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arXiv:1209.5925 · Physical Review A

Distributed entanglement generation between continuous-mode Gaussian fields with measurement-feedback enhancement

Hendra I. Nurdin, Naoki Yamamoto

Published Aug 29, 2012• 16 citations
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Abstract

This paper studies a scheme of two spatially distant oscillator systems that are connected by Gaussian fields and examines distributed entanglement generation between two continuous-mode output Gaussian fields that are radiated by the oscillators. It is demonstrated that using measurement-feedback control while a nonlocal effective entangling operation is on can help to enhance the Einstein-Podolski-Rosen--like entanglement between the output fields. The effect of propagation delays and losses in the fields interconnecting the two oscillators and the effect of other losses in the system are also considered. In particular, for a range of time delays the measurement-feedback controller is able to maintain stability of the closed-loop system and the entanglement enhancement, but the achievable enhancement is only over a smaller bandwidth that is commensurate with the length of the time delays.

DOI
10.1103/physreva.86.022337

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This paper studies a scheme of two spatially distant oscillator systems that are connected by Gaussian fields and examines distributed entanglement generation between two continuous-mode output Gaussian fields that are radiated by the oscillators. It is demonstrated that using measurement-feedback control while a nonlocal effective entangling operation is on can help to enhance the Einstein-Podolski-Rosen--like entanglement between the output fields. The effect of propagation delays and losses in the fields interconnecting the two oscillators and the effect of other losses in the system are also considered. In particular, for a range of time delays the measurement-feedback controller is able to maintain stability of the closed-loop system and the entanglement enhancement, but the achievable enhancement is only over a smaller bandwidth that is commensurate with the length of the time delays.
This paper studies a scheme of two spatially distant oscillator systems that are connected by Gaussian fields and examines distributed entanglement generation between two continuous-mode output Gaussian fields that are radiated by the oscillators. It is demonstrated that using measurement-feedback control while a non-local effective entangling operation is on can help to enhance the Einstein-Podolski-Rosen (EPR)-like entanglement between the output fields. The effect of propagation delays and losses in the fields interconnecting the two oscillators, and the effect of other losses in the system, are also considered. In particular, for a range of time delays the measurement feedback controller is able to maintain stability of the closed-loop system and the entanglement enhancement, but the achievable enhancement is only over a smaller bandwidth that is commensurate with the length of the time delays.
In this paper we show how Einstein-Podolski-Rosen (EPR)-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 shown that in ideal scenarios, in the absence and presence of transmission losses, the feedback connection is able to provide a moderate increase in the quality of entanglement while achieving this in a more efficient manner by consuming less power, compared to conventional distribution of entanglement using a single NOPA.
Recent work has shown that deploying two non-degenerate optical parametric amplifiers (NOPAs) separately at two distant parties in a coherent feedback loop generates stronger Einstein-Podolski-Rosen (EPR) entanglement between two propagating continuous-mode output fields than a single NOPA under same pump power, decay rate and transmission losses. This paper aims to investigate the stability and EPR entanglement of a dual-NOPA coherent feedback system under the effect of phase shifts in the transmission channel between two distant parties. It is shown that, in the presence of phase shifts, EPR entanglement worsens or can vanish, but can be improved to some extent in certain scenarios by adding a phase shifter at each output with a certain value of phase shift.
It has recently been shown that finding the optimal measurement on the environment for stationary linear quadratic Gaussian control problems is a semidefinite program. We apply this technique to the control of the Einstein-Podolsky-Rosen correlations between two bosonic modes interacting via a parametric Hamiltonian at steady state. The optimal measurement turns out to be nonlocal homodyne measurement---the outputs of the two modes must be combined before measurement. We also find the optimal local measurement and control technique. This gives the same degree of entanglement but a higher degree of purity than the local technique previously considered [S. Mancini, Phys. Rev. A 73, 010304(R) (2006)].
A study of an open nondegenerate parametric oscillator is presented below threshold in the undepleted pump regime with time-delayed coherent feedback. The figure of merit is the two-mode squeezing spectrum measuring the strength of continuous-variable Einstein-Podolsky-Rosen-type entanglement between the down-converted modes in the output field as a function of frequency. Exploring different areas of the parameter space reveals the possibility of significantly enhanced entanglement with tunable characteristic frequency. This is a result of the emerging dynamical features that are only accessible due to delayed feedback. The system is very sensitive to phase matching, which can be adjusted by various parameters of the system and the feedback loop. In this way, sharp, resonancelike features are obtained that show a level of robustness against extraneous losses.
This paper is concerned with linear quantum networks of NNN nondegenerate optical parametric amplifiers (NOPAs), with NNN up to 6, which are interconnected in a coherent feedback chain. Each network connects two communicating parties (Alice and Bob) over two transmission channels. In previous work we have shown that a dual-NOPA coherent feedback network generates better Einstein-Podolsky-Rosen (EPR) entanglement (i.e., more two-mode squeezing) between its two outgoing Gaussian fields than a single NOPA, when the same total pump power is consumed and the systems undergo the same transmission losses over the same distance. This paper aims to analyze stability, EPR entanglement between two outgoing fields of interest, and bipartite entanglement of two-mode Gaussian states of cavity modes of the NNN-NOPA networks under the effect of transmission and amplification losses, as well as the effect of time delays on the outgoing fields. It is numerically shown that, in the absence of losses and delays, the network with more NOPAs in the chain requires less total pump power to generate the same degree of EPR entanglement. Moreover, we report on the internal entanglement synchronization that occurs in the steady state between certain pairs of Gaussian oscillator modes inside the NOPA cavities of the networks.