We resolve an old problem about the existence of hidden parameters in a three-dimensional quantum system by constructing an appropriate Bell's type inequality. This reveals the nonclassical nature of most spin-1 states. We shortly discuss some physical implications and an underlying cause of this nonclassical behavior, as well as a perspective of its experimental verification.

Using the approach to quantum entanglement based on the quantum fluctuations of observables, we show the existence of perfect entangled states of a single "spin-1" particle. We give physical examples related to the photons, condensed matter physics, and particle physics.

We show that a system of 2n identical two-level atoms interacting with n cavity photons manifests entanglement and that the set of entangled states coincides with the so-called SU (2) phase states. In particular, violation of classical realism in terms of the GHZ and GHSH conditions is proved. We discuss a new property of entanglement expressed in terms of local measurements. We also show that generation of entangled states in the atom-photon systems under consideration strongly depends on the choice of initial conditions and that the parasitic influence of cavity detuning can be compensated through the use of Kerr medium.

Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. [A.A. Klyachko and A.S. Shumovsky, J. Phys: Conf. Series 36, 87 (2006), E-print quant-ph/0512213]. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states with maximal amount of uncertainty of all basic observables. The approach gives purely physical picture of entanglement. In particular, it separates principle physical properties of entanglement from inessential. Within the model example under consideration, we show relativity of entanglement with respect to dynamic symmetry and argue existence of single-particle entanglement. A number of physical examples are considered.

It is shown that the Rashba and Dresselhaus spin orbit couplings enhance the conclusive power in the experiments on the excitonic condensed state by at least three low temperature effects. First, spin orbit coupling facilitates the photoluminescense measurements via enhancing the bright contribution in the otherwise dominantly dark exciton condensed state. The second is the presence of a power law temperature dependence of the thermodynamic observables in low temperatures and the weakening of the second order transition at the critical temperature. The third is the appearance of the nondiagonal elements in the static spin susceptibility.PACS numbers: 71.70.Ej,03.75.Hh,03.75.Mn The existence of low temperature excitonic collective states in bulk semiconductors has been speculated in the early 1960s.[1] The idea was that, due to the attractive interaction between the electron-hole pairs, excitons act like single bosons in low densities and consequently, they should condense in 3D at sufficiently low temperatures. The difference of the speculated excitonic Bose Einstein condensate (BEC) from the atomic BEC is that, due to the small exciton band mass (m x 0.07m e where m e is the bare electron mass) the condensation is expected to occur at much higher critical temperatures than the atomic BEC. One of the first experimental results were on bulk CuO 2 samples. [2,3] In the last 15 years however experimental efforts were primarily focused on coupled quantum wells (CQW). The main motivation there is that, spatially indirect excitons can have much longer lifetimes (in the order of 10µs) in the presence of an additional electric field applied perpendicular to the plane, in contrast with the bulk where lifetimes are on the order of ns. Recent reviews [4] with CQWs remark the evidence of a low temperature exciton condensate (EC) in the observations of large indirect exciton mobility and radiative decay rates, enhancements in exciton scattering rate, and the narrowing of the photoluminescense (PL) spectra. It is also suggested that there is room for different conclusions other than the excitonic BEC [4,5].Here we propose an alternative method to examine the EC by breaking the spin degeneracy of the electrons (e) and holes (h) via a spin-orbit coupling (SOC) of the Rashba[6] (RSOC) and the Dresselhaus [7] (DSOC) types. The RSOC is manipulated by the external electric (E)-field whereas the DSOC is known to be intrinsically present in zinc-blende structures [8]. There are major differerences between the SOC induced effects in the non-centrosymmetric superconductors and the semiconductor electron hole (e-h) CQWs. In the former the SOC is strong relative to the typical condensation energy, i.e. ∆ 0 < ∼ E so E F where E so and ∆ 0 are typical SOC and condensation energies [9] and E F is the Fermi energy; whereas in the latter E so < ∆ 0 E F [10]. It may thus seem that such a perturbative effect may not play a significant role in the thermodynamics of the latter case. However, in an otherwise spin degenerate EC, the SOC changes ...