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Review of Scientific Instruments

Some Properties of Spin Generators

Richard J. Blume

Published Jan 1, 1959• 3 citations
Publisher
DOI
10.1063/1.1716357

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In this paper, we shall establish the connection between the group theory and quantum mechanics by showing how the group theory helps us to construct the spin operators. We look to the group generators SU (3). From these generators, new spin 1 operators will be constructed. These operators S-x, S-y and S-z satisfy all the properties of Pauli spin operators S-x, S-y and S-z. We shall discuss the notion of spin squeezing and correlations for pure spin 1 system using our spin operators S-x, S-y and S-z.
Abstract We study the concurrence of two qubits and spin squeezing of N qubits interacting with a common environment using an exactly solvable pure dephasing model. We show that the concurrence and spin squeezing generated via the interaction with the common environment depends on the properties of the environment. Consequently, we optimize over the environmental properties, and in particular the Ohmicity parameter, in order to achieve the maximal quantum resource generation. We also show that there is a weak dependence between the maximum concurrence and the temperature, allowing the results to be experimentally realized in a realistic temperature regime.
Spin squeezing is one of the most attractive methods for realizing high-precision metrology. In this paper we propose a protocol for generating spin squeezing in an atomic ensemble via a fully quantum degenerate parametric amplifier. We discuss the properties of generating spin squeezing with and without driving the pump cavity. Numerical simulation results show that the generated spin squeezing strength is sizable and is comparable to that obtained using a two-axis twisting model. Moreover, we demonstrate that the protocol is experimentally feasible by introducing the corresponding experimental parameters. Therefore, the proposed protocol provides a promising approach to realize spin squeezing in photon-spin coupling systems.