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arXiv:1212.1309 · Verhandlungen der Deutschen Physikalischen Gesellschaft

Entangling photons via the quantum Zeno effect

Nicolai ten Brinke, Andreas Osterloh, Ralf Schützhold

Published Dec 6, 2012• 0 citations
arXivHTMLPDF

Abstract

The quantum Zeno effect describes the inhibition of quantum evolution by frequent measurements. Here, we propose a scheme for entangling two given photons based on this effect. We consider a linear-optics set-up with an absorber medium whose two-photon absorption rate $ξ_{2γ}$ exceeds the one-photon loss rate $ξ_{1γ}$. In order to reach an error probability $P_{\rm error}$, we need $ξ_{1γ}/ξ_{2γ}<2P_{\rm error}^2/π^2$, which is a factor of 64 better than previous approaches (e.g., by Franson et al). Since typical media have $ξ_{2γ}

DOI
10.48550/arxiv.1212.1309

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The quantum Zeno effect describes the inhibition of quantum evolution by frequent measurements. Here, we propose a scheme for entangling two given photons based on this effect. We consider a linear-optics set-up with an absorber medium whose two-photon absorption rate ξ2γξ_{2γ}ξ2γ​ exceeds the one-photon loss rate ξ1γξ_{1γ}ξ1γ​. In order to reach an error probability PerrorP_{\rm error}Perror​, we need ξ1γ/ξ2γ<2Perror2/π2ξ_{1γ}/ξ_{2γ}<2P_{\rm error}^2/π^2ξ1γ​/ξ2γ​<2Perror2​/π2, which is a factor of 64 better than previous approaches (e.g., by Franson et al). Since typical media have $ξ_{2γ}
We propose a scheme for entangling two photons via the quantum Zeno effect, which describes the inhibition of quantum evolution by frequent measurements and is based on the difference between summing amplitudes and probabilities. For a given error probability Perror{P}_{\mathrm{error}}Perror​, our scheme requires that the one-photon loss rate ${\ensuremath{\xi}}_{1\ensuremath{\gamma}}$ and the two-photon absorption rate ${\ensuremath{\xi}}_{2\ensuremath{\gamma}}$ in some medium satisfy ${\ensuremath{\xi}}_{1\ensuremath{\gamma}}/{\ensuremath{\xi}}_{2\ensuremath{\gamma}}=2{P}_{\mathrm{error}}^{2}/{\ensuremath{\pi}}^{2}$, which is significantly improved compared to previous approaches. Again based on the quantum Zeno effect, as well as coherent excitations, we present a possibility to fulfill this requirement in an otherwise linear optics setup.
The phenomenon of quantum interrogation allows one to optically detect the presence of an absorbing object, without the measuring light interacting with it. In an application of the quantum Zeno effect, the object inhibits the otherwise coherent evolution of the light, such that the probability that an interrogating photon is absorbed can in principle be arbitrarily small. We have implemented this technique, achieving efficiencies of up to 7373%73, and consequently exceeding the 5050%50 theoretical maximum of the original ``interaction-free'' measurement proposal. We have also predicted and experimentally verified a previously unsuspected dependence on loss.
In this work we theoretically consider quantum Zeno effect for entangled (correlated) quantum states. (Our physical systems and calculations are simpler than it is case in remarkable work on entanglement protection via Zeno effect by Maniscalco et all. But Maniscalco et all and our final conclusions are the same.) Firstly, we demonstrate well-known quantum Zeno effect by frequent decay detection for single, simple, two-level quantum system, with stable, ground quantum state and one non-stable, excited quantum state which can decay, by photon emission, in the ground state. (In this case, by frequent decay detections, system stands in the excited state.) Further, we consider single photon with energy equivalent to energy difference between excited and ground energy level of mentioned system. After interaction with a half-silvered mirror, mentioned photon is in a quantum superposition of the reflected and transmitted quantum state or trajectory. Mentioned trajectories are directed toward two identical, but distant, mentioned simple two-level systems both of which are initially (before interaction with photon) in ground state. Immediately after interaction with photon (photon absorption) two two-level systems are described by entangled (correlated) quantum state ( (excited, ground) + (ground, excited) , symbolically). We prove that in this case, by frequent decay detections on both systems, mentioned two two-level systems are described by initial entangled (correlated) quantum state ( (excited, ground) +(ground, excited)).
Although two-photon absorption (TPA) is a nonlinear optical process, it is not typically considered a fundamental resource for optical quantum information processing (QIP). We have recently shown that TPA and the quantum Zeno effect can be used to make deterministic quantum logic devices (Zeno gates) from an otherwise linear optical system. In a Zeno gate, TPA is used to suppress the failure events that would normally occur in a linear optics device when multiple photons exit the device in the same optical mode. We have also recently shown that additional two-photon absorbing media can be used in a more conventional manner, along with a Zeno gate, to convert weak laser pulses into heralded single photon pulses. Sources of this kind could have many potential benefits; however, the use of detectors and classical switches could limit their scalability, and therefore their usefulness in larger QIP systems. Here we describe how TPA and Zeno gates alone could be used to make more efficient, and possibly scalable, single-photon sources. Because the Zeno gates also rely on TPA, we show that the only critical enabling resource for this approach is an efficient TPA medium.
We have previously shown that two-photon absorption and the quantum Zeno effect can be used to make deterministic quantum logic devices from an otherwise linear optical system. Here we show that this type of quantum Zeno gate can be used with additional two-photon absorbing media and weak laser pulses to make a heralded single photon source. A source of this kind is expected to have a number of practical advantages that make it well suited for large-scale quantum-information-processing applications.
Quantum logic gates for photonic qubits can be implemented using the quantum Zeno effect based on strong two-photon absorption. The fidelity of quantum Zeno gates of this kind may be substantially reduced by photon loss. Heralding on those outcomes in which both of the logical qubits emerge from the Zeno gate can increase the fidelity at the expense of a limited success rate (P.M. Leung et al., Phys. Rev. A 74, 062325 (2006)). We analyze the performance of heralded quantum Zeno gates by solving Schrodinger's equation for a system of photons coupled to three-level atoms. This approach identifies several potential error sources that are not described by earlier models that assumed a fixed rate of single-photon loss and two-photon absorption.