Tuning of magnetic exchange interactions between organic radicals through bond and space

The dissertation entitled "Tuning of magnetic exchange interactions between organic radicals through bond and space" comprises eight chapters. In the initial part of chapter 1, an overview of organic radicals and their applications were discussed and in the latter part motivation and objective of thesis was described. As the EPR spectroscopy is a necessary tool to study organic radicals, the basic principles of EPR spectroscopy were discussed in chapter 2. rnAntiferromagnetically coupled species can be considered as a source of interacting bosons. Consequently, such biradicals can serve as molecular models of a gas of magnetic excitations which can be used for quantum computing or quantum information processing. Notably, initial small triplet state population in weakly AF coupled biradicals can be switched into larger in the presence of applied magnetic field. Such biradical systems are promising molecular models for studying the phenomena of magnetic field-induced Bose-Einstein condensation in the solid state. To observe such phenomena it is very important to control the intra- as well as inter-molecular magnetic exchange interactions. Chapters 3 to 5 deals with the tuning of intra- and inter-molecular exchange interactions utilizing different approaches. Some of which include changing the length of π-spacer, introduction of functional groups, metal complex formation with diamagnetic metal ion, variation of radical moieties etc. During this study I came across two very interesting molecules 2,7-TMPNO and BPNO, which exist in semi-quinoid form and exhibits characteristic of the biradical and quinoid form simultaneously. The 2,7-TMPNO possesses the singlet-triplet energy gap of ΔEST = –1185 K. So it is nearly unrealistic to observe the magnetic field induced spin switching. So we studied the spin switching of this molecule by photo-excitation which was discussed in chapter 6. The structural similarity of BPNO with Tschitschibabin’s HC allowed us to dig the discrepancies related to ground state of Tschitschibabin’s hydrocarbon(Discussed in chapter 7). Finally, in chapter 8 the synthesis and characterization of a neutral paramagnetic HBC derivative (HBCNO) is discussed. The magneto liquid crystalline properties of HBCNO were studied by DSC and EPR spectroscopy.rn

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Probing strongly correlated states of ultracold atoms in optical lattices

This thesis describes experiments which investigate ultracold atom ensembles in an optical lattice. Such quantum gases are powerful models for solid state physics. Several novel methods are demonstrated that probe the special properties of strongly correlated states in lattice potentials. Of these, quantum noise spectroscopy reveals spatial correlations in such states, which are hidden when using the usual methods of probing atomic gases. Another spectroscopic technique makes it possible to demonstrate the existence of a shell structure of regions with constant densities. Such coexisting phases separated by sharp boundaries had been theoretically predicted for the Mott insulating state. The tunneling processes in the optical lattice in the strongly correlated regime are probed by preparing the ensemble in an optical superlattice potential. This allows the time-resolved observation of the tunneling dynamics, and makes it possible to directly identify correlated tunneling processes.

A scanning electron microscope for ultracold quantum gases

This thesis presents a new imaging technique for ultracold quantum gases. Since the first observation of Bose-Einstein condensation, ultracold atoms have proven to be an interesting system to study fundamental quantum effects in many-body systems. Most of the experiments use optical imaging rnmethods to extract the information from the system and are therefore restricted to the fundamental limitation of this technique: the best achievable spatial resolution that can be achieved is comparable to the wavelength of the employed light field. Since the average atomic distance and the length scale of characteristic spatial structures in Bose-Einstein condensates such as vortices and solitons is between 100 nm and 500 nm, an imaging technique with an adequate spatial resolution is needed. This is achieved in this work by extending the method of scanning electron microscopy to ultracold quantum gases. A focused electron beam is scanned over the atom cloud and locally produces ions which are subsequently detected. The new imaging technique allows for the precise measurement of the density distribution of a trapped Bose-Einstein condensate. Furthermore, the spatial resolution is determined by imaging the atomic distribution in one-dimensional and two-dimensional optical lattices. Finally, the variety of the imaging method is demonstrated by the selective removal of single lattice site. rn