Squeezing and non-oriented spin states

Spin squeezing of mixed systems

“…In other words, an oriented system is one in which the populations are distributed with respect to the basis states |sm 0 andẑ 0 is then called the axis of orientation. It may be noted here that this definition for mixed states is a natural generalization of the definition of an oriented pure state defined in our earlier paper [10]. If p m denote the fractional populations of an oriented system in the states |sm 0 , the density matrix ρ 0 is given by the expansion…”

“…Following Kitagawa and Ueda [1] and Puri [8], we have defined squeezing criterion in our earlier paper [10] as follows. Given the quantum state |ψ of spin s, the mean spin direction associated with it is given bŷ…”

“…On the other hand, a squeezed state of spin is depicted as being built out of the same number of the spins which possess quantum correlation. We have looked into this aspect, in all its details, in the case of spin 1 in our earlier paper [10] and an explicit connection between the spin-spin correlations and spin squeezing has been shown to exist. In the light of this we now adopt for the case of mixed states the generalized form of the above criterion.…”

“…Just as the idea of coherent states introduced by Schroedinger [5] for the harmonic oscillator was extended [6,16] to discuss coherence in optics, the notion of squeezed states was also extended to the radiation field [7] and to spin states [1,8,9] as well. A spin state may be said [10] to be squeezed if the variance ∆S ⊥ associated with a spin component normal to the mean spin directionV satisfies the condition, …”

“…Likewise a physical basis for (9) has also been discussed by Puri [8]. More recently [10], a classification of pure states |ψ into two classes referred to as 'oriented' and 'non-oriented' has been suggested employing a construction of states of spin s out of 2s non-collinear spinors and it was explicitly shown in the case of s = 1 that a state |ψ has to be necessarily non-oriented for it to be a squeezed state. The purpose of this paper is to extend the notion of spin squeezing to statistical assemblies of particles with spin s as it will not only provide a complete spin description of spin squeezing but also facilitate planning of experiments to study squeezed spin states.…”