Coherent feedback enabled distributed generation of entanglement between propagating Gaussian fields

In this paper, we show how Einstein–Podolsky–Rosen-like entanglement between a pair of spatially separated propagating continuous-mode Gaussian fields can be generated via a coherent feedback loop that connects two spatially distant nondegenerate optical parametric amplifiers (NOPAs) over two transmission channels. In particular, the scheme generates entanglement in a distributed manner using spatially distributed resources. It is shown that similar to a single NOPA, the coherent feedback scheme has parameters that determine the achievable frequency-dependent two-mode squeezing and entanglement bandwidth between the pair of continuous-mode fields. It is also shown that in ideal scenarios, the feedback connection is able to yield an increase in the quality of the entanglement while consuming less power, compared to conventional distribution of entanglement using a single NOPA and a two-cascaded NOPA system. Furthermore, in contrast to the two conventional systems, under the same pump power, the coherent feedback system provides more entanglement in the presence of transmission losses, which indicates that the feedback scheme increases tolerance to transmission losses.

[1]  Xiaolong Su,et al.  Cascaded Entanglement Enhancement , 2012, 1201.1159.

[2]  Wolfgang Dür,et al.  Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication , 1998 .

[3]  Luc Jaulin,et al.  Applied Interval Computation: A New Approach for Time-Delays Systems Analysis , 2007 .

[4]  Ryan Hamerly,et al.  Advantages of coherent feedback for cooling quantum oscillators. , 2012, Physical review letters.

[5]  G. Milburn,et al.  Quantum Measurement and Control , 2009 .

[6]  Viacheslav P. Belavkin,et al.  Quantum Filtering and Optimal Control , 2008 .

[7]  Hideo Mabuchi,et al.  Squeezed light in an optical parametric oscillator network with coherent feedback quantum control. , 2013, Optics express.

[8]  Single cold atom as efficient stationary source of EPR-entangled light , 2006, quant-ph/0605231.

[9]  M. R. James,et al.  Squeezing Components in Linear Quantum Feedback Networks , 2009, 0906.4860.

[10]  Jean Jacques Loiseau,et al.  Applications of Time Delay Systems , 1984 .

[11]  Naoki Yamamoto,et al.  Experimental Demonstration of Coherent Feedback Control on Optical Field Squeezing , 2011, IEEE Transactions on Automatic Control.

[12]  H. Nurdin,et al.  Distributed entanglement generation between continuous-mode Gaussian fields with measurement-feedback enhancement , 2012, 1209.5925.

[13]  Matthew R. James,et al.  Quantum feedback networks and control: A brief survey , 2012, 1201.6020.

[14]  Silvania F. Pereira,et al.  Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification , 1992 .

[15]  Dirk Roose,et al.  Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL , 2002, TOMS.

[16]  Wim Michiels,et al.  Stability and Stabilization of Time-Delay Systems (Advances in Design & Control) (Advances in Design and Control) , 2007 .

[17]  Nicolas Gisin,et al.  Quantum repeaters based on atomic ensembles and linear optics , 2009, 0906.2699.

[18]  J. D. Franson,et al.  Quantum relays and noise suppression using linear optics , 2002 .

[19]  S. Braunstein,et al.  Quantum Information with Continuous Variables , 2004, quant-ph/0410100.

[20]  Wenbin He,et al.  Generation of broadband entangled light through cascading nondegenerate optical parametric amplifiers , 2007 .

[21]  S. Niculescu,et al.  Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach , 2007 .

[22]  Hideo Mabuchi,et al.  Coherent-feedback quantum control with a dynamic compensator , 2008, 0803.2007.

[23]  V. Belavkin,et al.  Quantum stochastics and information : statistics, filtering, and control : University of Nottingham, UK, 15-22 July 2006 , 2008 .

[24]  Collett,et al.  Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation. , 1985, Physical review. A, General physics.

[25]  Changde Xie,et al.  Coherent feedback control of multipartite quantum entanglement for optical fields , 2011 .

[26]  Maira Amezcua,et al.  Quantum Optics , 2012 .

[27]  P. Knight,et al.  Introductory quantum optics , 2004 .

[28]  Ryan Hamerly,et al.  Coherent controllers for optical-feedback cooling of quantum oscillators , 2012, 1206.2688.