Complex systems dynamics in laser excited ensembles of Rydberg atoms

In this thesis I present experimental and theoretical results showing that an ultracold gas under laser excitation to Rydberg states offers a controllable platform for studying the interesting complex dynamics that can emerge in driven-dissipative systems. The findings can be summarized according to the following three main insights: (i) The discovery of self-organized criticality (SOC) in our Rydberg system under facilitated excitation via three signatures: self-organization of the density to a stationary state; scale invariant behavior; and a critical response in terms of power-law distributed excitation avalanches. Additionally, we explore a mechanism inherent to our system which stabilizes the SOC state. We further investigate this stabilization via a controlled, variable driving of the system. These analyses can help answer the question of why scale invariant behavior is so prevalent in nature. (ii) A striking connection between the power-law growth of the Rydberg excitation number and epidemic spreading is found. Based on this, an epidemic network model is devised which efficiently describes the collective excitation dynamics. The importance of heterogeneity in the emergent Rydberg network and associated Griffiths effects provide a way to explain the observation of non-universal power laws. (iii) A novel quantum cellular automata implementation is proposed using atomic arrays together with multifrequency laser fields. This provides a natural framework to study the relation between microscopic processes and global dynamics, where special rules are found to generate entangled states with applications in quantum metrology and computing

A suite of quantum algorithms for the shortestvector problem

Crytography has come to be an essential part of the cybersecurity infrastructure that provides a safe environment for communications in an increasingly connected world. The advent of quantum computing poses a threat to the foundations of the current widely-used cryptographic model, due to the breaking of most of the cryptographic algorithms used to provide confidentiality, authenticity, and more. Consequently a new set of cryptographic protocols have been designed to be secure against quantum computers, and are collectively known as post-quantum cryptography (PQC). A forerunner among PQC is lattice-based cryptography, whose security relies upon the hardness of a number of closely related mathematical problems, one of which is known as the shortest vector problem (SVP). In this thesis I describe a suite of quantum algorithms that utilize the energy minimization principle to attack the shortest vector problem. The algorithms outlined span the gate-model and continuous time quantum computing, and explore methods of parameter optimization via variational methods, which are thought to be effective on near-term quantum computers. The performance of the algorithms are analyzed numerically, analytically, and on quantum hardware where possible. I explain how the results obtained in the pursuit of solving SVP apply more broadly to quantum algorithms seeking to solve general real-world problems; minimize the effect of noise on imperfect hardware; and improve efficiency of parameter optimization.Open Acces

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Graduate School: Course Decriptions, 1972-73

Official publication of Cornell University V.64 1972/7

Development Of A Cold Atoms Platform For A DQC1 Implementation

In this work we report on the development progress of a cold atoms platform to demonstrate a model of quantum computation known as deterministic Quantum computing with One Clean Qubit (DQC1). This is a novel class of algorithms where interactions between qubits enable nonclassical correlations other than entanglement, namely discord. We aim to demonstrate the DQC1 protocol using a scheme in which the information processing is realized on cold neutral rubidium atoms through the cNOT gate based on a Rydberg blockade. The implementation of this protocol imposes very stringent requirements on the cloud of atoms: to realise the cNOT gate with high fidelity it is required that a full Rydberg blockade is operating throughout the extent of the ensemble. This means that a cloud of atoms needs to have a radius below approximately 5 μm (for Rydberg states of atoms n = 43). A dipole trap system was designed and implemented during the course of this PhD with the aim of satisfying these experimental constraints. In our setup, a vapour of 87Rb is first trapped in a Magneto-Optical Trap (MOT) and cooled to sub-Doppler temperatures. The atoms are then subsequently trapped in the dipole trap. Our dipole trapping setup is based on a high numerical aperture lens (NA=0.53) to achieve a sub-micron trapping potential and simultaneously observe trapped atoms with a micrometre resolution. According to the design and the optical tests, the system is capable of creating the trapping potential with about 1 μm waist and 4 μm Rayleigh length. The aim of this work was to examine and optimise experimental conditions under which the dipole trap should be operated, so that the sufficiently small trap for the DQC1 algorithm can be obtained in the future. For characterisation, a trap of a bigger volume (about 6 μm waist and 28 μm length) was setup instead of using the full capacity of the system. This enhanced the atom loading procedure and provided more convenient conditions for experiments. The temperature of atoms was typically around 250 μK, and the trap lifetime (2.5 s) was limited by the background collisions, which indicates that the vacuum was maintained on the expected level. The key findings of the thesis are that the properties of the atoms reservoir (MOT temperature and density), and the loading processes (intensity of MOT beams), need to be optimised to be able to load a micrometre size trap. These findings are instrumental for the future implementation of the DQC1 protocol and also have implications for other protocols founded on the use of a Rydberg blockade

Quantum mechanics in complex systems

This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. ^ In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system\u27s ability to stably bind \u27additional\u27 electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown. These nodes are spaced far enough from each other to minimized the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess elections into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more cost-effective method than the supporting D=3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in super-intense laser fields.^ Chapter 3, we delineate the model, and aspects therein, of inelastic electron tunneling and map this model to the protein environment. G protein-coupled receptors (GPCRs) constitute a large family of receptors that sense molecules outside of a cell and activate signal transduction pathways inside the cell. Modeling how an agonist activates such a receptor is important for understanding a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as the mechanism by which olfactory GPCRs are activated by an encapsulated agonist. In this note we apply this notion to GPCRs within the mammalian nervous system using ab initio quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a singular IET spectral aspect both amongst each other and with the serotonin molecule: a peak that scales in intensity with the known agonist activities. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its isotopologues in which hydrogen atoms are replaced by deuterium. If validated our theory may provide new avenues for guided drug design and better in silico prediction of efficacies. ^ Our final chapter, explores methods which may be explored to assist in the early instruction in quantum mechanics. The learning of quantum mechanics is contingent upon an understanding of the physical significance of the mathematics that one must perform. Concepts such as normalization, superposition, interference, probability amplitude and entanglement can prove challenging for the beginning student. This paper outlines several class exercises that use a non-classical version of tic-tac-toe to instruct several topics in an undergraduate quantum mechanics course. Quantum tic-tac-toe (QTTT) is a quantum analogue of classical tic-tac-toe (CTTT) benefiting from the use of superposition in movement, qualitative (and later quantitative) displays of entanglement and state collapse due to observation. QTTT can be used for the benefit of the students understanding in several other topics with the aid of proper discussion