Photonic polarization gears for ultra-sensitive angular measurements

In the paper

“The right-hand side is the standard quantum limit, and can always be reached in the asymptotic limit of large νN (ref. 1).”

What the sources say

• Supported

  The introduction (p. 1) says that averaging a large number of independent measurements yields the standard quantum limit’s 1/√n scaling. The interferometry section (p. 5) likewise describes standard procedures in which the νN photons contribute independently and achieve SQL scaling of 1/√(νN). (LLM, conf=0.88)

  cites [1] Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011). source

In the paper

“Moreover, as N grows, N-photon entangled states become increasingly sensitive to losses, as the loss of a single photon is enough to destroy all the phase information11.”

What the sources say

• Partly supported

  On p. 1, the paper says that losing one photon destroys the phase information in a N00N state. On p. 3, it reports that N00N-state precision worsens at larger photon numbers, but also describes other states designed so that losing a photon does not completely destroy coherence. The claim overgeneralizes the single-photon result from N00N states to N-photon entangled states generally. (LLM, conf=0.88)

  cites [11] Dorner, U. et al. Optimal quantum phase estimation. Phys. Rev. Lett. 102, 040403 (2009). sourceExperimental — accuracy not yet measured

In the paper

“To our knowledge, this constitutes the highest precision per-particle reported so far47918.”

What the sources say

• Partly supported

  The paper’s Abstract (page unavailable) reports a four-photon phase measurement that beats the standard quantum limit and says earlier demonstrations had done so only with two photons. It does not establish that this was the highest precision per particle reported so far; it also notes that source and detector inefficiencies meant many photons passed through the interferometer without contributing to a detection event. (LLM, conf=0.78)

  cites [4] Nagata, T., Okamoto, R., O‘Brien, J. L., Sasaki, K. & Takeuchi, S. Beating the standard quantum limit with four-entangled photons. Science 316, 726–729 (2007). sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [7] Leibfried, D. et al. Creation of a six-atom ‘Schrödinger cat’ state. Nature 438, 639–642 (2005). source
• ?Could not verify

  The cited paper reports a 9.4-fold enhancement in magnetic-field sensitivity for its 10-spin state (Abstract, page unavailable). The passages found for “highest precision per-particle” and related terms do not establish that the citing authors’ result was the highest precision per particle reported so far. (LLM, conf=0.73)

  cites [9] Jones, J. A. et al. Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states. Science 324, 1166–1168 (2009). sourceExperimental — accuracy not yet measured

In the paper

“It has been proved that, in the presence of losses or other types of noise, no two-mode quantum state can beat the standard limit by more than just a constant factor in the limit of large N12131415.”

What the sources say

• Partly supported

  The Introduction (p. 1) proves that, for phase estimation with loss, quantum strategies retain the standard-limit 1/√N scaling as N grows and gain only a smaller multiplicative constant. The Model (p. 1) specifies a two-mode photon state. The paper does not establish the sentence’s extension to other types of noise. (LLM, conf=0.87)

  cites [12] Kołodyński, J. & Demkowicz-Dobrzański, R. Phase estimation without a priori phase knowledge in the presence of loss. Phys. Rev. A 82, 053804 (2010). sourceExperimental — accuracy not yet measured
• Partly supported

  The section on lossy optical interferometry (p. 4) says that, even with the best strategy, losses limit the asymptotic improvement over standard light sources to a constant factor. The paper also establishes this behavior for dephasing (p. 5), but its introduction (p. 1) says the limit is not known in general for noisy processes. The claim is therefore too broad if “other types of noise” means noise of any kind. (LLM, conf=0.86)

  cites [13] Escher, B., Matos Filho, R. L. & Davidovich, L. General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology. Nat. Phys. 7, 406–411 (2011). sourceExperimental — accuracy not yet measured
• Partly supported

  The discussion on p. 2 states that, for fixed nonzero photon loss, the upper bound on quantum Fisher information scales linearly with N, matching shot-noise scaling up to a constant factor. The paper studies losses in one or both modes and notes broader applications of dissipation (p. 4), but it does not establish this bound for every other type of noise. (LLM, conf=0.86)

  cites [14] Knysh, S., Smelyanskiy, V. N. & Durkin, G. A. Scaling laws for precision in quantum interferometry and bifurcation landscape of optimal state. Phys. Rev. A 83, 021804(R) (2011). sourceExperimental — accuracy not yet measured

In the paper

“The right-hand side is now the Heisenberg limit, which can always be reached in the asymptotic limit of large ν (ref. 1).”

What the sources say

• Supported

  In “Quantum parameter estimation for channels” (p. 4), the paper calls the right-hand term the Heisenberg bound and says that this threshold is asymptotically attainable for ν ≫ 1. “Applications in Quantum interferometry” (p. 5) likewise says its corresponding bound is achievable for any given N in the limit of large ν. (LLM, conf=0.92)

  cites [1] Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011). source

In the paper

“In addition, we demonstrated ultra-sensitive two-photon entangled probes tailored for different target estimations.”

In the paper

“Furthermore, in Supplementary Fig. S2 and Supplementary Note 2, we discuss a three-step adaptive protocol which permits efficient and unambiguous estimation of such θ even when it is a completely unknown rotation in the full [0, 2π] interval.”

In the paper

“Here we demonstrate NOON-like photonic states of m quanta of angular momentum up to m=100, in a setup that acts as a ‘photonic gear’, converting, for each photon, a mechanical rotation of an angle θ into an amplified rotation of the optical polarization by mθ, corresponding to a ‘super-resolving’ Malus’ law.”

In the paper

“Notably, rather than in an asymptotic limit, this precision was attained already for total photon numbers as small as νN ≈102 to 104.”

In the paper

“We demonstrate two-photon entangled states where each photon has a different total angular momentum, m1 and m2, with a maximum of m1+m2=18.”

In the paper

“In Supplementary Fig. S3, we show that the rotational sensitivity enhancement due to the photonic gears effect can also be achieved in the classical regime with an intense laser, making it immediately applicable to real-world optical measurements, which we will now briefly discuss.”

In the paper

“When these SAM–OAM superposition states are passed through a second q-plate, they are converted back into pure polarization states with zero OAM and a uniform polarization.”

In the paper

“We obtain a maximum enhancement over the polarization-only strategy by ≈55.”

In the paper

“The oscillation frequency ∝ m=(2q±1) highlights the improving angular resolution for increasing q.”

In the paper

“The SAM–OAM superposition states that we generate involve m=l+1 quanta of angular momentum ħ, oriented either parallel or anti-parallel to the propagation axis of each photon.”

In the paper

“Moreover, we combine the gear effect with the quantum enhancement due to entanglement, thus exploiting the advantages of both approaches.”

In the paper

“The probability that Alice and Bob both detect H-polarized photons in their local frames is then , showing ‘amplified’ polarization correlations.”

In the paper

“In our case, all curves show a visibility greater than 0.73.”

In the paper

“Here we demonstrate the preparation of single-photon NOON-like quantum states that are superpositions of eigenstates of light with opposite total angular momentum quantum numbers.”

In the paper

“In the regime of single-photon probes, a precision of has been demonstrated experimentally, with νN the total number of photons.”

In the paper

“Here we demonstrate NOON-like photonic states of m quanta of angular momentum up to m=100, in a setup that acts as a ‘photonic gear’, converting, for each photon, a mechanical rotation of an angle θ into an amplified rotation of the optical polarization by mθ, corresponding to a ‘super-resolving’ Malus’ law.”

In the paper

“This state corresponds to a uniform linear polarization, but with the polarization direction forming an angle mθ with respect to Bob’s H axis, resulting in the photonic gear effect.”

In the paper

“However, a relative rotation of the transmitting and reading stages by a given angle θ is converted into a rotation of the light optical polarization by the angle mθ, which in our case can be as high as 101θ.”

In the paper

“As shown in Fig. 3c,d, our estimation protocol gives an estimate which converges to the true value θ in a limited number of trials ν~300, where ν is the number of single photons sent through the system.”

In the paper

“In particular, the experimental comparison between the two-photon quantum case with and the single-photon case with shows that in the former case a quantum enhancement by a factor 2 is superimposed to the classical photonic gear effect.”

In the paper

“So, in this case, for θA=θB=θ, the system is metrologically equivalent to NOON-state probes for N=2 and .”

In the paper

“When θA=θB=θ, the system can model two photons travelling in the same mode, subject to the same rotation, and hence yield results analogous to the NOON-state case discussed above for N=2.”

In the paper

“This enhancement is not quantum but due exclusively to the coherent rotational sensitivity of high-order angular momentum eigenmodes.”

In the paper

“Moreover, the experimental state production and detection are exponentially more efficient than for N-photon entangled states.”

In the paper

“Remarkably, already for the scaling (6) becomes better than the best precision (2) attainable with polarization-only NOON states.”

In the paper

“The high ‘gear ratio’ m boosts the current state of the art of optical non-contact angular measurements by almost two orders of magnitude.”

In the paper

“For example, the method reported in Liu et al.31 combined with our photonic-gear enhancement is expected to achieve a maximal sensitivity of 10−6 degrees, or about 0.01 arcsec.”

What the sources say

• ?Not checked — no full text of the sourcecites [31] Liu, Z., Lin, D., Jiang, H. & Yin, C. Roll angle interferometer by means of wave plates. Sensors Actuat. A 104, 127–131 (2003). source

In the paper

“It is this ‘gear ratio’ m that gives rise to the angular sensitivity enhancement.”

In the paper

“Such enhanced sensitivity can be seen as resulting from a ‘super-resolving’ interference between the two m-quanta angular momentum orientations appearing in the superposition, analogously to the two arms of the NOON-state interferometers.”

In the paper

“Although quantum-inspired, our approach is essentially classical because the enhancement does not come from quantum entanglement but results instead from the rotational sensitivity of large angular momentum eigenmodes.”

In the paper

“Furthermore, the photonic-gear strategies, both in the single-photon and classical regimes, greatly outperform the latter in realistic scenarios with large N.”

In the paper

“By exploiting such states in the single-photon regime, mechanical rotations can be measured with a precision scaling as m times the square root of the number of probes used.”

In the paper

“First, the production and detection of our SAM–OAM photon states is exponentially more efficient in N than those of NOON states.”

In the paper

“The precision attained in this case scales as mN times the square root of the number of probes used, the m originating from the gear ratio and the N (instead of the classical ) from quantum entanglement.”

In the paper

“When θA ≠ θB, one can instead align two distant frames remotely with two-photon probes produced by an unrelated common source, which sends one photon to each frame, by exploiting the quantum correlations among the two photons.”

In the paper

“For a linearly polarized input, the photonic states generated are superpositions of m=2q±1 quanta in opposite total angular momentum eigenmodes, where q is an integer or semi-integer ‘topological charge’ characterizing the device.”

In the paper

“In fact, our photonic gears can operate also in the fully classical regime, as described by coherent states.”