We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, th...We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.展开更多
Entropy squeezing is an important feature in performing different tasks in quantum information processing such as quantum cryptography and superdense coding. These quantum information tasks depend on finding the state...Entropy squeezing is an important feature in performing different tasks in quantum information processing such as quantum cryptography and superdense coding. These quantum information tasks depend on finding the states in which squeezing can be created. In this article, a new feature on entropy squeezing for a two level system with a class of nonlinear coherent state (NCS) is observed. An interesting result on the comparison between the coherent state (CS) and NCS is explored. The influence of the Lamb-Dick parameter in both absence and presence of the Kerr medium is examined. A rich feature of entropy squeezing in the case of NCS, which is observed to describe the motion of the trapped ion, has been obtained.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10674045 and 60538010)the National Natural Science Foundation of Hunan Province,China (Grant No 08jj3001)
文摘We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.
文摘Entropy squeezing is an important feature in performing different tasks in quantum information processing such as quantum cryptography and superdense coding. These quantum information tasks depend on finding the states in which squeezing can be created. In this article, a new feature on entropy squeezing for a two level system with a class of nonlinear coherent state (NCS) is observed. An interesting result on the comparison between the coherent state (CS) and NCS is explored. The influence of the Lamb-Dick parameter in both absence and presence of the Kerr medium is examined. A rich feature of entropy squeezing in the case of NCS, which is observed to describe the motion of the trapped ion, has been obtained.
