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Thesis (Ph. D.)--University of Rochester. Department of Physics and Astronomy, 2017., This thesis describes research I have conducted since late 2015 at the University of Rochester as part of my doctoral studies. The two experiments I cover are investigations into merging research into weak-value interferometry with atomic slow light research, with the eventual goal being to find practical application. Of interest to us was utilizing the noise suppression properties of weak-value interferometry to create remote sensing Doppler measurement and LIDAR systems. At the core of our Doppler and LIDAR tests was a displaced Sagnac interferometer with a cell of hot atomic rubidium in one arm that we used to detect minute changes in the frequency of the light entering the interferometer. The rubidium acted as a slow light medium due to the high normal dispersion in the transparency region between the ground state splitting of the 85Rb D1 line. The rubidium thus served to induce frequency-dependent phase shifts in the light of one of the interferometer arms. The interferometer translates phase shifts into shifts in the output profile from the interferometer's dark port, and by monitoring these dark port profile shifts we were able to detect changes in frequency. The first two chapters of this thesis serve to provide background information. Chapter 1 will serve as an introduction to weak values. I will introduce weak value formalism and discuss the history of weak values, with particular focus on the applications to precision interferometry. Similarly, chapter 2 will introduce the basic concepts of slow light and discuss past research performed in that field, with additional attention given regarding the usage of atomic resonances for slow light. Chapter 3 gives a detailed theoretical description of the Sagnac interferometer that was used during experiments. I derive the behavior of the interferometer's dark port profile, as well as the theoretical sensitivity and basic SNR performance of the system. I also discuss the theory behind some practical issues we encou

Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a message with a shorter key and still provide information-theoretic security. We present one of the first feasible experimental demonstrations of quantum data locking for direct communication and propose a scheme for a quantum enigma machine that encrypts 6 bits per photon (containing messages, new encryption keys, and forward error correction bits) with less than 6 bits per photon of encryption key while remaining information-theoretically secure., United States. Defense Advanced Research Projects Agency (W31P4Q-12-1-0015), United States. Air Force Office of Scientific Research (FA9550-13-1-0019)

Minimum error-probability laser radar point-target localization is analyzed, including the effects of dark counts, background counts, and target speckle. Results from preliminary table-top experiments are reported.

We show how one can demonstrate continuous-variable Einstein-Podolsky-Rosen (EPR) steering without needing to characterize entire measurement probability distributions. To do this, we develop a modified Fano inequality useful for discrete measurements of continuous variables, and use it to bound the conditional uncertainties in continuous-variable entropic EPR-steering inequalities. With these bounds, we show how one can hedge against experimental limitations including a finite detector size, dead space between pixels, and any such factors that impose an incomplete sampling of the true measurement probability distribution. Furthermore, we use experimental data from the position and momentum statistics of entangled photon pairs in parametric downconversion to show that this method is sufficiently sensitive for practical use., Comment: 7 pages, 2 figures

This report summarizes our accomplishments in the past 3+1 years concerning our investigation into the advantages of weak value approaches to precision measurements, as well as other investigations into weak measurements and weak values. The report is divided into two sections: The first focuses on a detailed discussion of results concerning applications and advantages of weak value amplification techniques to precision measurement. Here, we discuss four separate but connected projects. The first concerns the possibility of reusing the rejected photons in the post-selection portion of the weak value amplification. The second project concerns the technical merits of weak value amplification. We also discuss a third project using our interferometric weak value technique to make precision frequency measurements on an optical beam, reporting a resolution of 129 +/- 7 kHz per root Hz with only 2 mW of continuous-wave power. The fourth project deals with a weak value inspired phase amplification technique. The second main part of the report concerns results related to weak measurements and weak values, but not directly related to the amplification issue. We give a brief survey of our results in this area. We have investigated weak measurements as a test of quantum mechanics, by deriving generalized Leggett-Garg inequalities for multiple parties and violating them with entangled photons. We have extensively investigated a new approach to generalized measurement we call contextual values, which gives a precise connection between an indirectly measured system and the outcomes of the detector by assigning a set of generalized eigenvalues to each detector outcome. This assignment permits a principled definition of a conditioned average, which limits to the weak value under certain conditions that are usually satisfied in the laboratory. We have also discussed the significance of the imaginary part of the weak value., The original document contains color images.

We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.

We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.

In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering.

We demonstrate a compressed sensing, photon counting lidar system based on the single-pixel camera. Our technique recovers both depth and intensity maps from a single under-sampled set of incoherent, linear projections of a scene of interest at ultra-low light levels around 0.5 picowatts. Only two-dimensional reconstructions are required to image a three-dimensional scene. We demonstrate intensity imaging and depth mapping at 256 x 256 pixel transverse resolution with acquisition times as short as 3 seconds. We also show novelty filtering, reconstructing only the difference between two instances of a scene. Finally, we acquire 32 x 32 pixel real-time video for three-dimensional object tracking at 14 frames-per-second., Comment: 16 pages, 8 figures

High-dimensional Hilbert spaces used for quantum communication channels offer the possibility of large data transmission capabilities. We propose a method of characterizing the channel capacity of an entangled photonic state in high-dimensional position and momentum bases. We use this method to measure the channel capacity of a parametric down-conversion state by measuring in up to 576 dimensions per detector. We achieve a channel capacity over 7 bits/photon in either the position or momentum basis. Furthermore, we provide a correspondingly high-dimensional separability bound that suggests that the channel performance cannot be replicated classically., United States. Defense Advanced Research Projects Agency. System Science Division. Defense Sciences Office (Grant No. W911NF- 10-1-0404), United States. Army Research Office. Multidisciplinary University Research Initiative (Grant No. W911NF-05-1- 0197)

Atmospheric turbulence generally affects the resolution and visibility of an image in long-distance imaging. In a recent quantum ghost imaging experiment [P. B. Dixon et al. Phys. Rev. A 83 051803 (2011)], it was found that the effect of the turbulence can nevertheless be mitigated under certain conditions. This paper gives a detailed theoretical analysis to the setup and results reported in the experiment. Entangled photons with a finite correlation area and a turbulence model beyond the phase screen approximation are considered., United States. Defense Advanced Research Projects Agency. System Science Division. Defense Sciences Office (InPho Grant No. W911NF-10-1-0404), United States. Army Research Office. Multidisciplinary University Research Initiative (Grant No. W911NF-05-1-0197)

High-dimensional Hilbert spaces used for quantum communication channels offer the possibility of large data transmission capabilities. We propose a method of characterizing the channel capacity of an entangled photonic state in high-dimensional position and momentum bases. We use this method to measure the channel capacity of a parametric down-conversion state by measuring in up to 576 dimensions per detector. We achieve a channel capacity over 7 bits/photon in either the position or momentum basis. Furthermore, we provide a correspondingly high-dimensional separability bound that suggests that the channel performance cannot be replicated classically., United States. Defense Advanced Research Projects Agency. System Science Division. Defense Sciences Office (Grant No. W911NF- 10-1-0404), United States. Army Research Office. Multidisciplinary University Research Initiative (Grant No. W911NF-05-1- 0197)

We investigate the effect of turbulence on quantum ghost imaging. We use entangled photons and demonstrate that for a specific experimental configuration the effect of turbulence can be greatly diminished. By decoupling the entangled photon source from the ghost-imaging central image plane, we are able to dramatically increase the ghost-image quality. When imaging a test pattern through turbulence, this method increases the imaged pattern visibility from V=0.15±0.04 to 0.42±0.04., United States. Defense Advanced Research Projects Agency (DARPA DSO InPho Grant No. W911NF-10-1-0404), United States. Army Research Office (USARO MURI Grant No. W911NF-05-1-0197)

We investigate the effect of turbulence on quantum ghost imaging. We use entangled photons and demonstrate that for a specific experimental configuration the effect of turbulence can be greatly diminished. By decoupling the entangled photon source from the ghost-imaging central image plane, we are able to dramatically increase the ghost-image quality. When imaging a test pattern through turbulence, this method increases the imaged pattern visibility from V=0.15±0.04 to 0.42±0.04., United States. Defense Advanced Research Projects Agency (DARPA DSO InPho Grant No. W911NF-10-1-0404), United States. Army Research Office (USARO MURI Grant No. W911NF-05-1-0197)

Thesis (Ph. D.)--University of Rochester. Department of Physics and Astronomy, 2018., High-dimensional systems are desired for their ability to transfer large amounts of information. This dissertation focuses on the characterization and usage of high-dimensional optical systems for computational imaging, high-dimensional entanglement, and efficient secure-information transfer. Within computational imaging systems, capturing the most spatial frequencies results in sharper images. Utilizing the correlations within high-dimensional entanglement offers signal-to-noise ratio enhancements over lowlight imaging and spectroscopic systems. Finally, high-dimensional quantum channels offer a regime in which quantum data locking can encrypt information according to information-theoretic-secure standards more efficiently than classical systems. While high-dimensionality offers certain performance gains, characterizing and then harnessing high-dimensional systems for computational imaging, entanglementenhanced applications, and quantum-secure direct communication can be prohibitively difficult. This dissertation offers unique solutions to each of these problems. Compressive imaging is relied on heavily to improve measurement rates in limitedresource imaging systems. As such, compressive sensing is introduced in chapter 1 while entanglement and an experimental source of high-dimensional entangled photons is covered in chapter 2. Chapter 3 introduces Sylvester-Hadamard matrices for compressive measurement and efficient computational-recovery of high-dimensional correlations. Compressive imaging is then presented as an efficient means of converting a standard frequency-modulated continuous-wave LiDAR system into a high-resolution depth-imaging system in chapter 4. Chapter 5 introduces quantum data locking and presents one of the first experimental demonstrations made possible by the use of a large-area, high-efficiency, single-photon-counting detector array. For completeness, robust compressive sensing recovery algorithms using the alternating direction method of mul

Thesis (Ph. D.)--University of Rochester. Institute of Optics, 2016., This thesis presents mainly two methodologies for achieving practical invisibility cloaking. Thus, using commercial technologies, devices that are good approximations to an ideal cloak can be achieved - a cloak that is omnidirectional, broadband, operational for the visible spectrum, three-dimensional (3D), and phase-matching for the light field, among other attributes. We first describe ‘paraxial cloaking,’ where cloaking is considered as an imaging system. The small-angle (‘paraxial’) formalism provides a first-order design requirement for any ‘perfect’ cloaking device. A ray optics four-lens cloak (called the “Rochester Cloak”) is experimentally demonstrated, followed by theoretical work to match the phase for the entire visible spectrum. To extend our broadband, paraxial cloak to larger viewing angles, we then discretize space, angle, spectrum, and phase to approximate an ideal, omnidirectional cloak. Such ‘discretized cloaking’ is experimentally demonstrated as a digital cloak, where commercially available digital image capture and display technologies are used. In particular, we demonstrate an active cloak that uses lenticular lenslet arrays, similar to integral imaging for 3D displays. The ‘digital integral cloak’ we demonstrate is dynamic, but requires a time delay for image capture and processing, and is two-dimensional (2D) without phase-matching. Continuing improvements in commercial digital technology and computational power will minimize the resolution limitations of a digital cloak and enhance its processing speed. Thus, a wearable cloak can then be practically realized in the future.

Thesis (Ph. D.)--University of Rochester. Dept. of Physics and Astronomy, 2012., Quantum optics provides a unique avenue to investigate quantum mechanical effects. Typically, it is easier to observe the particle-like behavior of a physical object than it is to observe wave-like behavior. Optics presents us with the reverse case, observing the particle-like behavior of light is difficult. I investigate the utility and limitations of two quantum mechanical effects--weak values and spatial entanglement--in the context of experimental quantum optical communication channels. I show that weak values can be used to increase the signal power and effectively decrease the noise power in a physical communication channel, up to the standard quantum limit for signal to noise ratio. I also show show a method for decreasing the negative environmental effects on a communication channel using spatial entanglement and show that such a channel can be used to transmit over 7 bits of information per joint photon detection event.