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arXiv:2106.09273 · Physical Review Letters

Photonic Angular Superresolution Using Twisted N00N States

Markus Hiekkamäki, Frédéric Bouchard, Robert Fickler

Published Dec 23, 2021• 53 citations
arXivHTMLPDF

Abstract

The increased phase sensitivity of N00N states has been used in many experiments, often involving photon paths or polarization. Here we experimentally combine the phase sensitivity of N00N states with the orbital angular momentum (OAM) of photons up to 100 ℏ, to resolve rotations of a light field around its optical axis. The results show that both a higher photon number and larger OAM increase the resolution and achievable sensitivity. The presented method opens a viable path to unconditional angular supersensitivity and accessible generation of N00N states between any transverse light fields.

DOI
10.1103/physrevlett.127.263601

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The increased phase sensitivity of N00N states has been used in many experiments, often involving photon paths or polarization. Here we experimentally combine the phase sensitivity of N00N states with the orbital angular momentum (OAM) of photons up to 100 ℏ, to resolve rotations of a light field around its optical axis. The results show that both a higher photon number and larger OAM increase the resolution and achievable sensitivity. The presented method opens a viable path to unconditional angular supersensitivity and accessible generation of N00N states between any transverse light fields.
Photonic N00N-states, i.e. states of light where N photons are in an extremal superposition between two orthogonal states 12(∣N,0⟩+∣0,N⟩)\frac{1}{{\sqrt 2 }}\left({\left| {N,0} \right\rangle + \left| {0,N} \right\rangle }\right)2​1​(∣N,0⟩+∣0,N⟩) , have an increased phase-sensitivity in comparison to their classical counterparts. This phase sensitivity has been harnessed in multiple proof-of-principle experiments with one implementation even showing this advantage unconditionally [1] . Using the increased phase sensitivity, that quantum states of light offer, in conjunction with the increased angular sensitivity of states with large orbital angular momentum (OAM) [2] , has been the target of theoretical studies [3] as well experiments utilizing squeezed states [4] and entangled photon pairs [5] . Until recently however [6] , a reliable way of generating two-photon OAM N00N-states, in a single beam-line and for arbitrary OAM-values, had not been demonstrated.
We show that the use of path-entangled states of photons, having nonzero orbital angular momentum (OAM), increases the resolution and sensitivity of angular-displacement measurements performed using an interferometer. In the ideal case of maximally path-entangled states, the resolution of angular-displacement measurements increases by a factor of Nl\mathit{Nl}Nl, while the uncertainty in the measurement of angular displacements scales as 1/Nl1/\mathit{Nl}1/Nl, where NNN is the number of entangled photons, half of which carry, on average, an OAM of $+l\ensuremath{\hbar}$ per photon and the other half carry an OAM of $\ensuremath{-}l\ensuremath{\hbar}$ per photon. We analyze measurement schemes for two- and four-photon entangled states produced by parametric down-conversion and, by employing a 4$\ifmmode\times\else\texttimes\fi{}$4 matrix formalism to study the propagation of entangled OAM modes, obtain explicit expressions for the resolution and sensitivity in these schemes. These results constitute an improvement over what could be obtained with NNN nonentangled photons carrying an orbital angular momentum of $|l|\ensuremath{\hbar}$ per photon.
Photons with a twisted phase front carry a quantized amount of orbital angular momentum (OAM) and have become important in various fields of optics, such as quantum and classical information science or optical tweezers. Because no upper limit on the OAM content per photon is known, they are also interesting systems to experimentally challenge quantum mechanical prediction for high quantum numbers. Here, we take advantage of a recently developed technique to imprint unprecedented high values of OAM, namely spiral phase mirrors, to generate photons with more than 10,000 quanta of OAM. Moreover, we demonstrate quantum entanglement between these large OAM quanta of one photon and the polarization of its partner photon. To our knowledge, this corresponds to entanglement with the largest quantum number that has been demonstrated in an experiment. The results may also open novel ways to couple single photons to massive objects, enhance angular resolution, and highlight OAM as a promising way to increase the information capacity of a single photon.
Photon orbital angular momentum has led to many novel insights and applications in quantum measurement. Photon orbital angular momentum can increase the resolution and sensitivity of angular rotation measurement. However, quantum measurement strategy can further surpass this limit and improve the resolution of angular rotation measurement. This Letter proposes and demonstrates a parity measurement method in angular rotation measurement scheme for the first time. Parity measurement can make the resolution superior to the limit of the existing method. The sensitivity can be improved with higher orbital angular momentum photons. Moreover, this Letter gives a detailed discussion of the change of resolution and sensitivity in the presence of photon loss.
Photons are an ideal candidate for encoding both classical and quantum information. Besides spin angular momentum associated with circular polarization, single photon can also carry other fundamentally new degree of freedom of orbital angular momentum related to the spiral phase structure of light. The key significance of orbital angular momentum lies in its potential in realizing a high-dimensional Hilbert space and in encoding a high-dimensional quantum information. Since Allen et al. [Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185] recognized the physical reality of photon orbital angular momentum in 1992, rapidly growing interest has been aroused in orbital angular momentum (OAM) from both classical and quantum points of view. Here we present an overall review on the high-order orbital angular momentum of photon, including its preparation and manipulation based on some specific techniques and also its applications. The spatial light modulator is a commercial device that has been widely employed to generate the OAM beams. We make and identify the optical OAM superposition with very high quantum numbers up to l=360. Recently, the metallic spiral phase mirrors were also developed to produce high-order OAM beams up to l=5050. In addition, the Q-plates made of anisotropic and inhomogeneous liquid crystals were invented to generate high-order OAM beams in a polarization-controllable manner, and the OAM superposition of l=± 50 were achieved. Owing to high rotational symmetry, these high OAM beams have been found to have more and more important applications in the fields of high-sensitivity sensing and high-precision measurements. Two fascinating examples are discussed in detail. The first example is that the research group led by Prof. Zeilinger has prepared and observed the quantum entanglement of high orbital angular momenta up to l=±300 by the technique of polarization-OAM entanglement swapping, and they demonstrated that the angular resolution could be significantly improved by a factor of l. Their result was the first step for entangling and twisting even macroscopic, spatially separated objects in two different directions. The second example is that the research group led by Prof. Padgett has demonstrated an elegant experiment of rotational Doppler effects for visible light with l=±20 OAM superposition. They showed that a spinning object with an optically rough surface might induce a Doppler effect in light reflected from the direction parallel to the rotation axis, and the frequency shift was proportional to both the disk's angular speed and the optical OAM. The potential applications in noncontact measurement of angular speed and in significant improvement of angular resolution for remote sensing will be particularly fascinating.
Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM), and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper limit on how many quanta of OAM a single photon can carry, it is possible to create entanglement between two particles with an arbitrarily high difference in quantum number. By transferring polarization entanglement to OAM with an interferometric scheme, we generate and verify entanglement between two photons differing by 600 in quantum number. The only restrictive factors toward higher numbers are current technical limitations. We also experimentally demonstrate that the entanglement of very high OAM can improve the sensitivity of angular resolution in remote sensing.