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Register a new userMulti-mode Entanglement is Detrimental to Lossy Optical Quantum Metrology
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Paul Knott MPhys BSc
Publication date
2014
fields
Physics
and research's language is
English
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In optical interferometry multi-mode entanglement is often assumed to be the driving force behind quantum enhanced measurements. Recent work has shown this assumption to be false: single mode quantum states perform just as well as their multi-mode entangled counterparts. We go beyond this to show that when photon losses occur - an inevitability in any realistic system - multi-mode entanglement is actually detrimental to obtaining quantum enhanced measurements. We specifically apply this idea to a superposition of coherent states, demonstrating that these states show a robustness to loss that allows them to significantly outperform their competitors in realistic systems. A practically viable measurement scheme is then presented that allows measurements close to the theoretical bound, even with loss. These results promote a new way of approaching optical quantum metrology using single-mode states that we expect to have great implications for the future.
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The study of optical parametric amplifiers (OPAs) has been successful in describing and creating nonclassical light for use in fields such as quantum metrology and quantum lithography [Agarwal, et al., J. Opt. Soc. Am. B, 24, 2 (2007)]. In this paper we present the theory of an OPA scheme utilizing an entangled state input. The scheme involves two identical OPAs seeded with the maximally path-entangled N00N state (|2,0>+|0,2>)/sqrt{2}. The stimulated amplification results in output state probability amplitudes that have a dependence on the number of photons in each mode, which differs greatly from two-mode squeezed vacuum. The output contains a family of entangled states directly applicable to quantum key distribution. Specific output states allow for the heralded creation of N=4 N00N states, which may be used for quantum lithography, to write sub-Rayleigh fringe patterns, and for quantum interferometry, to achieve Heisenberg-limited phase measurement sensitivity.
Two-mode interferometers, such as Michelson interferometer based on two spatial optical modes, lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. However, the experimental demonstration still remains elusive. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form $left(left|0rightrangle +left|Nrightrangle right)/sqrt{2}$ are generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as $sim N^{-0.94}$. A $9.1$~$mathrm{dB}$ enhancement of the precision over the SNL at $N=12$, which is only $1.7$~$mathrm{dB}$ away from the HL, is achieved. Our experimental architecture is hardware efficient and can be combined with the quantum error correction techniques to fight against decoherence, thus promises the quantum enhanced sensing in practical applications.
This thesis is mainly devoted to the study of the quantum properties of optical parametric oscillators (OPOs), which are nowadays the sources of the highest-quality quantum-correlated light, apart from fundamental tools in the classical-optics realm, allowing for the conversion of laser light into virtually all regions of the optical spectrum. Regarding its content, the thesis might seem a bit unusual, because two thirds of it are devoted to a self-contained (though dense) introduction to quantum optics, including the quantum physics of harmonic oscillators, the quantization of the electromagnetic field in an open optical cavity and the detection of its output light, as well as the derivation of the basic model and known properties of OPOs. Hence, all the original results of the thesis are contained in the last third, were it is proven that all OPOs can be understood as multi-mode devices whose quantum properties can be explained in terms of three basic phenomena: bifurcation squeezing, spontaneous symmetry breaking, and pump clamping, which are introduced through simple, yet realistic examples.
Quantum systems allow one to sense physical parameters beyond the reach of classical statistics---with resolutions greater than $1/N$, where $N$ is the number of constituent particles independently probing a parameter. In the canonical phase sensing scenario the emph{Heisenberg Limit} $1/N^{2}$ may be reached, which requires, as we show, both the relative size of the largest entangled block and the geometric measure of entanglement to be nonvanishing as $Ntoinfty$. Yet, we also demonstrate that in the asymptotic $N$ limit any precision scaling arbitrarily close to the Heisenberg Limit ($1/N^{2-varepsilon}$ with any $varepsilon>0$) may be attained, even though the system gradually becomes noisier and separable, so that both the above entanglement quantifiers asymptotically vanish. Our work shows that sufficiently large quantum systems achieve nearly optimal resolutions despite their relative amount of entanglement being arbitrarily small. In deriving our results, we establish the continuity relation of the quantum Fisher information evaluated for a phaselike parameter, which lets us link it directly to the geometry of quantum states, and hence naturally to the geometric measure of entanglement.
We analyze the role of entanglement among probes and with external ancillas in quantum metrology. In the absence of noise, it is known that unentangled sequential strategies can achieve the same Heisenberg scaling of entangled strategies and that external ancillas are useless. This changes in the presence of noise: here we prove that entangled strategies can have higher precision than unentangled ones and that the addition of passive external ancillas can also increase the precision. We analyze some specific noise models and use the results to conjecture a general hierarchy for quantum metrology strategies in the presence of noise.
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