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arXiv:1110.1481

Measurement of Translational Diffusion Constant using Noon State

Abhishek Shukla, Manvendra Sharma, T. S. Mahesh

Published Oct 7, 2011• 3 citations
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Abstract

A method for measuring translational diffusion constant in liquids via NOON state is described using a quantum circuit and is experimentally demonstrated using a model system. When compared with the standard single quantum method, the NOON state method requirs shorter diffusion delays and weaker gradients. These improvements depend on the on the size of the NOON state. Due to the high sensitivity of the NOON state for the changes in the local magnetic fields, this method enables studying slow diffusion and studying diffusion with limited strengths of pulsed-field-gradients.

DOI
10.48550/arxiv.1110.1481

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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.

•May 1, 2018•3 citations
A method for measuring translational diffusion constant in liquids via NOON state is described using a quantum circuit and is experimentally demonstrated using a model system. When compared with the standard single quantum method, the NOON state method requirs shorter diffusion delays and weaker gradients. These improvements depend on the on the size of the NOON state. Due to the high sensitivity of the NOON state for the changes in the local magnetic fields, this method enables studying slow diffusion and studying diffusion with limited strengths of pulsed-field-gradients.
Utilizing the highly correlated quantum NOON states of particles, we have implemented a proof-of-principle quantum thermometer using the NMR technique for measuring the variation of local magnetic field with the temperature variation. The system used was the star-topology system of hexafluorophosphate molecules and the thermometer showed a sensitivity of 85nT/oC85nT/ ^o C85nT/oC. Using the hexafluorophosphate and the trimethylphosphite spin systems, we have quantified the advantage of the quantum protocol over the classical one for measuring magnetic field. The quantum protocol showed the best performance for a time evolution in the quantum circuit of T=20msT = 20msT=20ms, where the errors in the measurement scaled as the Heisenberg limit 1/N1/N1/N.
The maximum entangled number state (NOON state) can improve the sensitivity of physical quantity measurement to the Heisenberg limit 1/N. In this work, the magnetic field measurement based on the individual solid spin NOON state is investigated. Based on the tunable effective coupling coefficient, we propose a generation scheme of the three-spin NOON state, i.e, the Greenberger—Horne—Zeilinger (GHZ) state, and discussed the measurement resolution reduction due to decoherence. It is unnecessary to entangle spins as many as possible when decoherence exists. In practice, defect spins in diamond and 31 P donors with long coherence time can be applied with current techniques in the nano-scaled high resolution magnetic measurement.
We describe a method for quantitative characterization of radio-frequency (RF) inhomogeneity using NOON states. NOON states are special multiple-quantum coherences which can be easily prepared in star-topology spin-systems. In this method we exploit the high sensitivity of the NOON states for z-rotations. As a result, Torrey oscillations with NOON states decay much faster than that of single quantum coherences. Therefore the present method requires shorter pulse durations, and enables the study of inhomogeneity at higher RF powers. To model such a inhomogeneity profile, we propose a two-parameter asymmetric Lorentzian function. The experiments are carried out in 1H channels of two different high-resolution NMR probes and the results are compared. Finally, we also extend the NOON state method to characterize the inhomogeneity correlations between two RF channels. We obtain the correlation profile between 1H and 31P channels of an NMR probe by constructing a five-parameter asymmetric-3D Lorentzian model.
Quantum entangled states can be very delicate and easily perturbed by their external environment. This sensitivity can be harnessed in measurement technology to create a quantum sensor with a capability of outperforming conventional devices at a fundamental level. We compared the magnetic field sensitivity of a classical (unentangled) system with that of a 10-qubit entangled state, realized by nuclei in a highly symmetric molecule. We observed a 9.4-fold quantum enhancement in the sensitivity to an applied field for the entangled system and show that this spin-based approach can scale favorably as compared with approaches in which qubit loss is prevalent. This result demonstrates a method for practical quantum field sensing technology.
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.