The Mathematical Structure Of Arrangement Channel Quantum Mechanics, 2017 Iowa State University

#### The Mathematical Structure Of Arrangement Channel Quantum Mechanics, James W. Evans

*James W. Evans*

A non-Hermitian matrix Hamiltonian H appears in the wavefunction form of a variety of many-body scattering theories. This operator acts on an arrangement channel Banach or Hilbert space 1(;' = Ell ncr where ,r is the N-particle Hilbert space and a are certain arrangement channels. Various aspects of the spectral and semigroup theory for H are considered. The normalizable and weak (wavelike) eigenvectors ofH are naturally characterized as either physical or spurious. Typically H is scalar spectral and "equivalent" to H on an H-invariant subspace of physical solutions. If the eigenvectors form a basis, by constructing a suitable biorthogonal system, we ...

Quantum Optical Interferometry And Quantum State Engineering, 2017 The Graduate Center, City University of New York

#### Quantum Optical Interferometry And Quantum State Engineering, Richard J. Birrittella Jr

*All Graduate Works by Year: Dissertations, Theses, and Capstone Projects*

We highlight some of our research done in the fields of quantum optical interferometry and quantum state engineering. We discuss the body of work for which our research is predicated, as well as discuss some of the fundamental tenants of the theory of phase estimation. We do this in the context of quantum optical interferometry where our primary interest lies in the calculation of the quantum Fisher information as it has been shown that the minimum phase uncertainty obtained, the quantum Cramer-Rao bound, is saturated by parity-based detection methods. We go on to show that the phase uncertainty one obtains ...

The Iterative Method For Quantum Double-Well And Symmetry-Breaking Potentials, 2017 Clark Atlanta University

#### The Iterative Method For Quantum Double-Well And Symmetry-Breaking Potentials, Nada Alsufyani

*Electronic Theses & Dissertations Collection for Atlanta University & Clark Atlanta University*

Numerical solutions of quantum mechanical problems have witnessed tremendous advances over the past years. In this thesis, we develop an iterative approach to problems of double-well potentials and their variants with parity-time-reversal symmetry- breaking perturbations. We show that the method provides an efficient scheme for obtaining accurate energies and wave functions. We discuss in this thesis potential applications to a variety of related topics such as phase transitions, symmetry breaking, and external field-induced effects.

Orthogonal Representations, Projective Rank, And Fractional Minimum Positive Semidefinite Rank: Connections And New Directions, 2017 Iowa State University

#### Orthogonal Representations, Projective Rank, And Fractional Minimum Positive Semidefinite Rank: Connections And New Directions, Leslie Hogben, Kevin F. Palmowski, David E. Roberson, Simone Severini

*Electronic Journal of Linear Algebra*

Fractional minimum positive semidefinite rank is defined from r-fold faithful orthogonal representations and it is shown that the projective rank of any graph equals the fractional minimum positive semidefinite rank of its complement. An r-fold version of the traditional definition of minimum positive semidefinite rank of a graph using Hermitian matrices that fit the graph is also presented. This paper also introduces r-fold orthogonal representations of graphs and formalizes the understanding of projective rank as fractional orthogonal rank. Connections of these concepts to quantum theory, including Tsirelson's problem, are discussed.

Studies In Mesoscopics And Quantum Microscopies, 2017 Illinois Wesleyan University

#### Studies In Mesoscopics And Quantum Microscopies, Zhenghao Ding, Gabriel C. Spalding

*Honors Projects*

This thesis begins with a foundational section on quantum optics. The single-photon detectors used in the first chapter were obtained through the Advanced Laboratory Physics Association (ALPhA), which brokered reduced cost for educational use, and the aim of the single-photon work presented in Chapter 1 is to develop modules for use in Illinois Wesleyan's instructional labs beyond the first year of university. Along with the American Association of Physics Teachers, ALPhA encourages capstone-level work, such as Chapter 1 of this honors thesis, which is explicitly designed to play the role of passing on, to a next generation of physics ...

Holographic Non-Perturbative Thermodynamic Systems, 2017 College of William and Mary

#### Holographic Non-Perturbative Thermodynamic Systems, Michael C. Kopreski

*Undergraduate Honors Theses*

The anti-de Sitter/conformal field theory (AdS/CFT) correspondence conjectures a duality between field theories and higher dimensional theories of gravitation. Recent results describing thermodynamic systems in the AdS/CFT context include an exact description of the efficiency of black hole heat engines, suggesting questions regarding the nature of heat engines within this formulation and the extent to which thermodynamic principles may be applied. We verify the Clausius statement and the maximum efficiency of the Carnot engine, and show that these follow from the thermodynamic definitions of the heat engine.

In a related scope, we propose that, given the Ryu-Takayanagi ...

Key Encryption Through Quantum Optics, 2017 Georgia College and State University

#### Key Encryption Through Quantum Optics, Madison Durrance, Zach Galberd, Abbey Savage, Tristan Cabrera, Josh Hoffman

*Georgia College Student Research Events*

Cryptography has been around since the dawn of human civilization to send private messages for commercial, military, and political purposes. Some of the most important ciphers are the Vigenère cipher, the enigma, and the more modern RSA. Because of the development of the internet, private encryption has also become increasingly more important. The weakest link of encryption is the key creation and key distribution. A key is needed to encrypt and decipher codes and is needed by both the user and sender. A solution to this problem is the generation of quantum key distributions. In our experiment, we are now ...

On The Reality Of Mathematics, 2017 Southeastern University - Lakeland

#### On The Reality Of Mathematics, Brendan Ortmann

*Selected Student Publications*

Mathematics is an integral cornerstone of science and society at large, and its implications and derivations should be considered. That mathematics is frequently abstracted from reality is a notion not countered, but one must also think upon its physical basis as well. By segmenting mathematics into its different, abstract philosophies and real-world applications, this paper seeks to peer into the space that mathematics seems to fill; that is, to understand *how* and *why* it works. Under mathematical theory, Platonism, Nominalism, and Fictionalism are analyzed for their validity and their shortcomings, in addition to the evaluation of infinities and infinitesimals, to ...

The Case Of The Disappearing (And Re-Appearing) Particle, 2017 Chapman University

#### The Case Of The Disappearing (And Re-Appearing) Particle, Yakir Aharonov, Eliahu Cohen, Ariel Landau, Avshalom C. Elitzur

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a particle superposed over three boxes. Under appropriate pre- and post-selections, and with tunneling enabled between two of the boxes, it is possible to derive not only one, but three predictions for three different times within the intermediate interval. These predictions are moreover contradictory. The particle (when looked for using a projective measurement) seems to disappear from the first box where it would have been previously found with certainty, appearing instead within the third box, to which no tunneling is possible, and later re-appearing within the second. It turns out ...

Explorations Of Quantum Entanglement, 2017 DePauw University

#### Explorations Of Quantum Entanglement, John Stanton

*Student research*

This thesis develops an undergraduate level understanding of quantum entanglement by expressing its properties in three unique mediums: mathematical formalism, application in technology and experiment. The mathematical formalism of entanglement is developed by working through theoretical experiments that utilize the entangled polarization states of photons. Notation used to describe entangled photon states is then used to illustrate how other types of entangled quantum states can be used in real technology, such as is the case with quantum computing. Finally, the theoretical predictions associated with entanglement are discussed in reference to two quantum optics experiments.

Exploring The Multi-Mode Structure Of Atom-Generated Squeezed Light, 2017 College of William and Mary

#### Exploring The Multi-Mode Structure Of Atom-Generated Squeezed Light, Melissa A. Guidry

*Undergraduate Honors Theses*

Squeezed states of light, *i.e.*, quantum states exhibiting reduced noise statistics, may be used to greatly enhance the sensitivity of light-based measurements. We study a squeezed vacuum field generated in hot Rb vapor via the polarization self-rotation effect. By propagating a strong pump beam through an atomic vapor cell, we were able to achieve a noise suppression of 2.7 dB below shot noise. Our previous work revealed that this amount of noise suppression may be limited by the excitement of higher order modes in the squeezed field during the atom-light interaction. Once incident on the homodyne detection scheme ...

The Two-Time Interpretation And Macroscopic Time-Reversibility, 2017 Chapman University

#### The Two-Time Interpretation And Macroscopic Time-Reversibility, Yakir Aharonov, Eliahu Cohen, Tomer Landsberger

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

The two-state vector formalism motivates a time-symmetric interpretation of quantum mechanics that entails a resolution of the measurement problem. We revisit a post-selection-assisted collapse model previously suggested by us, claiming that unlike the thermodynamic arrow of time, it can lead to reversible dynamics at the macroscopic level. In addition, the proposed scheme enables us to characterize the classical-quantum boundary. We discuss the limitations of this approach and its broad implications for other areas of physics.

Squeezing Light With Atoms: Generation Of Non-Classical Light Via Four-Wave Mixing, 2017 College of William and Mary

#### Squeezing Light With Atoms: Generation Of Non-Classical Light Via Four-Wave Mixing, Nathan Super

*Science Research Symposium*

The goal of the project is to produce a pair of polarization-entangled light fields using four-wave mixing in hot Rb vapor. In this process, interaction of atoms with near-resonant strong control optical field results in strong amplification of a nearly-collinear probe optical field and in generation of a quantum correlated conjugate Stokes optical field. In order to establish the quantum correlation between the Stokes and probe fields, we have adopted a homodyne detection scheme. If the differential noise between the Stokes and probe fields is below the quantum noise limit, then intensity fluctuation entanglement has been achieved, and it is ...

Data Collection And Analysis At The Atlas Detector, 2017 Yale University

#### Data Collection And Analysis At The Atlas Detector, Savannah Thais

*Yale Day of Data*

No abstract provided.

Rapid Estimation Of Drifting Parameters In Continuously Measured Quantum Systems, 2017 University of Rochester

#### Rapid Estimation Of Drifting Parameters In Continuously Measured Quantum Systems, Luis Cortez, Areeya Chantasri, Luis Pedro García-Pintos, Justin Dressel, Andrew N. Jordan

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

We investigate the determination of a Hamiltonian parameter in a quantum system undergoing continuous measurement. We demonstrate a computationally rapid method to estimate an unknown and possibly timedependent parameter, where we maximize the likelihood of the observed stochastic readout. By dealing directly with the raw measurement record rather than the quantum-state trajectories, the estimation can be performed while the data are being acquired, permitting continuous tracking of the parameter during slow drifts in real time. Furthermore, we incorporate realistic nonidealities, such as decoherence processes and measurement inefficiency. As an example, we focus on estimating the value of the Rabi frequency ...

Experimental Demonstration Of Direct Path State Characterization By Strongly Measuring Weak Values In A Matter-Wave Interferometer, 2017 AtomInstitut

#### Experimental Demonstration Of Direct Path State Characterization By Strongly Measuring Weak Values In A Matter-Wave Interferometer, Tobias Denkmayr, Hermann Geppert, Hartmut Lemmel, Mordecai Waegell, Justin Dressel, Yuji Hasegawa, Stephan Sponar

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

A method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently, Vallone and Dequal [Phys. Rev. Lett. 116, 040502 (2016)] showed theoretically that weak measurements are not a necessary condition to determine the weak value. Here, we report a measurement scheme used in a matter-wave interferometric experiment in which the neutron path system’s quantum state was characterized via direct measurements, using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones for tomographic accuracy. Our results ...

Tunneling Assisted Forbidden Transitions In The Single Molecule Magnet Ni4, 2017 University of Massachusetts Amherst

#### Tunneling Assisted Forbidden Transitions In The Single Molecule Magnet Ni4, Yiming Chen

*Doctoral Dissertations May 2014 - current*

This dissertation presents work in exploring novel quantum phenomena in singlemolecule magnets (SMMs) and superconducting circuits. The degree of the freedom studied is the magnetic moment of a single molecule and the flux quantum trapped in a superconducting ring. These phenomena provide us with new insights into some basic questions of physics and may also find their application in quantum computing.

The molecule we studied is Ni4 ([Ni4(hmp)(dmp)Cl]4) which can be treated as a spin-4 magnet. The large magnetic anisotropy of the molecule leads to bistability of the magnetic moment at low temperatures, with spin-up and ...

Improving Chiral Perturbation Theory With Lattice Qcd Determined Pi-Pi Scattering, 2017 University of Colorado, Boulder

#### Improving Chiral Perturbation Theory With Lattice Qcd Determined Pi-Pi Scattering, Hu Zhao

*Undergraduate Honors Theses*

The first principle calculation of Lattice QCD is complicated and usually requires significant computational power to perform the calculation. By applying the Chiral Perturbation Theory (ChPT), the calculation becomes much simpler. This project is to find a set of parameters called low energy constants (LECs) in the ChPT calculation that gives results that agree with the Lattice QCD calculations. Once this is done, ChPT can be used to give a better prediction on experimental results.

Quantum Foundations With Astronomical Photons, 2017 Harvey Mudd College

#### Quantum Foundations With Astronomical Photons, Calvin Leung

*HMC Senior Theses*

Theoretical work in quantum information has demonstrated that a classical hidden-variable model of an entangled singlet state can explain nonclassical correlations observed in tests of Bell’s inequality if while measuring the Bell correlation, the underlying probability distribution of the hidden-variable changes depending on the measurement basis. To rule out this possibility, distant quasars can be utilized as random number generators to set measurement bases in an experimental test of Bell’s inequality. Here we report on the design and characterization of a device that uses the color of incoming quasar photons to output a random bit with nanosecond latency ...

Maximal Lelm Distinguishability Of Qubit And Qutrit Bell States Using Projective And Non-Projective Measurements, 2017 Harvey Mudd College

#### Maximal Lelm Distinguishability Of Qubit And Qutrit Bell States Using Projective And Non-Projective Measurements, Nathaniel Leslie

*HMC Senior Theses*

Many quantum information tasks require measurements to distinguish between different quantum-mechanically entangled states (Bell states) of a particle pair. In practice, measurements are often limited to linear evolution and local measurement (LELM) of the particles. We investigate LELM distinguishability of the Bell states of two qubits (two-state particles) and qutrits (three-state particles), via standard projective measurement and via generalized measurement, which allows detection channels beyond the number of orthogonal single-particle states. Projective LELM can only distinguish 3 of 4 qubit Bell states; we show that generalized measurement does no better. We show that projective LELM can distinguish only 3 of ...