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arXiv:1206.3673

Demonstrating macroscopic entanglement based on Kerr non-linearities requires extreme phase resolution

Roohollah Ghobadi, Sadegh Raeisi, Christoph Simon

Published Jun 16, 2012• 2 citations
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Abstract

Entangled coherent states, which can in principle be created using strong Kerr non-linearities, allow the violation of Bell inequalities for very coarse-grained measurements. This seems to contradict a recent conjecture that observing quantum effects in macroscopic systems generally requires very precise measurements. However, here we show that both the creation of the required states and the required measurements rely on being able to control the phase of the necessary Kerr-nonlinearity based unitary operations with extreme precision. This lends support to the idea that there is a general principle that makes macroscopic quantum effects difficult to observe, even in the absence of decoherence.

DOI
10.48550/arxiv.1206.3673

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Entangled coherent states, which can in principle be created using strong Kerr non-linearities, allow the violation of Bell inequalities for very coarse-grained measurements. This seems to contradict a recent conjecture that observing quantum effects in macroscopic systems generally requires very precise measurements. However, here we show that both the creation of the required states and the required measurements rely on being able to control the phase of the necessary Kerr-nonlinearity based unitary operations with extreme precision. This lends support to the idea that there is a general principle that makes macroscopic quantum effects difficult to observe, even in the absence of decoherence.
It has recently been conjectured that detecting quantum effects such as superposition or entanglement for macroscopic systems always requires high measurement precision. Analyzing an apparent counter-example involving macroscopic coherent states and Kerr non-linearities, we find that while measurements with coarse outcomes can be sufficient, the phase control precision of the necessary non-linear operations has to increase with the size of the system. This suggests a refined conjecture that either the {\it outcome precision} or the {\it control precision} of the measurements has to increase with system size.
It has recently been conjectured that detecting quantum effects such as superposition or entanglement for macroscopic systems always requires high measurement precision. Analyzing an apparent counterexample involving macroscopic coherent states and Kerr or higher-order nonlinearities, we find that while measurements with coarse outcomes can be sufficient, the phase control precision of the necessary nonlinear operations has to increase with the size of the system. This suggests a refined conjecture that either the outcome precision or the control precision of the measurements has to increase with system size.
Glorious victories have been achieved when quantum theory (QT) is applied to microscopic systems. However, although there might be good reasons for us to believe that QT applies at the macroscopic level as well, to give a definite answer ”yes” there is still a long journey. If it does apply, a direct result is that it predicts highly counter-intuitive macroscopic quantum superpositions and entanglements, which we never experience in our daily lives. In this thesis we assume that QT applies to the macroscopic level, and try to find out why we never really observe macroscopic quantum effects. The thesis contains two projects, aiming at two reasons for the above problem. In the first project (Chapter 3 and 4), we show that the required resolution to observe macroscopic quantum effects increases with the size of the system, when both outcome precision and control precision are taken into account. This means that for really large quantum effects we need a very good measuring resolution to observe them, while what we usually do are coarse-grained measurements, whose resolutions are much lower. In the second project (Chapter 5), we try to deal with decoherence, another obstacle preventing us from observing macroscopic quantum effects. We propose to create and detect strong entanglement of micro-macro and macro-macro beams of photons with very weak cross Kerr nonlinearities that are obtainable by current technology. We analyze the entanglement under environmental decoherence with various methods, and show that strong entanglement can still be created and detected under decoherence. We hope that the above results will help to push the boundary of the realm of QT towards the macroscopic level.
We find that Bell's inequality can be significantly violated (up to Tsirelson's bound) with two-mode entangled coherent states using only homodyne measurements. This requires Kerr nonlinear interactions for local operations on the entangled coherent states. Our example is a demonstration of Bell-inequality violations using classical measurements. We conclude that entangled coherent states with coherent amplitudes as small as 0.8420.8420.842 are sufficient to produce such violations.
Macroscopic quantum effects are of fundamental interest because they help us to understand the quantum-classical boundary, and may also have important practical applications in long-range quantum communications. Specifically we analyze a macroscopic generalization of the Franson interferometer, where violations of Bell's inequality can be observed using phase entangled coherent states created using weak nonlinearities. Furthermore we want to understand how these states, and other macroscopic quantum states, can be applied to secure quantum communications. We find that Bell's inequality can be violated at ranges of roughly 400 km in optical fiber when various unambiguous state discrimination techniques are applied. In addition Monte Carlo simulations suggest that quantum communications schemes based on macroscopic quantum states and random unitary transformations can be potentially secure at long distances. Lastly, we calculate the feasibility of creating the weak nonlinearity needed for the experimental realization of these proposals using metastable xenon in a high finesse cavity. This research suggests that quantum states created using macroscopic coherent states and weak nonlinearities may be a realistic path towards the realization of secure long-range quantum communications.