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arXiv:1808.07204 · Journal of Physics B Atomic Molecular and Optical Physics

Generating robust entanglement via quantum feedback

Kensuke Gallock‐Yoshimura, Naoki Yamamoto

Published Jan 23, 2019• 9 citations
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Abstract

Abstract Generating entangled states is one of the most important tasks in quantum information technology. However, in reality any entanglement generator must contain some characteristic uncertainty, and as a result the produced entangled state becomes an undesirable mixed state. This paper develops a coherent feedback control scheme that suppresses the characteristic uncertainty of a typical entanglement generator (the non-degenerate optical parametric oscillator) for producing robust Gaussian entangled states. In particular, we examine a two-mode squeezed state and Gaussian four-mode cluster states to demonstrate the effectiveness of the proposed control method.

DOI
10.1088/1361-6455/ab00c3

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Abstract Generating entangled states is one of the most important tasks in quantum information technology. However, in reality any entanglement generator must contain some characteristic uncertainty, and as a result the produced entangled state becomes an undesirable mixed state. This paper develops a coherent feedback control scheme that suppresses the characteristic uncertainty of a typical entanglement generator (the non-degenerate optical parametric oscillator) for producing robust Gaussian entangled states. In particular, we examine a two-mode squeezed state and Gaussian four-mode cluster states to demonstrate the effectiveness of the proposed control method.
Non-Gaussian continuous-variable states play a central role both in the foundations of quantum theory and for emergent quantum technologies. In particular, ``cat states,'' i.e., two-component macroscopic quantum superpositions, embody quantum coherence in an accessible way and can be harnessed for fundamental tests and quantum information tasks alike. Degenerate optical parametric oscillators can naturally produce single-mode cat states and thus represent a promising platform for their realization and harnessing. We show that a dissipative coupling between degenerate optical parametric oscillators extends this to two-mode entangled cat states, i.e., two-mode entangled cat states are naturally produced under such dissipative coupling. While overcoming single-photon loss still represents a major challenge towards the realization of sufficiently pure single-mode cat states in degenerate optical parametric oscillators, we show that the generation of two-mode entangled cat states under such dissipative coupling can then be achieved without additional hurdles. We numerically explore the parameter regime for the successful generation of transient two-mode entangled cat states in two dissipatively coupled degenerate optical parametric oscillators. To certify the cat-state entanglement, we employ a tailored, variance-based entanglement criterion, which can robustly detect cat-state entanglement under realistic conditions.
The non-measurement based coherent feedback control (CFC) is a control method without introducing any backaction noise into the controlled system, thus is specially suitable to manipulate various quantum optical systems for preparing nonclassical states of light. By simply tuning the transmissivity of an optical controller in a CFC loop attached to a non-degenerate optical parametric amplifier (NOPA), the quantum entanglement degree of the output optical entangled state of the system is improved. At the same time, the threshold pump power of the NOPA is reduced also. The experimental results are in reasonable agreement with the theoretical expectation.
We propose a scheme to manipulate entanglement and the direction of asymmetric Einstein-Podolsky-Rosen (EPR) steering between two interacting bosonic modes in a nonlinear optical apparatus, in which a pumped Fabry-P\'erot cavity system containing two nonlinear waveguides is coupled to two feedback loops. It is found that Markovian feedback plays a key role in controlling both entanglement and EPR steering, the maximal entanglement can only be achieved through two symmetric feedback loops, while one-way EPR steering can only occur when both asymmetric feedback loops and an unbalanced beam-splitter are satisfied simultaneously. Furthermore, in terms of an unequal beam-splitter and two different feedback loops, it is demonstrated that the directionality and extent of the asymmetric EPR steering can be readily controlled under certain conditions. A simple and sufficient condition is also revealed for generating two-way EPR steering. Moreover, the entanglement and EPR steering can be effectively enhanced by performing Markovian feedback. In addition, By choosing appropriate feedback strengths, two cavity modes can be driven into a pure two-mode squeezed vacuum state rather than a mixed two-mode Gaussian entangled state or a pure entangled dark state. We hope the proposed scheme will enhance our understanding of the fundamental asymmetry of EPR steering, and it may have potential applications in quantum computation and quantum communication.
Quantum control theory is a rapidly evolving research field, which has developed over the last three decades. Quantum optics has practical importance in quantum technology and provides a promising means of implementing quantum information and computing device. \nIn quantum control, it is difficult to acquire information about quantum states without destroying them since microscopic quantum systems have many unique characteristics such as entanglement and coherence which do not occur in classical mechanical system. Therefore, \nthe Lyapunov-based control methodology is used to first construct an artificial closed-loop controller and then an open-loop law is derived by simulation of the artificial closed-loop system. \n \nThis work considers the stabilization of laser cavity as the main integral part of quantum optical systems through squeezing the output beam of the cavity. As a comprehensive example of this type of system, quantum optomechanical sensors are investigated. To this end, a nonlinear model \nof quantum optomechanical sensors is first extended incorporating various noises. Then, linear quadratic Gaussian (LQG) control method is used to tackle the problem of mode-squeezing in optomechanical sensors. \nCoherent feedback quantum control is synthesized by incorporating both shot noise and back-action noise to attenuate the output noise well below the shot noise level (Two waves are said to be coherent if they have a constant relative phase). In the second phase of this work, due to entanglement of the system with critical uncertainties and technical limitations such as laser noise and detector imprecision, robust H [infinity] method is employed for the robust stabilization and robust performance of the system in practice. In H [infinity] methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this. The effectiveness of the proposed control strategy in squeezing the cavity output beam is demonstrated by simulation.
Continuous measurement and feedback hold tremendous potential for producing non-Gaussian quantum states that are useful for quantum communication and computation. We present a new feedback scheme to deterministically produce quantum non-Gaussian states from linear optical elements and feedback. In our scheme, measurement outcomes are used in two different ways. One implements a multiplicative feedback control which produces nonlinear effects in the system. The other stabilizes the system to produce a desired state deterministically. A design example of the multi-loop feedback structure is demonstrated for the deterministic generation of Schrodinger-cat states as the practical use of quantum feedback control.
We investigate the enhancement of the intracavity entanglement of a self-phase-locked type-II nondegenerate optical parameter oscillator (SPL NOPO) via homodyne-mediated quantum feedback. It is found that the feedback can effectively enhance the squeezing, entanglement, and purity of the two-mode field in the SPL NOPO. Especially for an ordinary NOPO, our feedback scheme can simulate a standard two-mode squeezed vacuum environment and a pure steady two-mode squeezed vacuum cavity field can be generated, different from the scheme proposed by Mancini [Phys. Rev. A 73, 010304(R) (2006)] in which only a mixed two-mode entangled state is generated.