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arXiv:1308.4293 · Physical Review A

Asymmetric Gaussian harmonic steering in second-harmonic generation

M. K. Olsen

Published Nov 21, 2013• 65 citations
arXivHTMLPDF

Abstract

Intracavity second-harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterized, both theoretically and experimentally. We show that it can be a source of continuous-variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering.

DOI
10.1103/physreva.88.051802

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Intracavity second-harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterized, both theoretically and experimentally. We show that it can be a source of continuous-variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering.
Abstract With the rapid advancements in fields such as quantum entanglement distillation and quantum metrology, the limitations of Gaussian states in certain applications within quantum computing and information processing have come to the forefront. This has necessitated the development of methods to prepare non-Gaussian states, which exhibit negative Wigner values and are indispensable for enhancing the capabilities of quantum systems in these tasks. Wigner negativity, a renowned indicator of nonclassicality, is integral to quantum computing and the simulation of continuous-variable systems. It is also employed to discern non-Gaussian characteristics in optical fields. We demonstrate Gaussian Einstein–Podolsky–Rosen (EPR) steering between second and third harmonic generations prior to performing non-Gaussian operations. Inducing non-Gaussian attributes in the second harmonic is achieved by coupling the third harmonic with a vacuum state and subtracting photons via a beamsplitter. The Wigner stochastic trajectory approach is utilized to investigate the non-Gaussian properties of both the second and third harmonics. By varying the coupling parameter lambda λ and the ratio of nonlinear coupling constants κ 2 / κ 1 , symmetric and asymmetric non-Gaussian EPR steering can be observed. This proposed scheme for non-Gaussian EPR steering holds promise for applications in quantum computing and quantum information processing.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlation and its intrinsic asymmetry makes it distinct from entanglement and Bell nonlocality. We propose here a scheme for realizing one-way Gaussian steering of two electromagnetic fields mediated by a mechanical oscillator. We reveal that the steady-state one-way steering of the intracavity and output fields is obtainable with different cavity losses or strong mechanical damping. The conditions for achieving this asymmetric steering are found, and it shows that the steering is robust against thermal mechanical fluctuations. The present scheme can realize hybrid microwave-optical asymmetric steering by optoelectromechanics. In addition, our results are generic and can also be applied to other three-mode parametrically coupled bosonic systems.
We show theoretically that two evanescently coupled χ(2)χ^{(2)}χ(2) second harmonic generators inside a Fabry-Perot cavity provide a tunable source of quadrature squeezed light, Einstein-Podolsky-Rosen correlations and quantum entanglement. Unlike systems using coupled downconverters, second harmonic generation has no oscillation threshhold, so that the entangled fields become macroscopically occupied as soon as the pumping fields are turned on. This system also gives two frequencies at which the entangled fields can have macroscopic intensity. We show how the entanglement properties can be controlled by adjusting the pumping, the coupling strengths and the cavity detunings.
We have explored quantum Einstein-Podolsky-Rosen steering in symmetric two-mode Gaussian states using Gaussian and non-Gaussian measurements. For Gaussian measurements, we show that steering between the output modes of a symmetric beam splitter is possible regardless of purity when a threshold input-state quadrature variance compression is achieved. Using the non-Gaussian operators introduced in Ji et al. [Sci. Rep. 6, 29729 (2016)] we show that non-Gaussian measurements can outperform Gaussian measurements for symmetrical states. We also analyze the possibility of asymmetric measurements setups made possible by non-Gaussian measurements and provide examples where such asymmetry is optimal for revealing steering.
Entanglement is a property of composite physical systems distinct from any classical description and therefore has fundamental significance in quantum theory. Although a great deal of progress has been made in understanding entanglement, there is still much unknown about this phenomenon and interest in the nature of entanglement alone continues to motivate research in this area. Moreover, a better understanding of entanglement inevitably leads to a deeper knowledge of physical processes in quantum systems. This thesis explores continuous-variable entanglement in many-body nonlinear bosonic systems with the overall aim of broadening our knowledge of entanglement, and in turn, the quantum optical systems under consideration. The secondary aim of this thesis is to further the development of entanglement as a resource for use in quantum information, communication or computing. After introducing some of the terminology and basics of entanglement theory (Chapter 1), we then provide a brief review of the main theoretical tools employed throughout this thesis (Chapter 2). We begin our investigations of entanglement by considering an evanescently coupled pair of nonlinear crystals contained in a pumped optical cavity (Chapter 3). This two-mode system is known as the intracavity Kerr nonlinear coupler and it is the output beams emerging from the cavity that provide a source of continuous-variable entangled states. Within this framework, we examine the concept of steering, a term introduced by Schr{\o}dinger to generalize the effect described by the Einstein-Podolsky-Rosen paradox. In particular, we investigate bipartite asymmetric steering. This is an effect whereby an inseparable bipartite system can be found to be described by either quantum mechanics or local hidden variable theories, depending on which one of Alice or Bob makes the required measurements. We show that, even with an inseparable bipartite system, situations can arise where Gaussian measurements on one half are not sufficient to answer the fundamental question of which theory gives an adequate description and the whole system must be considered. We predict that asymmetric steering should arise in experiments using the intracavity nonlinear coupler, at least in the case where Alice and Bob can only make Gaussian measurements. We continue our investigations of nonlinear quantum optical systems and entanglement by studying an experimentally feasible intra-cavity coupled down-conversion scheme that makes use of concurrent nonlinearities (Chapter 4). From a theoretical perspective, we demonstrate that this scheme gives rise to a set of continuous-variable multipartite entangled output beams. Specifically, we verify that genuine quadripartite entanglement is present in this system by calculating the output fluctuation spectra and then considering violations of multipartite entanglement inequalities. The entanglement characteristics both above and below the oscillation threshold of the cavity are considered. Finally, we build on these studies of quadripartite entanglement and examine a modified intra-cavity concurrent down-conversion scheme (Chapter 5). We analyze the feasibility and potential of this scheme for generating continuous-variable cluster states. Cluster states have been proposed as a resource state for continuous-variable one-way quantum computing. We demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. We find that above the oscillation threshold, the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. We also investigate squeezed joint operators, which must approach zero in the limit of large squeezing if the cluster state defining relation is to be satisfied. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity and even depletion alone inhibits cluster state formation.
Abstract Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein–Podolsky–Rosen steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.