Spin squeezing of mixed systems

Abstract

Abstract. The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin 1/2 states and study its squeezing behaviour as a function of the individual polarizations of the two spinors. §

Achieving spin-squeezed states by quench dynamics in a quantum chain

“…It would be extremely interesting to uncover the properties of this putative nonequilibrium transition, in the present case signaled by a cusp in ξ 2 s . Another very interesting problem is to understand how the properties of coherence and spin squeezing are imprinted in the limit of very large times [89], where, in the thermodynamic limit, the post-quench states are expected to equilibrate to a mixed state governed by a generalized Gibbs ensemble [56].…”

Squeezing of a coupled state of two spinors

“…In their paper [5] they suggest that every state of a spin s system can be visualized as a coupled state of 2s spinor states and claim that the squeezing behaviour of the spin s state is due to the correlations that exist among the 2s spinor states. In our earlier paper [1,2], we have indeed given an explicit method of construction of a general pure spin s state in terms of 2s spinor states. Based on this construction we have analysed the nature of a squeezed spin s state and in the case of s = 1, we have shown that the squeezing aspect is intimately connected with the pair-wise correlations defined through…”

“…

The notion of spin squeezing involves reduction in the uncertainty of a component of the spin vector S below a certain limit. This aspect has been studied earlier [1,2] for pure and mixed states of definite spin. In this paper, this study has been extended to coupled spin states which do not possess sharp spin value.

…”

Visualization of an entangled channel spin-1 system

“…Here we employ co-variance matrix formalism [6,7] as the elements of co-variance matrix are closely related to intrinsic quantum correlations that exist between the constituent spinors of a spin system. Such correlations are shown to explain the physical origin of the squeezing behavior of the coupled spin-1 system [8,9]. It can be noted that the spin squeezing inequalities generalize the concept of spin squeezing parameter and provide the necessary and sufficient condition for genuine two qubit entanglement of spin-1 system [10].…”

“…Let us consider the special Lakin frame (SLF) [9] which is widely used in studying nuclear reactions as follows : Chooseẑ 0 to be along p(1) + p(2). Since p(1), p(2) together define a plane in any general situation, we choosê x 0 to be in this plane such that the azimuths of p(1) , p(2) with respect tox 0 are respectively 0 and π. Theŷ 0 axis is then chosen to be alongẑ 0 ×x 0 .…”