Session B01: Contributed Talks II

Driven-dissipative creation of a topologically ordered state (AKLT State)

Dissipation in an open quantum system often destroys a quantum state of interest, but if carefully engineered, it can be used as a tool to prepare interesting quantum states. We propose an experimentally viable method to dissipatively create the AKLT (Affleck-Lieb-Kennedy-Tasaki) state which exhibits symmetry protected topological order and harbours gapped edge modes. We analyze a system of bosons trapped in a tilted optical lattice, driven by coherent Raman beams and coupled to a superfluid bath. We propose a protocol under which the AKLT state emerges as the steady state. We use exact diagonalization and DMRG methods to calculate the time scale for state preparation and find that the state preparation time scales quadratically with the system size.   

Lieb-Robinson bound and information propagation in long-range interacting systems

A fundamental principle of many-body physics is causality, that is, strict prohibition of information propagation outside the light cone. However, in non-relativistic systems, it is often unclear whether such a light cone can be well-defined. In 1972, this problem was completely solved by Lieb and Robinson in short-range interacting systems. The existence of the effective light-cone was proven; outside of it, the amount of information decays exponentially with the distance. This effective light-cone is characterized in the form of a ``Lieb-Robinson bound,'' and it is linear with respect to time. In the case where the interaction length is short-range, it is quite natural to expect that the information propagation is constrained by a finite velocity. However, beyond short-range interactions, the situation becomes highly non-trivial. In particular, for long-range interactions, information easily propagates to an arbitrarily distant point. Here, long-range interaction indicates that the interaction strength between separated sites demonstrates a power-law decay as $R^{-\alpha}$ for distance $R$. This intuitively leads to an impression that the linear-light cone can no longer be obtained in long-range interacting systems, as has been shown by Hastings and Koma [1]. Nevertheless, depending on the power-law exponent, it has been numerically [2] and experimentally [3] observed that a linear light cone still remains even under long-range interactions. This motivates the following linear light cone problem: ``what is the critical power-law exponent to induce the linear light cone?'' Owing to its importance and simplicity, the problem has received significant interest from researchers of various backgrounds. In this talk, we give the solution of the linear light cone problem [4]. Our result provides the complete proof of the linear light cone for $\alpha>2D+1$ in generic long-range interacting systems of arbitrary dimensions. The present study proves the optimality of our condition $\alpha>2D+1$ by showing an explicit counterexample which violates the linear light cone for $\alpha<2D+1$. In addition, we demonstrate that for $\alpha>D$ a polynomial form of the effective light cone still retains as long as if the out-of-time-order correlators are considered [5]. [1] M. B. Hastings and T. Koma, Communications in Mathematical Physics 265, 781 (2006). [2] P. Hauke and L. Tagliacozzo, Phys. Rev. Lett. 111, 207202 (2013). [3] P. Richerme, et al., Nature (London) 511, 198 (2014). [4] T. Kuwahara and K. Saito, Phys. Rev. X 10, 031010 (2020). [5] T. Kuwahara and K. Saito, Phys. Rev. Lett. 126, 030604 (2021).   

Experimental tests of isospin symmetry breaking in superallowed beta decay

In the search for physics beyond the standard model, the unitarity test of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is one of the most demanding. Superallowed $\beta $ transitions between $J^{\pi }=0^{+}$, $T=1$ analog states currently provide the most precise value for $V_{\mathrm{ud}}$, the up-down quark mixing element of the CKM-matrix. Since no axial current can contribute in first order to these transitions, they give a direct access to the vector coupling constant $G_{\mathrm{V}}$ of the weak interaction. The current value of $V_{\mathrm{ud}}$ is $\pm 0.03\% $ accurate [1] and is obtained from fifteen $ft$-values for superallowed $\beta $ decays, all measured with a precision of $0.3\% $ or better. There are four small theoretical corrections (all of the order of $1\% )$ required in the $V_{\mathrm{ud}}$ extraction. The current result's error is dominated by these theoretical corrections. From the experimentalist's perspective, precision can be further improved by testing the reliability of the predicted corrections. A powerful experimental test comes from measurements of mirror pair superallowed transitions [1,2] In these transitions the predicted corrections are relatively large and the ratio of their $ft$-values is very sensitive to the model calculation of the isospin-symmetry-breaking corrections $\delta_{NS} $ and $\delta_{C} $. The talk will focus on the experimental effort required, exemplifying with the mirror pair of superallowed $0^{+}\to 0^{+}\beta $ transitions ${ }^{34}\mbox{Ar}\to { }^{34}\mbox{Cl}$ and ${ }^{34}\mbox{Cl}\to { }^{34}\mbox{S.}$ [1] J. J. C. Hardy and I. S. Towner, Phys. Rev. C \textbf{102}, 045501 (2020) [2] V.E. Iacob \textit{et al.} Phys. Rev. C \textbf{101}, 045501 (2020)   

Mathematical Models for Living Forms in Medical Physics Submodel 2: Information Coding and Information Processing through Nerves

This talk continues the presentation Mathematical Models for Living Forms in Medical Physics Submodel 1: The information processing from teeth to Nerves from the Biophysics Annual Meeting 2020 Conference and American Physical Society Conferences. In the Submodel 1 the information processing from teeth to the nerves is modeled. The information is passed via p-waves through the tooth layers enamel and dentin. Odontoblasts located in the liquid in the tubules of the tooth dentin layer perform finally the transformation into electrical information (an electrical signal) that passes along nerves. The Submodel 2 of the project is dedicated to the information coding of the information from an entity hitting/touching a tooth and to the information processing of the coded unit through the nerves. Emphasized are the information representation as an electrical code and the coded information flow in the living system.   

Point with Precision Quaternion Series Quantum Mechanics

Prof. Scott Aaronson in a December, 2018 blog, "Why are amplitudes complex?" generalized QM to use quaternionic amplitudes. This led to the problem of superluminal signaling which is not physical, or as he put it, "a flaming garbage fire". I have chosen to study quaternions in quantum mechanics in a different way: use quaternion series where all the imaginary terms point in the same or opposite 3-direction which commute with themselves like complex numbers do. Experimentalists are exceptionally precise in their lab setups. This could be reflected in the math used. As Prof. Aaronson agreed, we will get back a body of work consistent with standard complex quantum mechanics and he asserted was so similar it doesn't deserve a different name. Complex numbers are a necessary mathematical abstraction. Yet what do they map to in the physical Universe? Quaternions have an interpretation in space-time: they are events, with time being real and 3D-space being three imaginary numbers. Quantum mechanics has been shown to be non-local based on experiments. I interpret that to mean one must only use space-like events because those are necessarily non-local. One must act on a quaternion series semi-group which is a finite or possibly infinite number of state dimensions.   

Quantum Mechanics: Electrons, Transistors, and LASERS

Quantum Mechanical (QM) principles have enabled the invention of transistors and LASERS that impact our daily lives. Why have there been over 14 different interpretations of QM in the last century? ``If you think you understand QM, you don't (Richard Feynman).'' The 1947 invention of the transistor at the Bell Telephone Laboratory came from the QM theory of electrons in semiconductors. In 1954, Charles Townes, by inverting the population of electron quantum states, invented the MASER (Microwave Amplification of the Stimulated Emission of Radiation). The LASER was demonstrated in 1960. Both are based on the following equation: the energy difference between quantum states equals the Planck constant times the frequency of the radiation. A reason there are so many different interpretations of QM is that we are using macroscopic concepts and language to describe microscopic phenomena. In some experiments, electrons exhibit particle properties. In other cases, they exhibit wave properties: the wavelength being equal to the Planck constant divided by the electron momentum. Niels Bohr called particle-wave duality the Complementarity Principle. The Heisenberg uncertainty principle states the fundamental limit to the accuracy of QM measurements.