Environment induced entanglement in many-body mesoscopic systems

We show that two, non interacting, infinitely long spin chains can become globally entangled at the mesoscopic level of their fluctuation operators through a purely noisy microscopic mechanism induced by the presence of a common heat bath. By focusing on a suitable class of mesoscopic observables, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of the dissipation strength and bath temperature. The presence of an external environment, typically a heat bath, modifies the dynamics of quantum systems in interaction with it, leading in general to loss of quantum correlations due to decohering and mixing-enhancing effects [1]. Nevertheless, it has also been established that suitable environments can enhance quantum entanglement instead of destroying it [2]. This mechanism of environment induced entanglement generation has been extensively studied for systems made of few qubits or oscillator modes [3], and specific protocols have been proposed able to prepare predefined entangled states via the action of suitably engi-neered environments [4]. Instead, in this paper, we study the possibility that entanglement be created through a purely noisy mechanism in many-body systems. In a quantum system made of a large number N of constituents, accessible observables are collective ones, i.e. those involving the degrees of freedom of all its elementary parts. For these “macroscopic ” observables, one usually expects that quantum effects fade away as N becomes large, even more so when the many-body system is in contact with an external environment. This is surely the case for the so-called “mean field ” observables, i.e averages over the whole system of microscopic operators; these quantities scale as 1/N and as such behave as classical observables when the number of system constituents becomes large. 1 a