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Universal Model for Multi-mode NOON State Generation Using Fock State Filters

Lu Zhang, Kam Wai Clifford Chan

Published Jan 1, 2018• 0 citations
Publisher

Abstract

We present a universal model for generating multi-mode NOON states using Fock state filters. The generation efficiencies for different input scenarios such as coherent states and squeezed vacuum states are calculated for comparisons.
DOI
10.1364/cleopr.2018.w3a.112

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Multi-mode NOON states have been attracting increasing attentions recently for their abilities of obtaining supersensitive and superresolved measurements for simultaneous multiple-phase estimation. In this paper, four different methods of generating multi-mode NOON states with a high photon number were proposed. The first method is a linear optical approach that makes use of the Fock state filtration to reduce lower-order Fock state terms from the coherent state inputs, which are jointly combined to produce a multi-mode NOON state with the triggering of multi-fold single-photon coincidence detections (SPCD) and appropriate postselection. The other three methods (two linear and one nonlinear) use N-photon Fock states as the inputs and require SPCD triggering only. All of the four methods can theoretically create a multi-mode NOON state with an arbitrary photon number. Comparisons among these four methods were made with respect to their feasibility and efficiency. The first method is experimentally most feasible since it takes considerably fewer photonic operations and, more importantly, requires neither the use of high-N Fock states nor high-degree of nonlinearity.
Quantum entanglement is a fascinating physical resource that is central to the field of quantum information processing with important applications in such areas as quantum computing, quantum communication, quantum metrology, and quantum imaging. \nIt describes the physical phenomenon in which the quantum state of a multipartite system cannot be written as consisting of constituents that are independent of each other. In this case, the state of the system is called an entangled state. In this \ndissertation, the entanglement of photons--the elementary excitations of the quantized electromagnetic field--is studied. A focus is made on a particular type of entangled states of light called the d-mode N-photon NOON state, which consists of N photons with the N photons as an ensemble appearing at d orthogonal modes simultaneously and are inseparable. \nIn quantum metrology, a field that investigates the ultimate precision of measurements of unknown physical parameters, the two-mode NOON state has been studied extensively with respect to its ability to achieve super-resolution and super-sensitivity in the estimation of a single parameter. A lot of theoretical research has been conducted on the generation of two-mode NOON states, and two-mode NOON states with up to 4 photons have been experimentally and efficiently produced. On the other hand, recently there has been increasing interest in the study of the simultaneous estimation of multiple parameters. Accordingly, the multi-mode NOON state has been attracting more and more attention in view of its potential for enhanced efficiency as compared to using multiple two-mode NOON states separately to estimate the parameters. Nevertheless, no known generation method of multi-mode NOON states with more than 2 photons or 2 modes exists so far. \nIn this dissertation, several scalable generation methods of multi-mode NOON states are proposed. These methods take advantage of multi-photon quantum interference and they can theoretically be applied to produce NOON states with an \narbitrary number of modes and an arbitrary number of photons. The intrinsic generation probability for each method is calculated, and the methods are compared in regards to their feasibility and efficiency. The advantages of using multi-mode NOON \nstates in quantum metrology are also analyzed and discussed in detail.
The simultaneous multiparameter estimation problem using a class of multimode entangled states is investigated in this paper. Specifically, the problem of optical phase imaging is considered, and the quantum probe is taken to be a balanced coherent superposition of components with an arbitrary quantum state in one mode and vacuum states in all the other modes, which is a generalization of the multimode NOON state. The analytical form for the quantum Cram\'er-Rao bound (QCRB) is presented, which shows the performance by providing a lower bound of the estimation uncertainty. It is shown that the NOON state has the worst performance among those in the class of the entangled states considered. We also analyze in detail four different scenarios, which are the NOON state, the entangled coherent state, the entangled squeezed coherent state, and the entangled squeezed vacuum state. From the comparison among these four states, we find that when the mean photon number is fixed, the squeezed vacuum state has the smallest QCRB, followed by the squeezed coherent state, entangled coherent state, and NOON state. Finally, we illustrate that the balanced entangled state can perform better than a more generalized unbalanced form studied in previous works for certain scenarios.