Representations of coherent and squeezed states in an extended two-parameter Fock space

M. H. Lake

doi:10.1088/1674-1137/36/8/004

Chinese Physics C> 2012, Vol. 36> Issue(8) : 703-709 DOI: 10.1088/1674-1137/36/8/004

Representations of coherent and squeezed states in an extended two-parameter Fock space

M. H. Lake

Abstract
HTML
Reference
Related

PDF

Abstract：
Recently an f-deformed Fock space which is spanned by |n〉_λ was introduced. These bases are the eigenstates of a deformed non-Hermitian Hamiltonian. In this contribution, we will use rather new non-orthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by |n〉_λ bases, to a new one, spanned by extended two-parameters bases |n〉λ₁,λ₂. These bases are now the eigenstates of a non-Hermitian Hamiltonian H_λ1,_λ2=a_λ1,_λ2⁺a+(1/2), where a_λ1,_λ2⁺=a⁺+ λ₁a + λ₂ and a are, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases |n〉λ₁,λ₂ are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of coherent and squeezed states in our two-parameter Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states numerically.

References

[1]

Roknizadeh R, Tavassoly M K. J. Phys. A: Math. Gen., 2004, 37: 5649[2] Peres A. Quantum Theory: Concepts and Methods. Kluwer Academic, Dordrecht. 1993[3] de Matos Filho R L, Vogel W. Phys. Rev. A, 1996, 54: 4560[4] Choi J R. Chinese Phys. C (HEP NP), 2011, 35: 233[5] JIANG J Q. Chinese Phys. C (HEP NP), 2010, 34: 325[6] AI Q, WANG Y D, LONG G L, SUN C P. Sci. China Ser. G, 2009, 52: 1898; DONG H, LIU X F, SUN C P. Chinese Sci. Bulletin, 2010, 55: 3256; REN X Z, CONG H L, WANG X W, XIA J P. Sci. China Phys., Mech. Astron., 2011, 54: 1625[7] Twareque A S, Antoine J P, Gazeau J P. Coherent States, Wavelets and Their Generalizations. New York: Springer-Verlag, 2000[8] Twareque A S, Roknizadeh R, Tavassoly M K. J. Phys. A: Math. Gen., 2004, 37: 4407[9] Klauder J R, Skagerstam B S. Coherent States: Applications in Physics and Mathematical Physics. Singapore: World Scientific, 1985[10] Perelomov A. Generalized Coherent States and Their Applications. New York: Springer, 1985[11] WANG X B, Kwek L C, Oh C H. Phys. Lett. A, 1999, 259: 7[12] Bardek V, Meljanace S. Eur. Phys. J. C, 2000, 17: 539[13] WANG X J. Opt. B: Quantum Semiclass. Opt., 2000, 2: 534[14] Das P K. Int. J. Theor. Phys., 2002, 41: 1099[15] Manko V I, Marmo G, Sudarshan E C G, Zaccaria F. Phys. Scr., 1997, 55: 528[16] Solomon A I, Katriel J J. Phys. A: Math. Gen., 1990, 23: 5L1209[17] Mandel L. Opt. Lett., 1979, 4: 205

[1]	Bao-Dong Sun , Yu-Bing Dong . ρ meson impact parameter distributions. Chinese Physics C, 2018, 42(6): 063104. doi: 10.1088/1674-1137/42/6/063104
[2]	Honey Sharma , H. M. Mittal . Band head spin determination of triaxial superdeformed bands in ^163,164,165Lu through two-parameter formulae. Chinese Physics C, 2018, 42(11): 114102. doi: 10.1088/1674-1137/42/11/114102
[3]	Wenyu Wang , Zhao-Hua Xiong , Xin-Yan Zhao . General scan in flavor parameter space in models with vector quark doublets and an enhancement in the B→X_sγ process. Chinese Physics C, 2016, 40(9): 093102. doi: 10.1088/1674-1137/40/9/093102
[4]	GUO Xing-Dao , FENG Tai-Fu , ZHAO Shu-Min , KE Hong-Wei , LI Xue-Qian . Constraining parameter space of the little Higgs model using data from tera-Z factory and ILC. Chinese Physics C, 2015, 39(2): 023103. doi: 10.1088/1674-1137/39/2/023103
[5]	S. S. Hosseini , S. Zarrinkamar . Dirac oscillator in noncommutative space. Chinese Physics C, 2014, 38(6): 063104. doi: 10.1088/1674-1137/38/6/063104
[6]	GAN Sheng-Xin , ZUO Wei . Nucleon effective mass in symmetric nuclearmatter from the extended Brueckner-Hartree-Fock approach. Chinese Physics C, 2012, 36(6): 513-518 . doi: 10.1088/1674-1137/36/6/006
[7]	JIANG Jun-Qin . kth-order antibunching effect for a new kind of excited even and odd q-coherent states. Chinese Physics C, 2010, 34(3): 325-329. doi: 10.1088/1674-1137/34/3/004
[8]	WEI Ning , ZHOU Xian-Rong , CHEN Fang-Qi . Properties of Zr hypernuclei in deformed Skyrme Hartree-Fock approach. Chinese Physics C, 2009, 33(S1): 116-118. doi: 10.1088/1674-1137/33/S1/037
[9]	BAO Tmurbagan , LIU Guang-Zhou , ZHU Ming-Feng . Properties of hybrid stars in an extended MIT bag model. Chinese Physics C, 2009, 33(5): 340-344. doi: 10.1088/1674-1137/33/5/004
[10]	PEI Jun-Cen , XU Fu-Rong . Understanding of Halo Nucleus ¹¹Be with Skyrme-Hartree-Fock. Chinese Physics C, 2004, 28(S1): 72-74.
[11]	HUANG Chun-Qing , JIANG Jun-Qin . Squeezing Property of the Excited Two-Parameter Deformed Even and Odd Coherent States. Chinese Physics C, 2003, 27(3): 196-199.
[12]	JIANG Jun-Qin . Antibunching Effect of the Excited Two-Parameter Deformed Even and Odd Coherent States. Chinese Physics C, 2003, 27(1): 15-18.
[13]	WANG Zhong-Qing . Higher Power Squeezing Properties for Odd and Even Two-Parameter Deformed Coherent States. Chinese Physics C, 2001, 25(12): 1158-1164.
[14]	Shen Yaosong , Ren Zhongzhou . Skyrme-Hartree-Fock Calculation on Exotic Nuclei. Chinese Physics C, 1997, 21(S2): 53-62.
[15]	Shen Yaosong , Ren Zhongzhou . Skyrme-Hartree-Fock Calculation on Exotic Nuclei. Chinese Physics C, 1997, 21(3): 248-256.
[16]	Zhou Huanqiang , Guan Xiwen , He Jingsong . A Two-Parameter Deformed Two-Dimensional Interacting Boson Model with U_qp(U₃)⊃U_qp(U₂)⊃U_qp(SO₂) Symmetry. Chinese Physics C, 1996, 20(S1): 39-46.
[17]	JING Xiaogong , ZHAO Guoquan , YAO Yujie , YANG Shande , WU Shishu . Study of Multiplicity of Hartree-Fock Solutions. Chinese Physics C, 1993, 17(11): 1026-1031.
[18]	Jing Xiaogong , Zhao Guoquan , Yao Yujie , Yang Shande , Wu Shishu . Study of Multiplicity of Hartree-Fock Solution. Chinese Physics C, 1993, 17(S3): 303-309.
[19]	XU Shu-Wei , PAN Qiang-Yan , LIU Guo-Xing . A TWO-PARAMETER ROTATING LIQUID DROP MODEL. Chinese Physics C, 1990, 14(2): 175-180.
[20]	PAN Zheng-Ying , QIU Zhi-Hong , SUN Yue-De . OCCUPATION RENORMALIZED HARTREE-FOCK APPROXIMATION IN LIPKIN MODEL. Chinese Physics C, 1984, 8(3): 298-305.

Access

Get Citation

M. H. Lake. Representations of coherent and squeezed states in an extended two-parameter Fock space[J]. Chinese Physics C, 2012, 36(8): 703-709. doi: 10.1088/1674-1137/36/8/004

M. H. Lake. Representations of coherent and squeezed states in an extended two-parameter Fock space[J]. Chinese Physics C, 2012, 36(8): 703-709. doi: 10.1088/1674-1137/36/8/004 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2011-10-31
Revised: 2012-02-07

Article Metric

Article Views(2249)
PDF Downloads(238)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Representations of coherent and squeezed states in an extended two-parameter Fock space

Received Date: 2011-10-31

Accepted Date: 2012-02-07

Available Online: 2012-08-05

Abstract: Recently an f-deformed Fock space which is spanned by |n〉_λ was introduced. These bases are the eigenstates of a deformed non-Hermitian Hamiltonian. In this contribution, we will use rather new non-orthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by |n〉_λ bases, to a new one, spanned by extended two-parameters bases |n〉λ₁,λ₂. These bases are now the eigenstates of a non-Hermitian Hamiltonian H_λ1,_λ2=a_λ1,_λ2⁺a+(1/2), where a_λ1,_λ2⁺=a⁺+ λ₁a + λ₂ and a are, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases |n〉λ₁,λ₂ are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of coherent and squeezed states in our two-parameter Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states numerically.

HTML

Reference (1)

Representations of coherent and squeezed states in an extended two-parameter Fock space

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Representations of coherent and squeezed states in an extended two-parameter Fock space

HTML

目录