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.
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.
The fields of quantum and nonlinear optics have given rise to a variety of nonclassical states of light that have been proven to surpass certain limitations set by classical physics. Namely, certain squeezed and entangled states have been shown to beat the shot-noise limit when making precision phase measurements in interferometry, as well as write lithographic patterns that are smaller than classically allowed by the Rayleigh diffraction limit. Additionally, single-photon sources and entangled photon pairs have given rise to provably secure quantum key distribution for cryptography. Producing these quantum states of light has proven a difficult task. Nonlinear crystals, when pumped by a laser, produce pairs of single photons via the process of spontaneous parametric down conversion (SPDC). This process is mediated by the second order nonlinear susceptibility of the material. When pumped in a high gain regime, these crystals give rise to optical parametric amplification, which is a viable source of squeezed light. The vast majority of research in this area has focused on crystals that are seeded by vacuum in their two modes. This dissertation concerns the field of quantum nonlinear optics. It is an investigation into the processes that occur when nonlinear materials interact with the electromagnetic field on the single photon level. I have focused on seeding nonlinear crystals with quantum states of light, including single photons and entangled states. This process results in various states directly applicable to interferometry, imaging, and cryptography. Another application investigated is an absolute radiance measurement via stimulated parametric down conversion resulting from non-vacuum seeding of a nonlinear crystal. Additionally, other nonlinear processes, including four-wave mixing, nonlinear magneto-optical effects and coherent population trapping in warm atomic vapor involving quantum states of light are investigated. The process of seeding third-order nonlinear interactions, such as in atomic vapors, gives rise to a variety of interesting, nonclassical phenomena such as entangled image transfer and nonlocal imaging. Strong analogies between SPDC and four-wave mixing are drawn. I also experimentally show an all optical pi-only phase shift of one light beam via another in warm Cesium vapor.
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.
Recent theoretical and experimental papers have shown how one can achieve Heisenberg-limited measurements by using entangled photons. Here we show how the photons in a noncollinear down-conversion process can be used for improving the sensitivity of magneto-optical rotation by a factor of 4 which takes us towards the Heisenberg limit. Our results apply to sources with arbitrary pumping. We also present several generalizations of earlier results for the collinear geometry. The sensitivity depends on whether the two-photon or four-photon coincidence detection is used.
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.
In recent years, quantum entanglement has attracted much; attention, because its unique properties provide potential; applications, which could not be achieved using conventional; techniques, such as quantum computing, quantum imaging and; lithography. To realize these advancements, one has to obtain an; entanglement-generation source, thoroughly master its physical; properties, and fully understand the light-matter interaction.; This dissertation is an attempt to address such issues as stated; above.; Conventionally, paired photons are created from; \textit{spontaneous parametric down-conversion} (SPDC). It is; known that the transverse correlation in biphotons may improve the; visibility and resolution in quantum imaging and lithography. In; this thesis, we described an alternative biphoton source --; Raman-EIT (\textit{electromagnetically induced transparency}); generator, and emphasize on its geometrical and optical; properties. We found that to utilize the transverse effects in; paired Stokes-anti-Stokes, it is necessary to make the product of; the EIT window times the group delay much greater than unity.; To gain further insight into quantum imaging and lithography, we; studied the transverse correlation in triphoton entanglement; theoretically. We found that in the two-image process, the quality; of images is determined by the optical path-lengths, even though; the Gaussian thin lens equations are satisfied. The ghost; interference-diffraction patterns of double slits show one more; fold interference, which is essentially different from the; biphoton case. Klyshko's advanced-wave model is still applicable,; with some modifications. We also generalized the transverse; correlation to the case of multi-photon entangled states.; To implement quantum computing, one key element is quantum memory.; In this thesis, we have theoretically explored the feasibility of; such a memory by using nonclassical SPDC light in an EIT system at; the single-photon level. We found that both the quantum coherence; of SPDC and atomic coherence of EIT can survive after interacting; within a vapor cell. Due to the inherent mismatch of magnitude; between the spectral bandwidth of SPDC and the very narrow; transmission width of EIT, the coincidence counts of the; two-photon interference is reduced to one pair per second, which; is barely doable in the current experimental situation.
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.