Entanglement concentration for two atomic ensembles using an effective atom-light beamsplitter

Abstract

Abstract. We present a protocol for increasing the entanglement between two entangled atomic ensembles based on applying an approximate atom-light beamsplitter transformation to both ensembles. The effective asymmetric atom-light beamsplitter is created via a double-pass quantum non-demolition interaction between polarized light and a spin polarized atomic ensemble, derived from the linearised dipole interaction. The entanglement concentration protocol itself uses the procrustean method, similar to that first devised for light by Browne et al [2003 Phys. Rev. A 67 062320] and includes photon counting after the interaction as the required non-Gaussian element. We calculate the output logarithmic negativity in this scheme and show that entanglement between macroscopic ensembles can be increased with probabilities comparable with those for the light scheme even if on-off detectors of low efficiency are used.

Entanglement concentration with quantum nondemolition Hamiltonians

“…That is, as the interaction strength decreases, it becomes more likely that just a single photon is subtracted from each mode of the two mode squeezed vacuum and these photons are then detected. As expected, this compares well to the case where beamsplitters are used in place of QND interactions, investigated numerically in [12] for light TMSV and in [11] for TMSVentangled atomic ensembles. After all, if the pure state resulting from a single photon subtraction in both modes of the entangled state is more entangled than the initial state, then it should not matter which interaction exactly is used to subtract the photons.…”

“…Conceivably, other interactions could be considered by modifying (10), such as double-pass schemes (see [11,30]). After the measurement, the total Wigner function of modes A and B is given by…”

“…On the theory side, Opartný et al [7] showed how beamsplitters and photon subtraction can be used to increase the entanglement in a two mode squeezed vacuum (TMSV) as part of a teleportation scheme. The distillation aspect of this was seized upon and improved [8][9][10][11] and a rigorous theoretical description was given by Kitagawa et al [12]. Experimentally, there have been some notable successes [13,14], including with non-Gaussian noise [15].…”

Fidelity Matters: The Birth of Entanglement in the Mixing of Gaussian States

“…The entangling power of bilinear interactions has been widely analyzed, either to optimize the generation of entanglement [23,24] or to find relations between their entanglement and purities [25] or teleportation fidelity [26,27].In this Letter we address bilinear, energy conserving, i.e., exchange, interactions described by Hamiltonians of the form H I = g(a † b + ab † ), where a and b are bosonic annihilation operators, [a, a † ] = 1 and [b, b † ] = 1, and g the coupling constant. Hamiltonians of this kind are suitable to describe very different kinds of quantum systems, such as, e.g., two light-mode in a beam splitter or a frequency converter, collective modes in a gases of cold atoms [28], atom-light nondemolition measurements [29], optomechanical oscillators [27,30], nanomechanical oscillators [31], and superconducting resonators [32], all of which are of interest for the quantum technology. Our analysis can be applied to all these systems and lead to very general results about the resources needed for Gaussian entanglement generation.The bilinear Hamiltonians H I generally describe the action of simple passive interactions and, in view of this simplicity, their fundamental quantum properties are often overlooked.…”

“…In this Letter we address bilinear, energy conserving, i.e., exchange, interactions described by Hamiltonians of the form H I = g(a † b + ab † ), where a and b are bosonic annihilation operators, [a, a † ] = 1 and [b, b † ] = 1, and g the coupling constant. Hamiltonians of this kind are suitable to describe very different kinds of quantum systems, such as, e.g., two light-mode in a beam splitter or a frequency converter, collective modes in a gases of cold atoms [28], atom-light nondemolition measurements [29], optomechanical oscillators [27,30], nanomechanical oscillators [31], and superconducting resonators [32], all of which are of interest for the quantum technology. Our analysis can be applied to all these systems and lead to very general results about the resources needed for Gaussian entanglement generation.…”