Internal Structure and Squeezing Properties of Some Macroscopic Quantum States

  • Coherent states and the extension to the even and odd coherent states, and further to the eigenstates of the higher power of the annihilation operator are basic and important macroscopic quantum states in quantum field theory. Recently, these investigations have been extended to the aharmonic oscillator and the quantum algebra with q -deformed or qs-deformed commutation relations. In this paper,the orthogonal eigenstates of the higher order of the annihilation operator of the q-deformed aharmonic oscillator are also derived. It is pointed out that these different macroscopic quantum states have similar squeezing properties of higher order amplitude. The reason is found that the orthogonal eigenstates of the higher order of the annihilation operator of the harmonic oscillator, the q-deformed oscillator, the qs -deformed oscillator, the Enharmonic oscillator and the q-deformed anharmonic oscillator all have even and odd structure, which is similar to the simple even and odd coherent states. For other systems like the system with SU(1,1) Lie algebra or q-deformed quantum algebra also have such properties.
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  • [1] Biedenharm L C . J Phys . ,1989, A22 : L8722 Pocek M. Phys. Lett. ,1991, B255:554 133 HA0 San-Ru. Acta Physica Sinica, 1993,42: 1057 (in Chinese)(郝三如. 物理学报, 1993,42:1057)4 FANG Xiang-Zheng, RUAN Tu-Nan. High Energy Phys. and Nucl. Phys. .2001,25:212(in Chinese)(方向正, 阮图南.高能物理与核物理,2001,25:212)5 Greenberg 0 W, Hilbom. Phys. Rev. Lett. ,1999.83 :4460 156 KUANG L M , WANG F B . Phys. Lett. ,1992, A169: 2257 WANGFB,KUANGLM.J. Phys.,1993,A26:2938 CHEN Chang-Yuan . High Energy Phys. and Nucl. Phys. ,2001.25: 16;193(in Chinese)(陈昌远, 刘友文.高能物理与核物理, 2001,25;193)9 WANG Ji-Suo, SUN Chang-Yong, TENG Ai-Ping. High Energy Phys. and Nucl. Phys. ,1997,21: 793( in Chinese)(王继锁, 孙长勇, 腾爱萍.高能物理与核物理, 1997,21:793)10 Hillery M. Phys. Rev. 1987, A36: 379611 ZHANG Z, XU L, CHAI J et al. Phys. Len. 19W,A150:2712 WANG Zhong-Qing . Acta Physica Sinica ,2001 ,50 : 690 (in Chinese)(汪仲清.物理学报, 2001,50:690)13 WANG Ji-Suo, LIU Tang-Kun, ZHAN Ming-Sheng . High Energy Phys .and Nucl. Phys. ,2001. 25: 11(in Chinese)(王继锁, 刘堂昆, 詹明生.高能物理与核物理, 2001,25:11)14 SUN Jin-Zuo. Chinese Journal of Quantum Electronics, 1992,9: 397 ( in Chinese)(孙金柞.量子电子学, 1992,9:397)15 WANG Ji-Suo, SUN Jin-Zuo, WANG Chum-Kui. Acta Photonica Sinica,1994,23:200(in Chinese)(王继锁, 孙金柞, 王传奎.光子学报, 1994,23:200)16 WANG Ji-Suo, LIU Tang-Kun, ZHAN Ming-Sheng . Acta Optonica Sinica,2000,20:1317 (in Chinese)(王继锁, 刘堂昆, 詹明生.光学学报, 2000,20:1317)17 XU Zi-Wen . High Energy Phys . and Nucl . Phys . , 1999,23 : 436 ( in Chinese)(徐子骏.高能物理与核物理, 1999,23:436)
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LIANG Mai-Lin and LI Yu-Rong. Internal Structure and Squeezing Properties of Some Macroscopic Quantum States[J]. Chinese Physics C, 2003, 27(1): 19-23.
LIANG Mai-Lin and LI Yu-Rong. Internal Structure and Squeezing Properties of Some Macroscopic Quantum States[J]. Chinese Physics C, 2003, 27(1): 19-23. shu
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Received: 2002-04-12
Revised: 1900-01-01
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Internal Structure and Squeezing Properties of Some Macroscopic Quantum States

    Corresponding author: LIANG Mai-Lin,
  • Department of Applied Physics,School of Science,Tianjin University, Tianjin 300072,China

Abstract: Coherent states and the extension to the even and odd coherent states, and further to the eigenstates of the higher power of the annihilation operator are basic and important macroscopic quantum states in quantum field theory. Recently, these investigations have been extended to the aharmonic oscillator and the quantum algebra with q -deformed or qs-deformed commutation relations. In this paper,the orthogonal eigenstates of the higher order of the annihilation operator of the q-deformed aharmonic oscillator are also derived. It is pointed out that these different macroscopic quantum states have similar squeezing properties of higher order amplitude. The reason is found that the orthogonal eigenstates of the higher order of the annihilation operator of the harmonic oscillator, the q-deformed oscillator, the qs -deformed oscillator, the Enharmonic oscillator and the q-deformed anharmonic oscillator all have even and odd structure, which is similar to the simple even and odd coherent states. For other systems like the system with SU(1,1) Lie algebra or q-deformed quantum algebra also have such properties.

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