Novel approaches to topological order involving open boundaries in closed and open quantum systems

The fundamental understanding of phases and their transitions has been a central theme in condensed matter physics. Until recently, it was largely believed that the Landau symmetry breaking principle was effective in distinguishing different phases of matter, with broken symmetries signaling the phase transition. But with the discovery of topological phases which are beyond the Landau symmetry breaking principle, the identification and classification of quantum phases at absolute zero has opened up new unexplored avenues thus leading to exciting theoretical discoveries further propelling technological advancement. Topological phases of matter are characterized by the notion of topological order and in this work we aim to explore and understand topological phases by introducing novel signatures which characterize topological order. The robustness of these phases to external perturbation makes them an ideal candidate to store and manipulate quantum information thus making them an unique and interesting prospect for realizing quantum computers. There have been several signatures to characterize intrinsic topological order, for instance the invariance of the topologically ordered state under local operators, the dependence of ground state degeneracy on the underlying manifold and its robustness to external perturbation, topological entanglement entropy related to the quantum dimension of the supers-selection sectors, the inability to construct the topologically ordered state from a product state via constant depth unitary transformations. With toric code as the toy model, we analyze the robustness of topological order on a manifold supporting open boundaries by computing some of the above signatures which effectively detect a topological to trivial phase transition. We then probe the existence of a quantum criticality between distinct topological phases obtained by varying the underlying manifold. In these scenarios, most of the above signatures turn out to be ineffective in detecting the distinct phases leading to the introduction of an non- local order parameter whose construction is facilitated by the phenomenon of anyon condensation. The signatures for quantitatively and qualitatively characterizing intrinsic topological order being highly scenario dependent and also with its definition for mixed states being elusive we introduce an operational definition based on concepts of topological error correction. We define a state to be topologically ordered if the errors in the state can be corrected by an error correction circuit of finite depth. To concretize the notion of topological to trivial phase transition in an open setting we turn to nonequilibrium phenomenon, for example: Directed Percolation, with the change in percolation rate driving a dynamical phase transition between absorbing and active states with the former being topologically ordered while the latter being topologically trivial. Additionally, we explore the notion of topological phase transitions between distinct topological phases obtained by varying underlying topology in an open setting, analogous to the closed setting discussed earlier. To summarize, we have introduced various mixed states which exhibit topological order and also an operational definition to quantify topological order applicable across multitude of scenarios. We extend the above operational definition to quantify and detect quantum phase transitions in the case of Symmetry Protected Topological (SPT) phases. To further validate the above notion, we consider the perturbed variants of the Su-Schrieffer–Heeger (SSH) models and detect quantum phase transitions to a high accuracy by employing the techniques from the framework of tensor networks. It is significant to note the distinction of the error correction algorithms applied earlier in the case of intrinsic topological order were independent of symmetry constraints while in the current scenario we impose additional symmetry constraints to accurately detect the phase transition. In addition, we also devise error correction strategies with respect to topologically trivial states to detect quantum phase transitions which do not involve topological phases. This gives rise to a very fundamental question on whether error correction statistics with a well defined error correction algorithm, not necessarily optimal, are capable of detecting a equivalence classes of phases and thereby acting as a reliable probe to effectively detect topological/quantum phase transitions? From theoretical and numerical end of the spectrum we shift gears to explore possible experimental platforms with an aim to realize some of the quantum many-body phenomenon discussed earlier. While there have been several innovative experimental avenues to realize the above, one such promising candidate has been ultracold polar molecules setups that offer additional degrees of freedom due to the ro-vibrational degrees of freedom. Based on the chemical reaction between atoms and molecules which results in a quantum Zeno-based blockade, we devise several optimal strategies to efficiently detect molecules using atom as probe, we further extend the above technique to entangle the internal states of molecules and atoms. In addition, we also present optimal strategies for dissipative state engineering using the atom-molecule interactions

Achieving High 1H Nuclear Hyperpolarization Levels with Long Lifetimes in a Range of Tuberculosis Drug Scaffolds

Despite the successful use of isoniazid, rifampicin, pyrazinamide and ethambutol in the treatment of tuberculosis (TB), it is a disease of growing global concern. We illustrate here a series of methods that will dramatically improve the magnetic resonance imaging (MRI) detectability of nineteen TB-relevant agents. We note that the future probing of their uptake and distribution in vivo would be expected to significantly enhance their efficacy in disease treatment. This improvement in detectability is achieved by use of the parahydrogen based SABRE protocol in conjunction with the 2H-labelling of key sites within their molecular structures and the 2H-labelling of the magnetization transfer catalyst. The T1 relaxation times and polarization levels of these agents are quantified under test conditions to produce a protocol to identify structurally optimized motifs for future detection. For example, deuteration of the 6-position of a pyrazinamide analogue leads to a structural form that exhibits T1 values of 144.5 s for 5-H with up to 20 % polarization. This represents a >7-fold extension in relaxation time and almost 10-fold improvement in polarization level when compared to its unoptimized structure

Network Analysis of Local Gene Regulators in Arabidopsis thaliana under Spaceflight Stress

Spaceflight microgravity affects normal plant growth in several ways. The transcriptional dataset of the plant model organism Arabidopsis thaliana grown in the international space station is mined using graph-theoretic network analysis approaches to identify significant gene transcriptions in microgravity essential for the plant’s survival and growth in altered environments. The photosynthesis process is critical for the survival of the plants in spaceflight under different environmentally stressful conditions such as lower levels of gravity, lesser oxygen availability, low atmospheric pressure, and the presence of cosmic radiation. Lasso regression method is used for gene regulatory network inferencing from gene expressions of four different ecotypes of Arabidopsis in spaceflight microgravity related to the photosynthetic process. The individual behavior of hub-genes and stress response genes in the photosynthetic process and their impact on the whole network is analyzed. Logistic regression on centrality measures computed from the networks, including average shortest path, betweenness centrality, closeness centrality, and eccentricity, and the HITS algorithm is used to rank genes and identify interactor or target genes from the networks. Through the hub and authority gene interactions, several biological processes associated with photosynthesis and carbon fixation genes are identified. The altered conditions in spaceflight have made all the ecotypes of Arabidopsis sensitive to dehydration-and-salt stress. The oxidative and heat-shock stress-response genes regulate the photosynthesis genes that are involved in the oxidation-reduction process in spaceflight microgravity, enabling the plant to adapt successfully to the spaceflight environment

Network Analysis of Local Gene Regulators in <i>Arabidopsis thaliana</i> under Spaceflight Stress

Spaceflight microgravity affects normal plant growth in several ways. The transcriptional dataset of the plant model organism Arabidopsis thaliana grown in the international space station is mined using graph-theoretic network analysis approaches to identify significant gene transcriptions in microgravity essential for the plant’s survival and growth in altered environments. The photosynthesis process is critical for the survival of the plants in spaceflight under different environmentally stressful conditions such as lower levels of gravity, lesser oxygen availability, low atmospheric pressure, and the presence of cosmic radiation. Lasso regression method is used for gene regulatory network inferencing from gene expressions of four different ecotypes of Arabidopsis in spaceflight microgravity related to the photosynthetic process. The individual behavior of hub-genes and stress response genes in the photosynthetic process and their impact on the whole network is analyzed. Logistic regression on centrality measures computed from the networks, including average shortest path, betweenness centrality, closeness centrality, and eccentricity, and the HITS algorithm is used to rank genes and identify interactor or target genes from the networks. Through the hub and authority gene interactions, several biological processes associated with photosynthesis and carbon fixation genes are identified. The altered conditions in spaceflight have made all the ecotypes of Arabidopsis sensitive to dehydration-and-salt stress. The oxidative and heat-shock stress-response genes regulate the photosynthesis genes that are involved in the oxidation-reduction process in spaceflight microgravity, enabling the plant to adapt successfully to the spaceflight environment