2 August 1999 Ž . Physics Letters A 259 1999 7–14 www.elsevier.nlrlocaterphysleta Extended two-parameter squeezed states Xiang-Bin Wang 1 , L.C. Kwek 2 , C.H. Oh 3 Department of Physics,Faculty of Science, National UniÕersity of Singapore, Lower Kent Ridge Road, Singapore 119260, Singapore Received 3 March 1999; received in revised form 26 April 1999; accepted 24 May 1999 Communicated by P.R. Holland Abstract w In a recent paper, a new l-dependent squeezed states was proposed J. Beckers, N. Debergh and F.H. Szafraniec, Phys. Ž . x Lett. A 243 1998 256–260 in which the usual Fock-space creation operator has been modified by introducing a simple translational term. In this paper, we generalize this approach by adding a new term proportional to the creation operator using exponential quadratic operators. q 1999 Elsevier Science B.V. All rights reserved. 1. Introduction Squeezed states provide a means of challenging the theoretical and experimental limits imposed by the uncertainty principle and the zero-point fluctua- tions of the vacuum. Consequently, these novel non- classical states have constantly stimulated much in- terest as the means for improving the signal-to-noise wx ratio in optical interferometry 1 , quantum teleporta- wx w x tion 2 , Raman scattering 3,4 and a myriad of other wx applications such as gravitational wave detection 5 . Amplitude squeezed states have been observed in negative feedback laser with quantum nondemolition wx measurement of photon number 6 . They can also be generated by parametric amplifiers. Conventionally, squeezed states have been defined through the 1 E-mail: scip7236@leonis.nus.edu.sg 2 E-mail: scip6051@leonis.nus.edu.sg 3 E-mail: phyohch@nus.edu.sg Ž. Ž . squeezed and displacement operators, Sz and D a wx respectively through the relations 7 < : < : a , z s D a S z 0 , 1 Ž . Ž . Ž. Ž. Ž . where Sz and D a are defined as the operators 1 ) 2 ²2 ² ) ŽŽ .. Ž . exp z a y za and exp a a y a a respec- 2 Ž ² . tively and a, a are the usual annihilator and creator operators. wx In a recent paper 8 , Becker et al. proposed a new family of squeezed states by considering a modifica- tion of creation operator in Fock space using the relation a ² s a ² q l , 2 Ž. l where a ² is the usual bosonic creation operator, a ² is l called as l-parametrized bosonic creation operator. The l-parametrized Hamiltonian is given by 1 ² H s a , a . 3 Ž.  4 l l 2 The eigenstates of l-parametrized Hamiltonian was investigated and it was shown that it is possible to obtain squeezed states for certain values of the pa- wx rameter l 8 . Unlike usual squeezed states in which 0375-9601r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž . PII: S0375-9601 99 00354-0