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## Full-Text Articles in Physics

Scheme For The Protective Measurement Of A Single Photon Using A Tunable Quantum Zeno Effect, Maximilian Schlosshauer

#### Scheme For The Protective Measurement Of A Single Photon Using A Tunable Quantum Zeno Effect, Maximilian Schlosshauer

*Physics Faculty Publications and Presentations*

This paper presents a proof-of-principle scheme for the protective measurement of a single photon. In this scheme, the photon is looped arbitrarily many times through an optical stage that implements a weak measurement of a polarization observable followed by a strong measurement protecting the state. The ability of this scheme to realize a large number of such interaction{protection steps means that the uncertainty in the measurement result can be drastically reduced while maintaining a sufficient probability for the photon to survive the measurement.

Quantum Fidelity Approach To The Ground-State Properties Of The One-Dimensional Axial Next-Nearest-Neighbor Ising Model In A Transverse Field, Oz De Alcantara Bonfim, B. Boechat, J. Florencio

#### Quantum Fidelity Approach To The Ground-State Properties Of The One-Dimensional Axial Next-Nearest-Neighbor Ising Model In A Transverse Field, Oz De Alcantara Bonfim, B. Boechat, J. Florencio

*Physics Faculty Publications and Presentations*

In this work we analyze the ground-state properties of the *s *=1/2 one-dimensional axial next-nearest-neighbor Ising model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field *B _{x}* and the strength of the next-nearest-neighbor interaction

*J*, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, and ⟨2,2⟩ phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L→∞). Paramagnetism only ...

_{2}Quantum Fidelity Approach To The Ground-State Properties Of The One-Dimensional Axial Next-Nearest-Neighbor Ising Model In A Transverse Field, O. F. De Alcantara Bonfim, B. Boechat, J. Florencio

#### Quantum Fidelity Approach To The Ground-State Properties Of The One-Dimensional Axial Next-Nearest-Neighbor Ising Model In A Transverse Field, O. F. De Alcantara Bonfim, B. Boechat, J. Florencio

*Physics Faculty Publications and Presentations*

In this work we analyze the ground-state properties of the *s* = 1/2 one-dimensional axial next-nearest-neighbor Ising model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field *B _{x}* and the strength of the next-nearest-neighbor interaction

*J*, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, and (2,2) phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L→∞). Paramagnetism only ...

_{2}Observation Of The Quantum Paradox Of Separation Of A Single Photon From One Of Its Properties, Maximilian Schlosshauer, James M. Ashby, Peter D. Schwarz

#### Observation Of The Quantum Paradox Of Separation Of A Single Photon From One Of Its Properties, Maximilian Schlosshauer, James M. Ashby, Peter D. Schwarz

*Physics Faculty Publications and Presentations*

We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called "quantum Cheshire cat"). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the ...

Delayed-Choice Quantum Eraser For The Undergraduate Laboratory, James M. Ashby, Peter D. Schwarz, Maximilian Schlosshauer

#### Delayed-Choice Quantum Eraser For The Undergraduate Laboratory, James M. Ashby, Peter D. Schwarz, Maximilian Schlosshauer

*Physics Faculty Publications and Presentations*

In a delayed-choice quantum eraser, interference fringes are obtained by erasing which-way information after the interfering particle has already been irreversibly detected. Following an introductory review of delayed-choice experiments and quantum erasure, we describe the experimental realization of an optical delayed-choice quantum eraser, suitable for advanced undergraduates, based on polarization-entangled pairs of single photons. In our experiment, the delay of the erasure is implemented using two different setups. The first setup employs an arrangement of mirrors to increase the optical path length of the photons carrying which-way information. In the second setup, we use fiber-optic cables to elongate the path ...

Measuring The Quantum State Of A Single System With Minimum State Disturbance, Maximilian Schlosshauer

#### Measuring The Quantum State Of A Single System With Minimum State Disturbance, Maximilian Schlosshauer

*Physics Faculty Publications and Presentations*

Conventionally, unknown quantum states are characterized using quantum-state tomography based on strong or weak measurements carried out on an ensemble of identically prepared systems. By contrast, the use of protective measurements offers the possibility of determining quantum states from a series of weak, long measurements performed on a single system. Because the fidelity of a protectively measured quantum state is determined by the amount of state disturbance incurred during each protective measurement, it is crucial that the initial quantum state of the system is disturbed as little as possible. Here we show how to systematically minimize the state disturbance in ...

Dynamics Of The Transverse Ising Model With Next-Nearest-Neighbor Interactions, P.R.C. Guimaraes, J.A. Plascak, O.F. De Alcantara Bonfirm, J. Florencio

#### Dynamics Of The Transverse Ising Model With Next-Nearest-Neighbor Interactions, P.R.C. Guimaraes, J.A. Plascak, O.F. De Alcantara Bonfirm, J. Florencio

*Physics Faculty Publications and Presentations*

We study the effects of next-nearest-neighbor (NNN) interactions on the dynamics of the one-dimensional spin-1/2 transverse Ising model in the high-temperature limit. We use exact diagonalization to obtain the time-dependent transverse correlation function and the corresponding spectral density for a tagged spin. Our results for chains of 13 spins with periodic boundary conditions produce results which are valid in the infinite-size limit. In general we find that the NNN coupling produces slower dynamics accompanied by an enhancement of the central mode behavior. Even in the case of a strong transverse field, if the NNN coupling is sufficiently large, then ...

What *Is* Quantum Mechanics?, Maximilian Schlosshauer

#### What Is Quantum Mechanics?, Maximilian Schlosshauer

*Physics Faculty Publications and Presentations*

No abstract provided.

Analysis Of Quantum-State Disturbance In A Protective Measurement Of A Spin-1/2 Particle, Maximilian Schlosshauer

#### Analysis Of Quantum-State Disturbance In A Protective Measurement Of A Spin-1/2 Particle, Maximilian Schlosshauer

*Physics Faculty Publications and Presentations*

A distinguishing feature of protective measurement is the possibility of obtaining information about expectation values while making the disturbance of the initial state arbitrarily small. Quantifying this state disturbance is of paramount importance. Here we derive exact and perturbative expressions for the state disturbance and the faithfulness of the measurement outcome in a model describing a spin -1/2 particle protectively measured by an inhomogeneous magnetic field. We determine constraints on the experimentally required field strengths from bounds imposed on the allowable state disturbance. We also demonstrate that the protective measurement may produce an incorrect result even when the particle ...

A Professor Of Wonder, Shannon K. Mayer

#### A Professor Of Wonder, Shannon K. Mayer

*Physics Faculty Publications and Presentations*

No abstract provided.

No-Go Theorem For The Composition Of Quantum Systems, Maximillian Schlosshauer, Arthur Fine

#### No-Go Theorem For The Composition Of Quantum Systems, Maximillian Schlosshauer, Arthur Fine

*Physics Faculty Publications and Presentations*

Building on the Pusey-Barrett-Rudolph theorem, we derive a no-go theorem for a vast class of deterministic hidden-variables theories, including those consistent on their targeted domain. The strength of this result throws doubt on seemingly natural assumptions (like the “preparation independence” of the Pusey-Barrett-Rudolph theorem) about how “real states” of subsystems compose for joint systems in nonentangled states. This points to constraints in modeling tensor-product states, similar to constraints demonstrated for more complex states by the Bell and Bell-Kochen-Specker theorems.

State Disturbance And Pointer Shift In Protective Quantum Measurements, Maximilian Schlosshauer

#### State Disturbance And Pointer Shift In Protective Quantum Measurements, Maximilian Schlosshauer

*Physics Faculty Publications and Presentations*

We investigate the disturbance of the state of a quantum system in a protective measurement for finite measurement times and different choices of the time-dependent system-apparatus coupling function. The ability to minimize this state disturbance is essential to protective measurement. We show that for a coupling strength that remains constant during the measurement interaction of duration *T*, the state disturbance scales as T^{−2}, while a simple smoothing of the coupling function significantly improves the scaling behavior to T^{−6}. We also prove that the shift of the apparatus pointer in the course of a protective measurement is independent of ...

Quantum Phase Transitions In A Chain With Two- And Four-Spin Interactions In A Transverse Field, O. F. De Alcantara Bonfim, A. Saguia, B. Boechat, K. Florencio

#### Quantum Phase Transitions In A Chain With Two- And Four-Spin Interactions In A Transverse Field, O. F. De Alcantara Bonfim, A. Saguia, B. Boechat, K. Florencio

*Physics Faculty Publications and Presentations*

We use entanglement entropy and finite-size scaling methods to investigate the ground-state properties of a spin-1/2 Ising chain with two-spin (*J*_{2}) and four-spin (*J*_{4}) interactions in a transverse magnetic field (*B*). We concentrate our study on the unexplored critical region *B* = 1 and obtain the phase diagram of the model in the (*J*_{4}—*J*_{2}) plane. The phases found include ferromagnetic (F), antiferromagnetic (AF), as well as more complex phases involving spin configurations with multiple periodicity. The system presents both first- and second-order transitions separated by tricritical points. We find an unusual phase boundary on the ...

Critical Behavior Of A Quantum Chain With Four-Spin Interactions In The Presence Of Longitudinal And Transverse Magnetic Fields, B. Boechat, J. Florencio, A. Saguia, O. F. De Alcantara Bonfim

#### Critical Behavior Of A Quantum Chain With Four-Spin Interactions In The Presence Of Longitudinal And Transverse Magnetic Fields, B. Boechat, J. Florencio, A. Saguia, O. F. De Alcantara Bonfim

*Physics Faculty Publications and Presentations*

We study the ground-state properties of a spin-1/2 model on a chain containing four-spin Ising-like interactions in the presence of both transverse and longitudinal magnetic fields. We use entanglement entropy and finite-size scaling methods to obtain the phase diagrams of the model. Our numerical calculations reveal a rich variety of phases and the existence of multicritical points in the system. We identify phases with both ferromagnetic and antiferromagnetic orderings. We also find periodically modulated orderings formed by a cluster of like spins followed by another cluster of opposite like spins. The quantum phases in the model are found to ...

Collimated Blue Light Generation In Rubidium Vapor, Marcus B. Kienlen, Noah T. Holte, Hunter A. Dassonville, Andrew M. C. Dawes, Kurt D. Iverson, Ryan M. Mclaughlin, Shannon K. Mayer

#### Collimated Blue Light Generation In Rubidium Vapor, Marcus B. Kienlen, Noah T. Holte, Hunter A. Dassonville, Andrew M. C. Dawes, Kurt D. Iverson, Ryan M. Mclaughlin, Shannon K. Mayer

*Physics Faculty Publications and Presentations*

We describe an experiment for generating and characterizing a beam of collimated blue light (CBL) in a rubidium vapor.Two low-power, grating-feedback diode lasers, operating at 780.2 nm (5*S*_{3/2} → 5*D*_{5/2}) and 776.0 nm (5*P*_{3/2} → 5*D*_{5/2}), respectively, provide step-wise excitation to the 5D excited state in rubidium. Under the right experimental conditions, cascade decay through the 6P excited state will yield a collimated blue (420-nm) beam of light with high temporal and spatial coherence. We investigate the production of a blue beam under a variety of experimental ...

Enumerating Quasiplatonic Cyclic Group Actions, Robert Benim, Aaron Wootton

#### Enumerating Quasiplatonic Cyclic Group Actions, Robert Benim, Aaron Wootton

*Physics Faculty Publications and Presentations*

It is an open problem to determine the number of topologically distinct ways that a finite group can act upon a compact oriented surface *X* of genus *g*(X) ≥ 2. We provide an explicit answer to this problem for special classes of cyclic groups and illustrate our results with detailed examples.

Phase Transitions In The Two-Dimensional Superantiferromagnetic Ising Model With Next-Nearest-Neighbor Interactions, A. Saguia, B. Boechat, J. Florencio, O. F. De Alcantara Bonfim

#### Phase Transitions In The Two-Dimensional Superantiferromagnetic Ising Model With Next-Nearest-Neighbor Interactions, A. Saguia, B. Boechat, J. Florencio, O. F. De Alcantara Bonfim

*Physics Faculty Publications and Presentations*

We use Monte Carlo and transfer matrix methods in combination with extrapolation schemes to determine the phase diagram of the two-dimensional superantiferromagnetic (SAF) Ising model with next-nearest-neighbor (NNN) interactions in a magnetic field. The interactions between nearest-neighbor (NN) spins are ferromagnetic along *x*, and antiferromagnetic along *Y*. We find that for sufficiently low temperatures and fields, there exists a region limited by a critical line of second-order transitions separating a SAF phase from a magnetically induced paramagnetic phase. We did not find any region with either first-order transition or with reentrant behavior. The NNN couplings produce either an expansion or ...

Dynamical Properties Of An Harmonic Oscillator Impacting A Vibrating Wall, O. F. De Alcantara Bonfim

#### Dynamical Properties Of An Harmonic Oscillator Impacting A Vibrating Wall, O. F. De Alcantara Bonfim

*Physics Faculty Publications and Presentations*

The dynamics of a spring-mass system under repeated impact with a vibrating wall is investigated using the static wall approximation. The evolution of the harmonic oscillator is described by two coupled difference equations. These equations are solved numerically, and in some cases exact analytical expressions have also been found. For a periodically vibrating wall, Fermi acceleration is only found at resonance. There, the average rebounding velocity increases linearly with the number of collisions. Near resonance, the average rebounding velocity grows initially with the number of collisions and eventually reaches a plateau. In the vicinity of resonance, the motion of the ...

Decoherence And Dissipation Of A Quantum Harmonic Oscillator Coupled To Two-Level Systems, Maximillian Schlosshauer, Andrew P. Hines, Gerard J. Milburn

#### Decoherence And Dissipation Of A Quantum Harmonic Oscillator Coupled To Two-Level Systems, Maximillian Schlosshauer, Andrew P. Hines, Gerard J. Milburn

*Physics Faculty Publications and Presentations*

We derive and analyze the Born–Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four “canonical” system–environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum- electromechanical systems and micron-scale ion traps. Decoherence and dissipation rates are found to exhibit ...

Two-Photon Spectroscopy Of Rubidium Using A Grating-Feedback Diode Laser, Abraham J. Olson, Evan J. Carlson, Shannon K. Mayer

#### Two-Photon Spectroscopy Of Rubidium Using A Grating-Feedback Diode Laser, Abraham J. Olson, Evan J. Carlson, Shannon K. Mayer

*Physics Faculty Publications and Presentations*

We describe an experiment for investigating the 5S_{1/2}→5D_{5/2} two-photon transition in rubidium using a single grating-feedback diode laser operating at 778.1nm (385 THz). Continuous tuning of the laser frequency over 4GHz allows for the clear resolution of the Doppler-free spectral features and allows accurate measurement of the hyperfine ground-state splitting. A direct comparison between Doppler-broadened and Doppler-free spectral features is possible because both are distinctly evident in the two-photon spectra. By independently modifying the polarization state of the two laser fields, the impact of electric dipole selection rules on the two-photon transition spectra is ...

Quantum Phase Transitions In The Transverse One-Dimensional Ising Model With Four-Spin Interactions, O. F. De Alcantara Bonfim, J. Florencio

#### Quantum Phase Transitions In The Transverse One-Dimensional Ising Model With Four-Spin Interactions, O. F. De Alcantara Bonfim, J. Florencio

*Physics Faculty Publications and Presentations*

In this work we investigate the quantum phase transitions at zero temperature of the one-dimensional transverse Ising model with an extra term containing four-spin interactions. The competition between the energy couplings of the model leads to an interesting zero-temperature phase diagram. We use a modified Lanczos method to determine the ground state and the first excited state energies of the system, with sizes of up to 20 spins. We apply finite size scaling to the energy gap to obtain the boundary region where ferromagnetic to paramagnetic transition takes place. We also find the critical exponent associated with the correlation length ...

Exact And Approximate Energy Spectrum For The Finite Square Well And Related Potentials, O. F. De Alcantara Bonfim, David J. Griffiths

#### Exact And Approximate Energy Spectrum For The Finite Square Well And Related Potentials, O. F. De Alcantara Bonfim, David J. Griffiths

*Physics Faculty Publications and Presentations*

We investigate the problem of a quantum particle in a one-dimensional finite square well. In the standard approach the allowed energies are determined implicitly as the solutions to a transcendental equation. We obtain the spectrum analytically as the solution to a pair of parametric equations and algebraically using a remarkably accurate approximation to the cosine function. The approach is also applied to a variety of other quantum wells.

Self-Induced Decoherence Approach: Strong Limitations On Its Validity In A Simple Spin Bath Model And On Its General Physical Relevance, Maximillian Schlosshauer

#### Self-Induced Decoherence Approach: Strong Limitations On Its Validity In A Simple Spin Bath Model And On Its General Physical Relevance, Maximillian Schlosshauer

*Physics Faculty Publications and Presentations*

The "self-induced decoherence" (SID) approach suggests that (1) the expectation value of any observable becomes diagonal in the eigenstates of the total Hamiltonian for systems endowed with a continuous energy spectrum, and (2), that this process can be interpreted as decoherence. We evaluate the first claim in the context of a simple spin bath model. We find that even for large environments, corresponding to an approximately continuous energy spectrum, diagonalization of the expectation value of random observables does in general not occur. We explain this result and conjecture that SID is likely to fail also in other systems composed of ...

Decoherence, The Measurement Problem, And Interpretations Of Quantum Mechanics, Maximillian Schlosshauer

#### Decoherence, The Measurement Problem, And Interpretations Of Quantum Mechanics, Maximillian Schlosshauer

*Physics Faculty Publications and Presentations*

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.

Direct Observation Of Normal Modes In Coupled Oscillators, Ryan Givens, O. F. De Alcantara Bonfim, Robert B. Ormond

#### Direct Observation Of Normal Modes In Coupled Oscillators, Ryan Givens, O. F. De Alcantara Bonfim, Robert B. Ormond

*Physics Faculty Publications and Presentations*

We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier analysis or using expensive apparatus. The method consists of applying a frequency dependent force to the system and using the resonance to excite each mode separately. The frequency of the excited mode is determined by measuring the resonance frequency of the system. We found that the measurednormal mode frequencies of coupled oscillators exhibiting two and three normal modes are in very good agreement with the theoretical estimates. The method is ...

Comment On: “Charge Density On A Thin Straight Wire, Revisited,” By J. D. Jackson, O. F. De Alcantara Bonfim, David Griffiths

#### Comment On: “Charge Density On A Thin Straight Wire, Revisited,” By J. D. Jackson, O. F. De Alcantara Bonfim, David Griffiths

*Physics Faculty Publications and Presentations*

No abstract provided.

Breakdown Of The Perturbative Renormalization Group For S >= 1 Random Antiferromagnetic Spin Chains, A. Saguia, B. Boechat, M. A. Continentino, O. F. De Alcantara Bonfim

#### Breakdown Of The Perturbative Renormalization Group For S >= 1 Random Antiferromagnetic Spin Chains, A. Saguia, B. Boechat, M. A. Continentino, O. F. De Alcantara Bonfim

*Physics Faculty Publications and Presentations*

We investigate the application of a perturbative renormalization group (RG) method to random antiferromagnetic Heisenberg chains with arbitrary spin size. At zero temperature we observe that initial arbitrary probability distributions develop a singularity at *J* = 0, for all values of spin *S*. When the RG method is extended to finite temperatures, without any additional assumptions, we find anomalous results for *S* >= 1. These results lead us to conclude that the perturbative scheme is not adequate to study random chains with *S* >= 1. Therefore a random singlet phase in its more restrictive definition is only assured for spin-1/2 chains.

Dynamical Behavior Of The Random·Bond Transverse Ising Model With Four-Spin Interactions, Beatriz Boechat, Claudette Cordeiro, J. Florencio, F. C. Sá Barreto, O. F. De Alcantara Bonfim

#### Dynamical Behavior Of The Random·Bond Transverse Ising Model With Four-Spin Interactions, Beatriz Boechat, Claudette Cordeiro, J. Florencio, F. C. Sá Barreto, O. F. De Alcantara Bonfim

*Physics Faculty Publications and Presentations*

We study the effect of random bonds and fields on the dynamical behavior of the one-dimensional transverse Ising model with four-spin interactions. We consider finite chains of increasing size to determine the time-dependent correlation function and the longitudinal relaxation function of the infinite chain. In this fully disordered system we observe a crossover from a collective modetype of dynamics to that of a central regime.

Comment On “Inelastic Collapse Of A Randomly Forced Particle” By Cornell Et Al., J. Florencio, F. C. Sá Barreto, O. F. De Alcantara Bonfim

#### Comment On “Inelastic Collapse Of A Randomly Forced Particle” By Cornell Et Al., J. Florencio, F. C. Sá Barreto, O. F. De Alcantara Bonfim

*Physics Faculty Publications and Presentations*

A Comment on the Letter by Stephen J. Cornell, Michael R. Swift, and Alan J. Bray, Phys. Rev. Lett. **81**, 1142 (1998). The authors of the Letter offer a Reply.

Quantum Chaos In A Double Square-Well: An Approach Based On Bohm's View Of Quantum Mechanics, O. F. De Alcantara Bonfim, J. Florencio, F. C. Sá Barreto

#### Quantum Chaos In A Double Square-Well: An Approach Based On Bohm's View Of Quantum Mechanics, O. F. De Alcantara Bonfim, J. Florencio, F. C. Sá Barreto

*Physics Faculty Publications and Presentations*

We study the dynamics of a quantum particle in a double square-well potential within a deterministic framework using Bohm’s quantum mechanics. Phase portraits, Fourier spectral analysis, Poincaré sections, and Lyapunov exponents clearly indicate that the particle undergoes periodic, quasiperiodic, and chaotic motions depending on the initial form of the wave packet. We also make a detailed comparison between the predictions of the present approach and those of conventional quantum mechanics for the same problem.