Engineering asymmetric steady-state Einstein-Podolsky-Rosen steering in macroscopic hybrid systems

Generation of quantum correlations between separate objects is of significance both in fundamental physics and in quantum networks. One important challenge is to create the directional "spooky action-at-a-distanc" effects that Schr\"{o}dinger called "steering" between two macroscopic and massive objects. Here, we analyze a generic scheme for generating steering correlations in cascaded hybrid systems in which two distant oscillators with effective masses of opposite signs are coupled to a unidirectional light field, a setup which is known to build up quantum correlations by means of quantum back-action evasion. The unidirectional coupling of the first to the second oscillator via the light field can be engineered to enhance steering in both directions and provides an active method for controlling the asymmetry of steering. We show that the resulting scheme can efficiently generate unconditional steady-state Einstein-Podolsky-Rosen steering between the two subsystems, even in the presence of thermal noise and optical losses. As a scenario of particular technological interest in quantum networks, we use our scheme to engineer enhanced steering from an untrusted node with limited tunability (in terms of interaction strength and type with the light field) to a trusted, highly tunable node, hence offering a path to implementing one-sided device-independent quantum tasks.Comment: 11 pages, 8 figure

Convergence of Adaptive Finite Element Approximations for Nonlinear Eigenvalue Problems

In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.Comment: 24 pages, 12 figure

On Neutralization of Charged Black Holes

For non-spinning, charged (Reissner–Nordström) black holes, the particles with an opposite sign of charge with respect to that of the black hole will be pulled into the black hole by the extra electromagnetic force. Such a hole will be quickly neutralized so that there should not exist significantly charged, non-spinning black holes in the universe. The case of spinning, charged (Kerr–Newmann, KN) black holes is more complicated. For a given initial position and initial velocity of the particle, an oppositely charged particle does not always more easily fall into the black hole than a neutral particle. The possible existence of a magnetosphere further complicate the picture. One therefore cannot straightforwardly conclude that a charged spinning black hole will be neutralized. In this paper, we make the first step to investigate the neutralization of KN black holes without introducing a magnetosphere. We track the particle trajectories under the influence of the curved space–time and the electromagnetic field carried by the spinning, charged black hole. A statistical method is used to investigate the neutralization problem. We find a universal dependence of the falling probability into the black hole on the charge of the test particle, with the oppositely charged particles having a higher probability of falling. We therefore conclude that charged, spinning black holes without a magnetosphere should be quickly neutralized, consistent with people’s intuition. The neutralization problem of KN black holes with a corotating force-free magnetosphere is subject to further studies

Role of thermal noise in tripartite quantum steering

The influence of thermal noise on bipartite and tripartite quantum steering induced by a short laser pulse in a hybrid three-mode optomechanical system is investigated. The calculation is carried out under the bad cavity limit, the adiabatic approximation of a slowly varying amplitude of the cavity mode, and with the assumption of driving the cavity mode with a blue detuned strong laser pulse. Under such conditions, explicit expressions of the bipartite and tripartite steering parameters are obtained, and the concept of collective tripartite quantum steering, recently introduced by He and Reid [Phys. Rev. Lett. 111, 250403 (2013)], is clearly explored. It is found that both bipartite and tripartite steering parameters are sensitive functions of the initial state of the modes and distinctly different steering behaviour could be observed depending on whether the modes were initially in a thermal state or not. We find that the initial thermal noise is more effective in destroying the bipartite rather than the tripartite steering which, on the other hand, can persist even for a large thermal noise. For the initial vacuum state of a steered mode, the tripartite steering exists over the entire interaction time even if the steering modes are in very noisy thermal states. When the steered mode is initially in a thermal state, it can be collectively steered by the other modes. There are thresholds for the average number of the thermal photons above which the existing tripartite steering appears as the collective steering. Finally, we point out that the collective steering may provide a resource in a hybrid quantum network for quantum secret sharing protocol.Comment: 13 pages, 9 figure