems physics” framing of integrated system design produces stress–strain relationships in design space. From these stress–strain relationships, we find that both the mathematical and intuitive notions of strong versus weak and brittle versus directly characterize the robustness of designs. We use this to show that the relative robustness of designs against changes in problem objectives has a simple graphical representation. This graphical representation, and its underlying stress–strain foundation, provide new metrics that can be applied to classes of designs to assess robustness from feature- to system-level.

Robust Design from Systems Physics

Crowded soft-matter and biological systems organize locally into preferred motifs. Locally-organized motifs in soft systems can, paradoxically, arise from a drive to maximize overall system entropy. Entropy-driven local order has been directly confirmed in model, synthetic colloidal systems, however similar patterns of organization occur in crowded biological systems ranging from the contents of a cell to collections of cells. In biological settings, and in soft matter more broadly, it is unclear whether entropy generically promotes or inhibits local organization. Resolving this is difficult because entropic effects are intrinsically collective, complicating efforts to isolate them. Here, we employ minimal models that artificially restrict system entropy to show that entropy drives systems toward local organization, even when the model system entropy is below reasonable physical bounds. By establishing this bound, our results suggest that entropy generically promotes local organization in crowded soft and biological systems of rigid objects.

When does entropy promote local organization?

Accelerator Mass Spectrometry (AMS) provides high sensitivity measurements (typically at or below 1 part in $10^{12}$) for rare, long-lived radioisotopes when isobars (other elements with the same atomic weight as the isotope of interest) can be eliminated. In AMS laboratories, established techniques are used for the removal of the interfering isobars of some light isotopes. However, for smaller, lower-energy AMS systems separating the abundant isobars of many isotopes, such as the sulfur-36 in measurements of chlorine-36, remains a challenge. For some heavy isotopes, such as strontium-90 and cesium-135,137, even high energy accelerators are unable to separate the interfering isobars. 

The Isobar Separator for Anions (ISA), which has been integrated into a second injection line of the 3 MeV tandem accelerator system at the A. E. Lalonde AMS Laboratory, will provide a universal way to measure rare radioisotopes without the interference of abundant isobars. The ISA is a radiofrequency quadrupole (RFQ) reaction cell system, including a DC deceleration region, a combined cooling and reaction cell, and a DC acceleration region. The deceleration region accepts a mass analyzed beam from the ion source (with energy 20-35 keV) and reduces the energy to a level that the reaction cell can accept. RFQ segments along the length of the cell create a potential well which limits the divergence of the traversing ions. DC rod offset voltages on these RFQ segments maintain a controlled ion velocity through the cell. The cell is filled with an inert cooling gas that has been experimentally selected to provide the lowest ion energy and the highest transmission, and with nitrogen dioxide, a reaction gas chosen to preferentially react with the interfering isobar. In the case of chlorine-36, the sulfur-36 isobar has been shown to be reduced by over $10^{6}$. Preliminary characterization of the ISA and its incoming and outgoing ion beams will be presented.

Characterization of the Isobar Separator for Anions for Accelerator Mass Spectrometry measurements

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

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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Quantum Gravity Phenomenology from the Generalized Uncertainty Principle

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