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

  • Recently an f-deformed Fock space which is spanned by |nλ 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 |nλ bases, to a new one, spanned by extended two-parameters bases |n〉λ12. These bases are now the eigenstates of a non-Hermitian Hamiltonian Hλ1,λ2=aλ1,λ2+a+(1/2), where aλ1,λ2+=a++ λ1a + λ2 and a are, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases |n〉λ12 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.
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  • [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
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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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Representations of coherent and squeezed states in an extended two-parameter Fock space

Abstract: Recently an f-deformed Fock space which is spanned by |nλ 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 |nλ bases, to a new one, spanned by extended two-parameters bases |n〉λ12. These bases are now the eigenstates of a non-Hermitian Hamiltonian Hλ1,λ2=aλ1,λ2+a+(1/2), where aλ1,λ2+=a++ λ1a + λ2 and a are, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases |n〉λ12 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.

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