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Civil War Book Review

Quantum light for quantum technologies

William N. Plick

Published Apr 14, 2010• 0 citations
Publisher

Abstract

In this thesis we will theoretically investigate three potentially useful physical systems, after first developing the theoretical framework necessary for studying them. First, we will study the multiphoton absorption properties of maximally path entangled number (N00N) states. This is directly relevant to quantum lithography, and beating the Rayleigh diffraction limit. Next, we will develop a new scheme for quantum interferometry: dubbed coherent-light boosted super-sensitive quantum interferometry, which has the potential to reach below the shot noise limit for high photon fluxes, and requires no esoteric detection protocol, or technological elements that have yet to be developed. Finally we propose a method to perform parity detection on the output modes of a Mach-Zehnder interferometer that has been fed with two-mode squeezed vacuum. This detection scheme relies on a double homodyning technique, that makes intensity correlation measurements at a series of chosen bias phases. Sub-Heisenberg sensitivity scaling is expected for this setup.

DOI
10.31390/gradschool_dissertations.1032

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In this thesis we will theoretically investigate three potentially useful physical systems, after first developing the theoretical framework necessary for studying them. First, we will study the multiphoton absorption properties of maximally path entangled number (N00N) states. This is directly relevant to quantum lithography, and beating the Rayleigh diffraction limit. Next, we will develop a new scheme for quantum interferometry: dubbed coherent-light boosted super-sensitive quantum interferometry, which has the potential to reach below the shot noise limit for high photon fluxes, and requires no esoteric detection protocol, or technological elements that have yet to be developed. Finally we propose a method to perform parity detection on the output modes of a Mach-Zehnder interferometer that has been fed with two-mode squeezed vacuum. This detection scheme relies on a double homodyning technique, that makes intensity correlation measurements at a series of chosen bias phases. Sub-Heisenberg sensitivity scaling is expected for this setup.
In this dissertation we begin with a brief introduction to quantum optics concentrating on the topics of the noise of quantum optical states, quantum estimation theory, quantum interferometry and the atom-field interaction. This background is necessary for understanding the discussions in later chapters. In particular, quantum interferometry, which is optical interferometry when the light source is a quantum mechanical state, plays a central role in this dissertation. In Chapter 2 we discuss the phase estimation sensitivity of quantum metrology when photon loss is present. In Chapter 3 we extend the discussion to include the phase fluctuation of the system caused by the environment. We model our metrological system with the Mach-Zehnder interferometer (MZI) and use a light field in the symmetric number-path entangled state as the source. In both chapters we use the parity operator as the detection scheme and show that it is optimal under pure dephasing. In Chapter 4 we discuss the application of quantum optical states in remote sensing and propose a new scheme for a quantum radar. Again, our scheme consists of a MZI and a coherent light source. It is shown that using only coherent states of light and quantum homodyne detection, super-resolving ranging and angle determination are achievable. Chapter 5 is devoted to the generation of a super-resolving single-photon number-path entangled state which may serve as a proof-of-principle prototype for quantum lithography. The repeated implementation of MZIs is shown to be able to remove photons coherently from both modes of a symmetric number-path entangled state with arbitrarily high photon number. Lastly, in Chapter 6 we introduce the phenomenon known as polarization self-rotation and discuss its potential in generating a squeezed vacuum state, which has a huge impact in quantum interferometry.
One important problem in quantum optics is to resolve an extremely small change of phase shift. The complementarity between photon number and phase sets an ultimate limit, the so-called Heisenberg limit, on the phase measurement sensitivity. The precise phase estimation has many technological applications, such as optical gyroscopes, gravitational wave detection, quantum imaging and sensing. In this thesis I show that the utilization of the parity measurement in the optical interferometry is actually applicable to a wide range of quantum entangled input states. Comparison of the performance of the various quantum states then can be made within such a unified output measurement scheme. Based on such a universal detection scheme, we present a comparison of the phase sensitivity reduction for various quantum states of light in the presence of photon loss. I also provide a simple condition that could be used to check whether an arbitrary state can achieve the Heisenberg limit independently of the detection scheme. It implies that the fidelity between the two output states with zero phase and minimal detectable phase applied respectively should significantly different from unity as the minimal phase shift scaling as 1/N, whereas the average number of input photons N goes to infinity. Next I give several measures to characterize the which-way information in the interference experiment. We define a new distinguishability associated with the fidelity between two density matrices to measure the which-way information. We demonstrate that the changes of mutual entropy as well as the entanglement of formation of the whole system, i.e. the physical system plus the which-way detector can also be used to describe the which-way information. With such quantities, we show that as the fringe visibility of the interference pattern gets larger, the less which-way information is obtained. Finally, I show that coherent light coupled with photon number resolving detectors can provide a super-resolution much below the Rayleigh diffraction limit, with sensitivity no worse than shot-noise in terms of the detected photon power. This scheme would have applications to laser radar, given the difficulty in making entangled states of light, as well as their susceptibility to atmospheric absorption.
This dissertation contains new theoretical work on how to utilize the entangled photons produced in a parametric down conversion to improve resolution and sensitivity in quantum interferometry, magnetometry and lithography. Chapter 1 introduces some basics of quantum imaging and sensing systems and gives an outline of the thesis. Chapter 2 deals with the use of entangled photons in Sagnac interferometry. We introduce the Sagnac ring interferometer and analyze the Sagnac phase shift with classical and quantum inputs of light. We compare the results obtained from entangled photon pairs input with classical and single-photon inputs. We show how the photon-photon correlation measurements increase the resolution and the sensitivity in the phase shift. In chapter three, we present an analysis of how parametric down-converted photons could be utilized in getting better spectroscopic information about a medium which has magnetic field induced anisotropy. We demonstrate how the improvement in magneto-optical rotation (MOR) of light could be realized by employing two different schemes with collinear and noncollinear down-conversion geometries compared to the use of coherent light. We calculate the resolution that can be achieved in the MOR's both by the use of coherent light and down-converted light. We discuss the possibility that the Heisenberg limit could be reached in magnetometry by the use of down-converted light. In chapter 4, we propose a new idea of using coherent beam stimulated parametric processes along with spontaneous ones to produce resolution improvement in two-photon interferometry. The stimulated processes enhance the count rate by several orders of magnitude while at the same time maintaining high visibility at large gains of the parametric process. We further find that the phases of coherent fields can also be used as tuning knobs to control the visibility of the pattern. We use coherent beams at the signal and idler frequencies as the seed light for the down-conversion process. In chapter 5, we analyze the minimum phase uncertainty of the phase measurement in a Mach-Zehnder interferometer using stimulated parametric down-conversion. We calculate the phase sensitivities for different measurement schemes. We conclude the thesis in chapter 6 and give an outlook for future work.
We present in this paper a new scheme for optical interferometry. We utilize coherent-beam-stimulated two-mode squeezed light, which interacts with a phase shifter and is then squeezed again before detection. Our theoretical device has the potential to reach far below the shot-noise limit in phase sensitivity. This new proposal avoids the pitfalls of other setups, such as difficulty in creating the required resource. Furthermore, our scheme requires no complicated detection protocol, relying instead only on simple intensity measurement. Also, bright, coherent sources 'boost' squeezed light, creating a very sensitive device. This hybrid scheme relies on no unknown components and can be constructed with current technology. In this paper, we present our analysis of this relatively straightforward device, using the operator propagation method. We derive the phase sensitivity and provide a simple numerical example of the power of our new proposal. Sensitivity to unknown phase shifts scales as a shot-noise-limited Mach–Zehnder interferometer, multiplied by a sub-Heisenberg contribution from the squeezed light.
We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.
In this dissertation we begin with a brief introduction of quantum mechanics, its impact on technology in the 20th century, and the likely impact quantum optics will have on the next generation of technology. The following chapters display research performed in many of these next generation areas. In Chapter 2 we describe work performed in the area of designing quantum optical logic gates for use in quantum computing. In Chapter 3 we discuss findings made in regards to using quantum states of light for remote sensing and imaging. We move on to Fabry-Perot interferometers in Chapter 4 and show discoveries made in the differences between classical and non-classical detection schemes with non-classical states of light. Lastly, in Chapter 5 we discuss how to create photonic bandgap coatings that have unique thermal emissivity properties that could have benefits ranging from increased energy efficiency in light bulbs to better thermal management of satellites.