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arXiv:1205.4585 · Physical Review A

Probabilistic phase-insensitive optical squeezer in compliance with causality

Christos N. Gagatsos, Evgueni Karpov, Nicolas J. Cerf

Published Jul 20, 2012• 10 citations
arXivHTMLPDF

Abstract

A non-trace-preserving map describing a probabilistic but heralded noiseless linear amplifier has recently been proposed and experimentally demonstrated. Here, we exhibit another remarkable feature of this peculiar transformation, namely its ability to serve as a universal single-mode squeezer regardless of the quadrature that is initially squeezed. Hence, it acts as a heralded phase-insensitive optical squeezer, conserving the signal-to-noise ratio just as a phase-sensitive optical amplifier but for all quadratures at the same time, which may offer interesting perspectives in quantum optical communications. Although this ability to squeeze all quadratures seemingly opens a way to instantaneous signaling by circumventing the quantum no-cloning theorem, we explain the subtle mechanism by which such a causality violation is forbidden, even on an heralded basis.

DOI
10.1103/physreva.86.012324

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A non-trace-preserving map describing a probabilistic but heralded noiseless linear amplifier has recently been proposed and experimentally demonstrated. Here, we exhibit another remarkable feature of this peculiar transformation, namely its ability to serve as a universal single-mode squeezer regardless of the quadrature that is initially squeezed. Hence, it acts as a heralded phase-insensitive optical squeezer, conserving the signal-to-noise ratio just as a phase-sensitive optical amplifier but for all quadratures at the same time, which may offer interesting perspectives in quantum optical communications. Although this ability to squeeze all quadratures seemingly opens a way to instantaneous signaling by circumventing the quantum no-cloning theorem, we explain the subtle mechanism by which such a causality violation is forbidden, even on an heralded basis.
A noiseless linear amplifier (NLA) can probabilistically amplify an optical state without the noise required by deterministic phase-insensitive amplification. We study a hybrid amplifier in which a finite-cutoff quantum-scissor NLA is placed between two single-mode squeezers. Analysis based on an ideal (infinite cutoff) NLA finds a gain enhancement from the squeezing. We explore the physics of this enhancement as the cutoff of the quantum scissors is increased. The low-cutoff sequence shows how this gain enhancement emerges from the truncated Fock space. Cutoff 3 is the lowest order at which the additional even- and odd-photon components can both contribute to gain enhancement, albeit with some skewing of the coefficients which reduces the fidelity. As the cutoff is increased the fidelity improves. However, unlike the ideal transformation, the finite-cutoff device depends on the phase of the coherent amplitude relative to the squeezing axes, with states aligned with the anti-squeezing requiring higher cutoffs to achieve high fidelity. We track behavior to high cutoffs and eventually see the performance predicted in the ideal theory emerge.
A process which strongly amplifies both quadrature amplitudes of an oscillatory signal necessarily adds noise. Alternatively, if the information in one quadrature is lost in phase-sensitive amplification, it is possible to completely reconstruct the other quadrature. Here we demonstrate such a nearly perfect phase-sensitive measurement using a cavity optomechanical scheme, characterized by an extremely small noise less than 0.2 quanta. The device also strongly squeezes microwave radiation by 8 dB below vacuum. A source of bright squeezed microwaves opens up applications in manipulations of quantum systems, and noiseless amplification can be used even at modest cryogenic temperatures.
The minimum resolvable signal in optical metrology and sensing applications is usually limited by the so-called standard quantum limit. One way to improve the signal-to-noise ratio is to use squeezed states of light. Squeezed light can be generated using different types of nonlinear interactions either in solid-state nonlinear crystals or in atomic systems. One way to generate squeezed light is to use a phase sensitive amplifier that will amplify one quadrature of the considered mode and deamplify the other one. We have recently shown that metastable helium vapor at room temperature can exhibit strong four-wave mixing effects and behave like a perfect phase sensitive amplifier when it is prepared in coherent population trapping situation. In this talk, we will present the application of this phase sensitive amplification to the generation of squeezed vacuum states of light and detail the performances and limitations of the system
An ideal phase-preserving linear amplifier is a deterministic device that adds to an input signal the minimal amount of noise consistent with the constraints imposed by quantum mechanics. A noiseless linear amplifier takes an input coherent state to an amplified coherent state, but only works part of the time. Such a device is actually better than noiseless, since the output has less noise than the amplified noise of the input coherent state; for this reason we refer to such devices as immaculate. Here we bound the working probabilities of probabilistic and approximate immaculate amplifiers and construct theoretical models that achieve some of these bounds. Our chief conclusions are the following: (i) The working probability of any phase-insensitive immaculate amplifier is very small in the phase-plane region where the device works with high fidelity; (ii) phase-sensitive immaculate amplifiers that work only on coherent states sparsely distributed on a phase-plane circle centered at the origin can have a reasonably high working probability.
The no-cloning theorem states that an unknown quantum state cannot be cloned exactly and deterministically due to the linearity of quantum mechanics. Associated with this theorem is the quantitative no-cloning limit that sets an upper bound to the quality of the generated clones. However, this limit can be circumvented by abandoning determinism and using probabilistic methods. Here, we report an experimental demonstration of probabilistic cloning of arbitrary coherent states that clearly surpasses the no-cloning limit. Our scheme is based on a hybrid linear amplifier that combines an ideal deterministic linear amplifier with a heralded measurement-based noiseless amplifier. We demonstrate the production of up to five clones with the fidelity of each clone clearly exceeding the corresponding no-cloning limit. Moreover, since successful cloning events are heralded, our scheme has the potential to be adopted in quantum repeater, teleportation and computing applications.
Due to the pervasive nature of decoherence, protection of quantum information during transmission is of critical importance for any quantum network. A linear amplifier that can enhance quantum signals stronger than their associated noise while preserving quantum coherence is therefore of great use. This seemingly unphysical amplifier property is achievable for a class of probabilistic amplifiers that does not work deterministically. Here we present a linear amplification scheme that realises this property for coherent states by combining a heralded measurement-based noiseless linear amplifier and a deterministic linear amplifier. The concatenation of two amplifiers introduces the flexibility that allows one to tune between the regimes of high-gain or high noise-reduction, and control the trade-off of these performances against a finite heralding probability. We demonstrate an amplification signal transfer coefficient of Ts>1\mathcal{T}_s > 1Ts​>1 with no statistical distortion of the output state. By partially relaxing the demand of output Gaussianity, we can obtain further improvement to achieve a Ts=2.55±0.08\mathcal{T}_s = 2.55 \pm 0.08Ts​=2.55±0.08. Our amplification scheme only relies on linear optics and post-selection algorithm. We discuss the potential of using this amplifier as a building block in extending the distance of quantum communication.