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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (9): 1161-1167.doi: https://doi.org/10.1007/s10483-009-0910-y

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Two-mode squeezed state of nanomechanical resonators

范瑞琴1 羊红光2 白志明2   

  1. 1. Department of Mathematics and Physics, Shijiazhuang Railway Institute,Shijiazhuang 050043, P. R. China;
    2. College of Science, Hebei University of Science and Technology,Shijiazhuang 050018, P. R. China
  • 收稿日期:2008-10-10 修回日期:2009-07-31 出版日期:2009-09-01 发布日期:2009-09-01

Two-mode squeezed state of nanomechanical resonators

FAN Rui-Qin1, YANG Hong-Guang2, BAI Zhi-Ming2   

  1. 1. Department of Mathematics and Physics, Shijiazhuang Railway Institute,Shijiazhuang 050043, P. R. China;
    2. College of Science, Hebei University of Science and Technology,Shijiazhuang 050018, P. R. China
  • Received:2008-10-10 Revised:2009-07-31 Online:2009-09-01 Published:2009-09-01

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摘要： In this paper, we introduce a flexible model for the control and measurement of NAMRs (nanomechanical resonators). We obtain the free Hamiltonian of the dc-SQUID (direct current superconducting quantum interference device) and the interaction Hamiltonian between these two NAMRs and the dc-SQUID by introducing the annihilation and creation operators under the rotating wave approximation. We can treat the mode of the dc-SQUID as a classical field. In the Heisenberg picture, the generation of two-mode squeezed states of two nanomechanical resonators is shown by their collective coordinate and momentum operators.

关键词: squeezed state, two-mode, mechanical resonator

Abstract: In this paper, we introduce a flexible model for the control and measurement of NAMRs (nanomechanical resonators). We obtain the free Hamiltonian of the dc-SQUID (direct current superconducting quantum interference device) and the interaction Hamiltonian between these two NAMRs and the dc-SQUID by introducing the annihilation and creation operators under the rotating wave approximation. We can treat the mode of the dc-SQUID as a classical field. In the Heisenberg picture, the generation of two-mode squeezed states of two nanomechanical resonators is shown by their collective coordinate and momentum operators.

Key words: squeezed state, two-mode, mechanical resonator

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