The Common Invariant Subspace Problem And Tarski’S Theorem, 2017 Nicolaus Copernicus University of Toruń

#### The Common Invariant Subspace Problem And Tarski’S Theorem, Grzegorz Pastuszak

*Electronic Journal of Linear Algebra*

This article presents a computable criterion for the existence of a common invariant subspace of $n\times n$ complex matrices $A_{1}, \dots ,A_{s}$ of a fixed dimension $1\leq d\leq n$. The approach taken in the paper is model-theoretic. Namely, the criterion is based on a constructive proof of the renowned Tarski's theorem on quantifier elimination in the theory $\ACF$ of algebraically closed fields. This means that for an arbitrary formula $\varphi$ of the language of fields, a quantifier-free formula $\varphi'$ such that $\varphi\lra\varphi'$ in $\ACF$ is given explicitly. The construction of $\varphi'$ is ...

Linear Feedback Stabilization Of A Dispersively Monitored Qubit, 2017 Chapman University

#### Linear Feedback Stabilization Of A Dispersively Monitored Qubit, Taylor Lee Patti, Areeya Chantasri, Luis Pedro García-Pintos, Andrew N. Jordan, Justin Dressel

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

The state of a continuously monitored qubit evolves stochastically, exhibiting competition between coherent Hamiltonian dynamics and diffusive partial collapse dynamics that follow the measurement record. We couple these distinct types of dynamics together by linearly feeding the collected record for dispersive energy measurements directly back into a coherent Rabi drive amplitude. Such feedback turns the competition cooperative and effectively stabilizes the qubit state near a target state. We derive the conditions for obtaining such dispersive state stabilization and verify the stabilization conditions numerically.We include common experimental nonidealities, such as energy decay, environmental dephasing, detector efficiency, and feedback delay, and ...

Quantum Control Via A Genetic Algorithm Of The Field Ionization Pathway Of A Rydberg Electron, 2017 Bryn Mawr College

#### Quantum Control Via A Genetic Algorithm Of The Field Ionization Pathway Of A Rydberg Electron, Vincent C. Gregoric, Xinyue Kang, Zhimin Cheryl Liu, Zoe A. Rowley, Thomas J. Carroll, Michael W. Noel

*Physics and Astronomy Faculty Publications*

Quantum control of the pathway along which a Rydberg electron field ionizes is experimentally and computationally demonstrated. Selective field ionization is typically done with a slowly rising electric field pulse. The (1/n^{*})^{4} scaling of the classical ionization threshold leads to a rough mapping between arrival time of the electron signal and principal quantum number of the Rydberg electron. This is complicated by the many avoided level crossings that the electron must traverse on the way to ionization, which in general leads to broadening of the time-resolved field ionization signal. In order to control the ionization pathway, thus directing ...

Optimizing An Electron's Path To Ionization Using A Genetic Algorithm, 2017 Ursinus College

#### Optimizing An Electron's Path To Ionization Using A Genetic Algorithm, Jason Bennett, Kevin Choice

*Physics and Astronomy Summer Fellows*

A Rydberg atom is an atom with a highly excited and weakly bound valence electron. A widespread method of studying quantum mechanics with Rydberg atoms is to ionize the electron and measure its arrival time. We use a Genetic Algorithm (GA) to control the electron's path to ionization. The Rydberg electron's energy levels are strongly shifted by the presence of an electric field. The energy levels shift and curve, but never cross. At an avoided crossing the electron can jump from one level to the next. By engineering the electric field's time dependence, we thereby control the ...

Is A Time Symmetric Interpretation Of Quantum Theory Possible Without Retrocausality?, 2017 Chapman University

#### Is A Time Symmetric Interpretation Of Quantum Theory Possible Without Retrocausality?, Matthew S. Leifer, Matthew F. Pusey

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

Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called *λ*-mediation, that plausibly holds independently of the status of ...

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 ...

On-Sight Shifting At The Cryogenic Underground Observatory For Rare Events, 2017 California Polytechnic State University, San Luis Obispo

#### On-Sight Shifting At The Cryogenic Underground Observatory For Rare Events, Aaron C. Wong

*Physics*

During the summer of 2016, four Cal Poly students traveled to Assergi, Italy to contribute to the CUORE collaboration which is in search of a rare process called neutrinoless double beta decay. If detected, neutrinoless double beta decay will make break throughs in particle and nuclear physics, and will be the first observation of lepton number violation. The Cal Poly students provided on-sight shifting support during the installation phase of the project. This is a breakdown of the physics behind CUORE and Cal Poly's contribution.

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 ...

Silver Nanoparticles As A Potential Solar Absorber, 2017 Bowling Green State University

#### Silver Nanoparticles As A Potential Solar Absorber, Benjamin Hardy

*Honors Projects*

This work reports the development of Silver nanoparticles implanted into a polymer as a solar absorber. The plasmonic nature of silver nanoparticle allows for adjustments to be made in its UV-VIS-NIR absorbance spectrum. A combination of different sized/shaped particles could result in ideal absorption of the majority of the solar spectrum. Allotting this with the stability of a polymer leads to potential solids or solutions that could work as a solar absorber. Tests were also performed to determine whether or not UV-C irradiation during synthesis effects the characteristics of silver nanoparticles, in particular the absorbance. Successful synthesis of silver ...

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 ...

Neutron-Unbound Excited States Of 23n, 2017 Michigan State University

#### Neutron-Unbound Excited States Of 23n, M. Jones, T. Baumann, J. Brett, J. Bullaro, P. A. Deyoung, J.E. Finck, N. Frank, K. Hammerton, J. Hinnefeld, Z. Kohley, A. N. Kuchera, J. Pereira, A. Rabeh, J. K. Smith, A. Spyrou, Sharon L. Stephenson, K. Stiefel, M. Tuttle-Timm, R. G.T. Zegers, M. Thoennessen

*Physics and Astronomy Faculty Publications*

Neutron unbound states in 23N were populated via proton knockout from an 83.4 MeV/nucleon 24O beam on a liquid deuterium target. The two-body decay energy displays two peaks at E1∼100keV and E2∼1MeV with respect to the neutron separation energy. The data are consistent with shell model calculations predicting resonances at excitation energies of ∼3.6MeV and ∼4.5MeV. The selectivity of the reaction implies that these states correspond to the first and second 3/2− states. The energy of the first state is about 1.3 MeV lower than the first excited 2+ in 24O. This ...

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.