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Physical Review A

Entangled, coherent, and squeezed states of a single SU(2) qutrit

Sinem Binicioǧlu, M. Ali Can, Alexander A. Klyachko, A.S. Shumovsky

Published Apr 25, 2006• 1 citation
OpenAlex

Abstract

Using the single SU(2) qutrit (spin-1 like system), we show that entanglement may take place for a single particle with respect to its internal degrees of freedom, in other words, beyond the conventional requirements of nonlocality and nonseparability. We show that the SU(2) or spin coherent states do not manifest entanglement, while the so-called squeezed spin states are entangled. We reveal the principle difference between the spin coherent and spin squeezed states in terms of quantum correlations. A number of physical realizations of the SU(2) qutrit is discussed.

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arXiv:quant-ph/0212114•Physical Review A•Jul 11, 2003•66 citations
Using the single SU(2) qutrit (spin-1 like system), we show that entanglement may take place for a single particle with respect to its internal degrees of freedom, in other words, beyond the conventional requirements of nonlocality and nonseparability. We show that the SU(2) or spin coherent states do not manifest entanglement, while the so-called squeezed spin states are entangled. We reveal the principle difference between the spin coherent and spin squeezed states in terms of quantum correlations. A number of physical realizations of the SU(2) qutrit is discussed.
This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to SU(2) rotations, and is significant for both entanglement detection and high-precision metrology. We first present various definitions of spin squeezing parameters, explain their origin and properties for typical states, and then discuss spin-squeezed states produced with nonlinear twisting Hamiltonians. Afterwards, we explain pairwise correlations and entanglement in spin-squeezed states, as well as the relations between spin squeezing and quantum Fisher information, where the latter plays a central role in quantum metrology. We also review the applications of spin squeezing for detecting quantum chaos and quantum phase transitions, as well as the influence of decoherence on spin squeezing. Finally, we review several experimental realizations of spin squeezing, as well as their corresponding theoretical backgrounds, including: producing spin-squeezed states via particle collisions in Bose-Einstein condensates, transferring photon squeezing to atomic ensembles, and generating spin squeezing via quantum non-demolition measurements.
We develop a systematic method to construct the Bell states of a qubit bipartite system while taking SU(2)SU(2)SU(2) group as the basis group. An alternative formulation of fidelity, called SU(2)SU(2)SU(2) fidelity, is proposed which gives the Bell-CHSH inequality. Taking analogy from the octet theory governed by the SU(3)SU(3)SU(3) group, it is shown that the method can be easily generalized to derive all possible entangled states and the SU(3)SU(3)SU(3) fidelity of the higher dimensional bipartite qutrit system. The properties of these states are studied which reveal the existence of some inequalities for the qutrit bipartite system.
Abstract In this paper, we investigate quantum correlations in a qutrit-like superposition of spin coherent states. In particular, the quantum entanglement, the lower bound of the geometric measure of quantum discord, and the lower bound of local quantum uncertainty for the superposition of spin coherent states are examined, and their properties are characterized and compared. The specific dependence of these different correlation quantities on the spin of the system, the coefficient parameters, and the involved coherence parameters is found. As a part of this analysis, conditions for enhanced quantum correlations of qutrit-like superposition states have been identified, which exposes the characteristics of the states based on which the quantum correlations can be controlled and improved.
Squeezed states, a special kind of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors they allow to overcome the "classical" projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as wells as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose-Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.
We analyze the entanglement of SU(2)-invariant density matrices of two spins S1,{S}_{1},S1​, S2{S}_{2}S2​ using the Peres-Horodecki criterion. Such density matrices arise from thermal equilibrium states of isotropic-spin systems. The partial transpose of such a state has the same multiplet structure and degeneracies as the original matrix with the eigenvalue of largest multiplicity being non-negative. The case S1=S,{S}_{1}=S,S1​=S, S2=1/2{S}_{2}=1/2S2​=1/2 can be solved completely and is discussed in detail with respect to isotropic Heisenberg spin models. Moreover, in this case the Peres-Horodecki criterion turns out to be a sufficient condition for nonseparability. We also characterize SU(2)-invariant states of two spins of length 1.