We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method with the minimum-uncertainty method for obtaining the squeezed and coherent states of general potential systems, and comment on the distinctions between these two methods and the displacement-operator method. PACS numbers: 03.65.-w, 02.20.-a, 42.50.-pCoherent states are important in many fields of theoretical and experimental physics [1,2]. Similarly, the generalization of coherent states, squeezed states, has become of more and more interest in recent times [3,4]. This is especially true in the fields of quantum optics [5] and gravitational wave detection [6], However, one limitation is that, with the exception we describe below, essentially all work on squeezed states has concentrated on the harmonic oscillator system. In this Letter we describe a generalization of squeezed states to arbitrary symmetry systems, and its relationship to squeezed states obtained for general potentials.We begin by reviewing coherent states and squeezed states.(Displacement^operator method.-For the harmonic oscillator, coherent states are described by the unitary displacement operator acting on the ground state [7,8]: £>(a)|0)= exp[aa f -a*a]|0) exp ~2 N £^?i n > s i*>-v^!The generalization of this method to arbitrary Lie groups has a long history [1,2,7,9]. One simply applies the displacement operator, which is the unitary exponentiation of the factor algebra, onto an extremal state. As to squeezed states, this method has basically only been applied to harmonic oscillatorlike systems [3,4].One applies the SU(1,1) displacement operator onto the coherent state,
D(a)S(z)\0)= |(a,z)>, S{z) = exp[zK+ -z*K.(2)where K + , K~, and KQ form an su(l,l) algebra among themselves:The ordering of DS vs SD in Eq.(2) is unitarily equivalent, amounting to a change of parameters. (Supersymmetric extensions of the above exist [10].)(2) Ladder-(annihilation-) operator method.-For the harmonic oscillator, the coherent states are the eigenstates of the destruction operator:This follows from Eq. (1), since 0 = D(a)a\0) -(aa)|a). These states are the same as the displacementoperator coherent states. The generalization to arbitrary Lie groups is straightforward, and has also been widely studied [1,2].Minimum-uncertainty method.-This method, which intuitively harks back to Schrodinger's discovery 0031 -9007/93/71 (18)/2843 (4)$06.00