Einstein-Podolsky-Rosen paradox and quantum steering in pulsed optomechanics

We describe how to generate an Einstein-Podolsky-Rosen (EPR) paradox between a mesoscopic mechanical oscillator and an optical pulse. We find two types of paradox, defined by whether it is the oscillator or the pulse that shows the effect Schrodinger called "steering". Only the oscillator paradox addresses the question of mesoscopic local reality for a massive system. In that case, EPR's "elements of reality" are defined for the oscillator, and it is these elements of reality that are falsified (if quantum mechanics is complete). For this sort of paradox, we show that a thermal barrier exists, meaning that a threshold level of pulse-oscillator interaction is required for a given thermal occupation n_0 of the oscillator. We find there is no equivalent thermal barrier for the entanglement of the pulse with the oscillator, nor for the EPR paradox that addresses the local reality of the optical system. Finally, we examine the possibility of an EPR paradox between two entangled oscillators. Our work highlights the asymmetrical effect of thermal noise on quantum nonlocality.Comment: 9 pages, 7 figure

Dynamical preparation of EPR entanglement in two-well Bose-Einstein condensates

We propose to generate Einstein-Podolsky-Rosen (EPR) entanglement between groups of atoms in a two-well Bose-Einstein condensate using a dynamical process similar to that employed in quantum optics. The local nonlinear S-wave scattering interaction has the effect of creating a spin squeezing at each well, while the tunneling, analogous to a beam splitter in optics, introduces an interference between these fields that results in an inter-well entanglement. We consider two internal modes at each well, so that the entanglement can be detected by measuring a reduction in the variances of the sums of local Schwinger spin observables. As is typical of continuous variable (CV) entanglement, the entanglement is predicted to increase with atom number, and becomes sufficiently strong at higher numbers of atoms that the EPR paradox and steering non-locality can be realized. The entanglement is predicted using an analytical approach and, for larger atom numbers, stochastic simulations based on truncated Wigner function. We find generally that strong tunnelling is favourable, and that entanglement persists and is even enhanced in the presence of realistic nonlinear losses.Comment: 15 pages, 19 figure

Dynamical Quantum Memories

We propose a dynamical approach to quantum memories using an oscillator-cavity model. This overcomes the known difficulties of achieving high quantum input-output fidelity with storage times long compared to the input signal duration. We use a generic model of the memory response, which is applicable to any linear storage medium ranging from a superconducting device to an atomic medium. The temporal switching or gating of the device may either be through a control field changing the coupling, or through a variable detuning approach, as in more recent quantum memory experiments. An exact calculation of the temporal memory response to an external input is carried out. This shows that there is a mode-matching criterion which determines the optimum input and output mode shape. This optimum pulse shape can be modified by changing the gate characteristics. In addition, there is a critical coupling between the atoms and the cavity that allows high fidelity in the presence of long storage times. The quantum fidelity is calculated both for the coherent state protocol, and for a completely arbitrary input state with a bounded total photon number. We show how a dynamical quantum memory can surpass the relevant classical memory bound, while retaining a relatively long storage time.Comment: 16 pages, 9 figure

Unified criteria for multipartite quantum nonlocality

Wiseman and co-workers (Phys. Rev. Lett. 98, 140402, 2007) proposed a distinction between the nonlocality classes of Bell's nonlocality, steering and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.Comment: V2: corrected image display; V3: substantial changes including new proofs, arguments, and result

EPR entanglement strategies in two-well BEC

Criteria suitable for measuring entanglement between two different potential wells in a Bose- Einstein condensation (BEC) are evaluated. We show how to generate the required entanglement, utilizing either an adiabatic two-mode or dynamic four-mode interaction strategy, with techniques that take advantage of s-wave scattering interactions to provide the nonlinear coupling. The dynamic entanglement method results in an entanglement signature with spatially separated detectors, as in the Einstein-Podolsky-Rosen (EPR) paradox.Comment: 4 pages, 4 figure

Bell inequalities for Continuous-Variable Measurements

Tests of local hidden variable theories using measurements with continuous variable (CV) outcomes are developed, and a comparison of different methods is presented. As examples, we focus on multipartite entangled GHZ and cluster states. We suggest a physical process that produces the states proposed here, and investigate experiments both with and without binning of the continuous variable. In the former case, the Mermin-Klyshko inequalities can be used directly. For unbinned outcomes, the moment-based CFRD inequalities are extended to functional inequalities by considering arbitrary functions of the measurements at each site. By optimising these functions, we obtain more robust violations of local hidden variable theories than with either binning or moments. Recent inequalities based on the algebra of quaternions and octonions are compared with these methods. Since the prime advantage of CV experiments is to provide a route to highly efficient detection via homodyne measurements, we analyse the effect of noise and detection losses in both binned and unbinned cases. The CV moment inequalities with an optimal function have greater robustness to both loss and noise. This could permit a loophole-free test of Bell inequalities.Comment: 17 pages, 6 figure