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

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Recently an f-deformed Fock space which is spanned by | n〉 _λwas 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〉 _λbases, to a new one, spanned by extended two-parameters bases | n〉λ ₁,λ ₂. 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 ⁺+ λ ₁ a+ λ ₂and aare, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases | n〉λ ₁,λ ₂are 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.

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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

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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

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

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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

M. H. Lake

Received Date:2011-10-31
Accepted Date:2012-02-07
Available Online:2012-08-05

Abstract:Recently anf-deformed Fock space which is spanned by |n〉_λwas 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〉_λbases, to a new one, spanned by extended two-parameters bases |n〉λ₁,λ₂. These bases are now the eigenstates of a non-Hermitian HamiltonianH_λ1,_λ2=a_λ1,_λ2⁺a+(1/2), wherea_λ1,_λ2⁺=a⁺+ λ₁a+ λ₂andaare, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases |n〉λ₁,λ₂are 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.