Heisenberg Limited Phase Estimation using Quantum Optical Interferometry

Abstract

Quantum optical interferometry has played a crucial role in precision measurements and quantum sensing, which laid the foundation of quantum metrology the science of precision measurements using the laws of quantum mechanics. The precision of any measurement may be limited by experimental human error and/or ingenuity of measuring apparatus. However, beyond these limitations quantum mechanics imposes a fundamental restriction on metrology which can be expressed by Heisenberg Uncertainty principle. Fortunately, on the other hand, solution to this quantum-induced limitation is also provided by quantum theory using some non-classical concepts. Hence, quantum metrology deals with techniques to improve the measurement precision beyond the limit set by standard quantum uctuations. In many physical situations, precision measurement process can be reduced to detection of a small phase shift by using optical interferometric set up. This thesis is focused on studying the quantum optical phase-estimation and exploring the fundamental bounds on its ultimate precision in the perspective of classical and quantum measurement theories. Using the notion of Fisher information entropy, we nd the so-called Cramér Rao bounds on optical phase-estimation while using classical as well as quantum probes at our optical set up. We show that by using classical probe as initial state, the estimation error is estimated at the best as 1= p n. This limit is known as Short Noise Limit (SNL). Interestingly, it is shown that using quantum probes the ultimate precision limit surpasses SNL and approaches the value as 1= n, which is known as Heisenberg-limit. It is important to note that in the Heisenberglimited phase-estimation, the accuracy is enhanced by a factor of p n with respect to SNL.