Pairing correlations and phase transitions in mesoscopic or small systems are studied through out this dissertation. We start our discussion by showing the importance of short range correlations and their role in forming bound Cooper pairs. For a model Hamiltonian, we solved the Schr¨odinger equation in the harmonic oscillator basis analytically, the concept of self consistency is used to get the whole energy spectrum. Using variational methods applied to a trial wave function, we derived the BCS equations, which again should be solved self consistently with particle number to produce the total energy. Some examples of BCS calculations in realistic case like in the Sn isotopes are shown. Various approximations such as one level, two levels and five levels systems are discussed. In the five levels model calculations, we compare our results with the previous works by other authors. We also find a good agreement with the experimental data. We extend our BCS calculations by adding the three body interaction term. This additional term is unlikely to improve our results compared to the experiment. In a separate work, using numerical and analytical methods implemented for different models we conduct a systematic study of thermodynamic properties of pairing correlations in mesoscopic nuclear systems. Various quantities are calculated and analyzed using the exact solution of pairing. An in-depth comparison of canonical, grand canonical, and microcanonical ensemble is conducted. The nature of the pairing phase transition in a small system is of particular interest. We discuss the onset of discontinuities in the thermodynamic variables, fluctuations, and evolution of zeros of the canonical and grand canonical partition functions in the complex plane. The behavior of the Invariant Correlational Entropy is also studied in the transitional region of interest. The change in the character of the phase transition due to the presence of magnetic field is discussed along with studies of superconducting thermodynamics. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Fall Semester, 2007. / Date of Defense: October 8, 2007. / Nuclear structure, Thermodynamics, BCS, Phase Transitions, Pairing, Mesoscopic Systems, Exact solution of pairing / Includes bibliographical references. / Alexander Volya, Professor Directing Dissertation; Hong Li, Outside Committee Member; Jorge Piekarewicz, Committee Member; Grigory Rogachev, Committee Member; Vladimir Dobrosavljevic, Committee Member.

This dissertation presents the first measurement of top quark pair production cross-section in events containing a muon and a tau lepton. The measurement was done with 1 fb−1 of data collected during April 2002 through February 2006 using the DØ detector at the Tevatron proton-antiproton collider, located at Fermi National Accelerator Laboratory (Fermilab), Batavia, Illinois. Events containing one isolated muon, one tau which decays hadronically, missing transverse energy, and two or more jets (at least one of which must be tagged as a heavy flavor jet) were selected.Twenty-nine candidate events were observed with an expected background of 9.16 events. The top quark pair production cross-section is measured to beσ (t¯t) = 8.0+2.8 −2.4 (stat)+1.8−1.7 (syst) ± 0.5 (lumi) pb.Assuming a top quark pair production cross-section of 6.77 pb for Monte Carlo signal top events without a real tau, the measured σ × BR isσ (t¯t) × BR(t¯t μ +τ + 2ν + 2b) = 0.18+0.13−0.11 (stat)+0.09−0.09 (syst) ± 0.01 (lumi) pb. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Spring Semester, 2008. / Date of Defense: November 26, 2007. / Cross-section, D0, Tevatron, Fermilab, Tau lepton, Top quark / Includes bibliographical references. / Todd Adams, Professor Directing Dissertation; Ettore Aldrovandi, Outside Committee Member; Horst Wahl, Committee Member; Laura Reina, Committee Member; Simon Capstick, Committee Member.

Results are reported on the reaction gamma p -> p p anti-p with beam energy in the range 4.8-5.5 GeV. The data were collected at the Thomas Jefferson National Accelerator Facility in CLAS experiment E01-017(G6C). The focus of this study is an understanding of the mechanisms of photoproduction of proton-antiproton pairs, and to search for intermediate resonances, both narrow and broad, which decay to p anti-p. The total measured cross section in the photon energy range 4.8-5.5 GeV is sigma = 33 +/- 2 nb. Measurement of the cross section as a function of energy is provided. An upper limit on the production of a narrow resonance state previously observed with a mass of 2.02 GeV/c^2 is placed at 0.35 nb. No intermediate resonance states were observed. Meson exchange production appears to dominate the production of the proton-antiproton pairs. p p anti-p with beam energy in the range 4.8-5.5 GeV. The data were collected at the Thomas Jefferson National Accelerator Facility in CLAS experiment E01-017(G6C). The focus of this study is an understanding of the mechanisms of photoproduction of proton-antiproton pairs, and to search for intermediate resonances, both narrow and broad, which decay to p anti-p. The total measured cross section in the photon energy range 4.8-5.5 GeV is sigma = 33 +/- 2 nb. Measurement of the cross section as a function of energy is provided. An upper limit on the production of a narrow resonance state previously observed with a mass of 2.02 GeV/c^2 is placed at 0.35 nb. No intermediate resonance states were observed. Meson exchange production appears to dominate the production of the proton-antiproton pairs. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Fall Semester, 2006. / Date of Defense: June 16, 2006. / Proton, Antiproton, pbar, Anti-p, Photoproduction, Reso / Includes bibliographical references. / Paul Eugenio, Professor Directing Dissertation; Gregory Riccardi, Outside Committee Member; Todd Adams, Committee Member; Larry Dennis, Committee Member; Alexander Ostrovidov, Committee Member; Jorge Piekarewicz, Committee Member; Dennis Weygand, Committee Member.

LnBaCo2O5.5 (Ln=Gd, Eu) and Sr3Ru2O7 are examples of weakly magnetic systems of 3d and 4d transition metal oxides, respectively. The former is nonmetallic and exhibits magnetic properties of two sublattice magnetic systems with an in-plane ferromagnetic interaction and a relatively weak temperature dependent inter-plane magnetic coupling. The latter is a paramagnetic metal with strongly correlated electrons near a magnetic instability. The magnetization, resistivity and magnetoresistance (MR) of single crystals of GdBaCo2O5.5 and EuBaCo2O5.5 are measured over a wide range of dc magnetic fields (up to 30 T) and temperature. We confirm that GdBaCo2O5.5 and EuBaCo2O5.5 have a metal-insulator transition accompanied by a spin-state transition at TMI » 365 and 335 K, respectively. The data suggest an equal ratio of low spin (S=0) and intermediate spin (S=1) Co3+ ions below TMI, with no indication of additional spin state transitions. The low field magnetization shows a transition to a highly anisotropic ferromagnetic phase, followed by another magnetic transition to an antiferromagnetic phase at a slightly lower temperature. Significant anisotropy between the a-b plane and c axis was observed in magnetic and magnetotransport properties for both compounds. For GdBaCo2O5.5, the resistivity and MR data imply a strong correlation between the spin-order and charge carriers. For EuBaCo2O5.5, the magnetic phase diagram is very similar to its Gd counterpart, but the low-T MR with current flow in the ab plane is positive rather than negative as for GdBaCo2O5.5. The magnitude and the hysteresis of the MR for EuBaCo2O5.5 decrease with increasing temperature, and at higher T the MR changes sign and becomes negative. The difference in the behavior of both compounds may arise from a small valence admixture in the nonmagnetic Eu ions, i.e. a valence slightly less than 3+. The specific heat and electrical resistivity of Sr3Ru2O7 single crystals are measured in several magnetic fields applied along the c-axis for temperatures below 2 K and at fields up to 17 T. Near the critical metamagnetic field at B1*~7.8 T, the electronic specific heat divided by temperature increases logarithmically as the temperature decreases, over a large range of T, before saturating below a certain T* (which is sample dependent). This crossover from a non-Fermi Liquid to a Fermi Liquid state is also observed in the resistivity data near the critical metamagnetic field for I || c and B || c. At the lowest temperatures, a Schottky-like upturn with decreasing temperature is observed. The coefficient of the Schottky anomaly exhibits a field dependence similar to that of g, implying an influence by the electrons near the Fermi surface on the Schottky level splitting. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Fall Semester, 2004. / Date of Defense: September 24, 2004. / Metamagnetic transition, Spin state transition, Strongly correlated electron systems, Quantum critical point, Ruthenate, Cobalt oxide, Magnetic Phase Transition, Giant magnetoresistance / Includes bibliographical references. / Jack Crow (Deceased), Professor Directing Dissertation; Pedro Schlottmann, Professor Co-Directing Dissertation; Naresh Dalal, Outside Committee Member; Jorge Piekarewicz, Committee Member; Peng Xiong, Committee Member; James Brooks, Committee Member.

This thesis presents the first measurement of the differential production cross section of a heavy flavor (bottom or charm) jet and direct photon at the Fermilab Tevatron. These measurements were performed using data recorded with the D0 detector from proton-antiproton collisions at a center of mass energy of sqrt(s) = 1.96 TeV. These results probe a kinematic range for the photon transverse momentum of 30 to 150 GeV and photon rapidity |y| / A Dissertation submitted to the Department of Physics in partial requirements for the degree of Doctor of Philosophy. / Degree Awarded: Spring Semester, 2009. / Date of Defense: March 26, 2009. / Photon, Heavy Flavor, Jet, Tevatron, Cross Section / Includes bibliographical references. / Horst Wahl, Professor Directing Dissertation; Chris Schatschneider, Outside Committee Member; Todd Adams, Committee Member; Joseph Owens III, Committee Member; Efstratios Manousakis, Committee Member.

The question of how do the properties of nuclei evolve with increasing excitation energy and angular momentum is one of the current frontiers in nuclear physics. State of the art $gamma$-ray detector systems have been used to investigate this question, in a series of rare-earth nuclei with mass extit{A}$sim$158. Significant extensions to the high-spin excitation spectrum of the $N$=91, 92, 93 isotopes $^{157,158,159}$Dy have been achieved using the high-efficiency $gamma$-ray spectrometers EUROBALL and GAMMASPHERE. These nuclei were populated via weak 3$n$ or $alpha xn$ exit channels in fusion evaporation reactions. In $^{157}$Dy, the yrast band has been extended to extit{I}$^pi$=$frac{101}{2}^{+}$ (tentatively to $frac{105}{2}^{+}$) with four sideband structures (two of which are new) observed in the 35$-$50 $hbar$ spin range. In $^{158}$Dy, three bands have been extended to 42$^{+}$ (44$^{+}$), 40$^{-}$, and 41$^{-}$ (43$^{-}$), while in $^{159}$Dy the yrast band is observed to $frac{81}{2}^{+}$ ($frac{85}{2}^{+}$). A total of 84 (99) new transitions, including 2 new bands, were added to the level schemes of $^{157,158,159}$Dy. The high-spin behavior and band crossing systematics of the Dy isotopes and of the neighboring $N$=91, 92, and 93 isotones are discussed in terms of rotational alignments and shape transitions. Cranked Nilsson-Strutinsky calculations without pairing have been performed for detailed comparisons with the very high-spin states observed in $^{157}$Dy. Results on $^{157,158,159}$Dy have been published in extit{Phys. Rev. C.} Moreover, the angular-momentum induced transition from a deformed state of collective rotation to a non-collective configuration has been studied. In $^{158}$Er this transition manifests itself as favored band termination near extit{I}$approx$45$hbar$. The feeding of these band terminating states has been investigated for the first time using the GAMMASPHERE spectrometer. A large number of weakly populated states, lying at high excitation energy, that decay into these special states have been discovered. Cranked Nilsson-Strutinsky calculations suggest that these states arise from weakly collective configurations that break the $Z$=64 semi-magic core. Additionally, a new frontier of discrete-line $gamma$-ray spectroscopy at ultra-high spin has been opened in the rare-earth nucleus $^{158}$Er. Two rotational structures, displaying high moments of inertia, have been identified, which extend up to spin $sim$65$hbar$ and bypass the band-terminating states in these nuclei near extit{I}$sim$45$hbar$. Cranked Nilsson-Strutinsky calculations suggest that these structures arise from well-deformed triaxial configurations that lie in a valley of favored shell energy, which also includes the well-known triaxial strongly deformed bands in $^{161-167}$Lu. Overall, 182 (209) new transitions, including 10 new bands, were placed in the greatly augmented level scheme of $^{158}$Er, as a result of our work in this thesis. Four of the new bands are based on high$-$ extit{K} quasiparticle excitations, which provide a stringent test of the Cranked Shell Model. This enables the investigation and interpretation of many different quasiparticle configurations from their alignment properties and band crossings systematics. Results on $^{158}$Er have been published in extit{Phys. Rev. Lett.} and extit{Phys. Scr.} Finally, a local experiment, using the FSU tandem accelerator and the FSU $gamma$-ray detectors, was performed to investigate the odd-odd nucleus $^{158}$Tb. Unfortunately, no new significant results on the latter were obtained except for the tentative assignment of a new, strongly-coupled, rotational structure.} / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Fall Semester, 2006. / Date of Defense: October 31, 2006. / 157158159Dysprosium, 158Erbium, 158Terbium, High-Spin, Rare-Earth, Nuclear Structure, Band Termination, Gamma-Ray / Includes bibliographical references. / Mark A. Riley, Professor Directing Dissertation; Ettore Aldrovandi, Outside Committee Member; Jorge Piekarewicz, Committee Member; Laura Reina, Committee Member; Paul M. Eugenio, Committee Member.

The exploration of new paradigms for micro- and nanoelectronics has engendered several exciting new research fields including molecular electronics and spintronics. Two essential ingredients of the device structures are materials and interfaces. The overarching theme of this dissertation is the study of the (spin-dependent) electronic states and transport in novel magnetic materials and through molecular interfaces. These experiments are necessary first steps in ascertaining potential utilities in molecular electronic and spintronics applications. More importantly for this thesis, the materials and hybrid device structures provide a fertile ground for studying basic physics of magnetism, magnetotransport, and spin transport. In this dissertation, various techniques of superconducting spectroscopy have been used to investigate the spin-dependent electronic density of states of the thiol/Au molecular interface and the ferromagnetic semimetal EuB6. In addition, a fresh analysis of the electronic transport properties of EuB6 reveals a new type of nonlinear Hall effect intimately related to its magnetic state and culminates in a model that offers excellent quantitative understanding of the data and appears applicable to a wide varieties of magnetic materials. In order to directly probe possible induced magnetism at the thiol-gold interface, spin polarized tunneling measurements were performed on planar tunnel junctions incorporating a molecular monolayer of mercaptohexadecanoic acid [HS(CH2)15COOH] (MHA) between aluminum and gold electrodes. The Zeeman resolved tunneling spectra yield no measurable spin polarization at the thiol-gold interface, contrary to the expectations from the reported induced giant magnetic moments at the interface. On the other hand, variations in the resistance of the fabricated tunnel junctions with changing environmental conditions were consistently observed. A systematic investigation revealed that the effect is directly linked to the interaction of water molecules with the carboxylate groups of the MHA monolayer at the AlOx surface. Analyses of the I-V characteristics produce compelling evidence for significant modifications of the tunnel barrier height of the AlOx upon adsorption of the MHA monolayer, and subsequently by the reaction of water molecules with the carboxylate group at the AlOx surface. The results demonstrate that environmental effects could significantly impact the electron transport even in molecular junctions of macroscopic dimensions and closed architecture. Andreev reflection spectroscopy measurements performed on junctions consisting of EuB6 single crystals and lead electrodes clearly demonstrated that EuB6 is not a half metal with a fully spin polarized Fermi surface. Instead, the measured spin polarization values range from 47% to 65%. Analyses based on the measured spin polarization together with Fermi surface and transport measurements lead to a quantitatively consistent picture in agreement with a semimetallic band structure with a substantial band splitting for the valence band only in the ferromagnetic phase. Moreover, the analyses also indicate a semimetallic band structure with localized holes in the paramagnetic phase and a delocalization of the holes near ferromagnetic ordering. Our studies on EuB6 provide important clarification of its spin dependent band structure. Hall effect and magnetoresistance measurements were also performed on EuB6 single crystals. The data are consistent with previous reports. However, we offer a new analysis of the Hall effect which has led to significant new insights. An unusual change in the Hall resistivity slope with increasing magnetic field was observed in the paramagnetic phase. The change in Hall resistivity slope was found to occur at a universal critical magnetization at all temperatures. A two-component model based on a picture of intrinsic (non-chemical) electronic/magnetic inhomogeneities and coalescing of a phase with higher conductivity and degree of magnetic ordering was proposed to fit the observed Hall effect. Excellent quantitative agreement was obtained and with this model all the Hall resistivity data were scaled onto a single curve. Significantly, this model and picture were found to offer consistent description of the nonlinear Hall effect in a diverse group of magnetic materials including the mixed valence perovskites and the heavy fermion metal YbRh2Si2. The results indicate that this may be a common form of Hall effect associated with percolative magnetic phase transitions. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctorate of Philosophy. / Degree Awarded: Summer Semester, 2008. / Date of Defense: June 2, 2008. / Andreev Reflection, Molecular Electronics, Magnetism, Colossal Mgagnetoresistance, Hall Effect, Spin Polarization / Includes bibliographical references. / Peng Xiong, Professor Directing Thesis; Naresh Dalal, Outside Committee Member; Stephan von Molnár, Committee Member; Oskar Vafek, Committee Member; Jorge Piekarewicz, Committee Member.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2013. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Cataloged from student-submitted PDF version of thesis. / Includes bibliographical references (pages 137-153). / A new generation of interferometric gravitational wave detectors, currently under construction, will closely approach the fundamental quantum limits of measurement, serving as a prominent example of quantum mechanics at the macroscale. Simultaneously, numerous experiments involving micro-mechanical oscillators are beginning to explore the quantum regime, with the help of optical cooling techniques. We discuss the approach to the quantum regime in a gram-scale opto-mechanical experiment, and in large-scale gravitational wave detectors. The gram-scale experiment is designed so that radiation pressure forces completely dominate the dynamics of the mechanical mirror suspensions. We review a series of optical trapping and cooling techniques that we have demonstrated using this apparatus. A variant of these techniques is applied to a gravitational wave interferometer -- yielding an effective temperature of 1.4 microkelvin and a phonon occupation number of 234 in a kilogram-scale oscillator. Then we analyze the displacement noise spectrum in the gram-scale system, which is currently limited by thermally driven fluctuations of the mirror suspensions. We identify methods for improving the suspension, in order to reveal the quantum fluctuations attributable to back-action of a displacement measurement. Finally, we propose a scheme for exploiting the opto-mechanical coupling in this system to generate optical entanglement. / by Christopher Wipf. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1999. / Includes bibliographical references (p. 143-147). / by Adam D. Polcyn. / Ph.D.

A quantum computer is a proposed device which would be capable of initializing, coherently manipulating, and measuring quantum states with sufficient accuracy to carry out new kinds of computations. In the standard scenario, a quantum computer is built out of quantum bits, or qubits, two-level quantum systems which replace the ordinary classical bits of a classical computer. Quantum computation is then carried out by applying quantum gates, the quantum equivalent of Boolean logic gates, to these qubits. The most fundamental barrier to building a quantum computer is the inevitable errors which occur when carrying out quantum gates and the loss of quantum coherence of the qubits due to their coupling to the environment (decoherence). Remarkably, it has been shown that in a quantum computer such errors and decoherence can be actively fought using what is known as quantum error correction. A closely related proposal for fighting errors and decoherence in a quantum computer is to build the computer out of so-called topologically ordered states of matter. These are states of matter which allow for the storage and manipulation of quantum states with a built in protection from error and decoherence. The excitations of these states are non-Abelian anyons, particle-like excitations which satisfy non-Abelian statistics, meaning that when two excitations are interchanged the result is not the usual +1 and -1 associated with identical Bosons or Fermions, but rather a unitary operation which acts on a multidimensional Hilbert space. It is therefore possible to envision computing with these anyons by braiding their world-lines in 2+1-dimensional spacetime. In this Dissertation we present explicit procedures for a scheme which lives at the intersection of these two approaches. In this scheme we envision a functioning "conventional" quantum computer consisting of an array of qubits and the ability to carry out quantum gates on these qubits. We then give explicit quantum circuits (sequences of quantum gates) which can be used to create and maintain a topologically ordered state with non-Abelian anyon excitations using the "conventional" qubits of the computer. Our circuits perform measurements on these qubits which detect "errors" corresponding to deviations from the topologically ordered ground state of interest. We also give circuits which can be used to move these errors and eventually fuse them with other errors to eliminate them. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2015. / August 31, 2015. / Error Correction, Fibonacci anyon, Levin-Wen model, Non-Abelian, Quantum Computation / Includes bibliographical references. / Nicholas E. Bonesteel, Professor Directing Dissertation; Philip L. Bowers, University Representative; Jorge Piekarewicz, Committee Member; Kun Yang, Committee Member; Peng Xiong, Committee Member.