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arXiv:1011.2833 · Physical Review A

Supersensitive measurement of angular displacements using entangled photons

Anand K. Jha, G. S. Agarwal, Robert W. Boyd

Published May 20, 2011• 85 citations

Abstract

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 $\mathit{Nl}$, while the uncertainty in the measurement of angular displacements scales as $1/\mathit{Nl}$, where $N$ 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 $N$ nonentangled photons carrying an orbital angular momentum of $|l|\ensuremath{\hbar}$ per photon.

DOI: 10.1103/physreva.83.053829

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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

\mathit{Nl}

, while the uncertainty in the measurement of angular displacements scales as

1/\mathit{Nl}

, where

N

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

N

nonentangled photons carrying an orbital angular momentum of

|l|\ensuremath{\hbar}

per photon.

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.

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.

The orbital angular momentum (OAM) carried by twisted photons provides a promising playground for high-dimensional quantum information processing. While Bell-state measurement is the cornerstone for various quantum information applications, the deterministic discrimination of the complete high-dimensional Bell states with linear optics remains relatively unexplored in the OAM state space. Here, we demonstrate a theoretical scheme for the complete four-dimensional OAM Bell-state measurement by using the single-photon hyperentangled state analyzer, in which the auxiliary two-dimensional polarization entanglement and two-dimensional path entanglement are utilized. Our scheme offers an alternative route toward enhancing the channel capacity in quantum communication and increasing the robustness against deleterious noise in practical experiments with twisted photons.

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.

Abstract We theoretically explore the angular rotation measurement sensitivity of SU(1,1) interferometers with a coherent beam and a vacuum beam input by using orbital angular momentum (OAM). Compared with the OAM in an SU(2) interferometer, the SU(1,1) interferometer employing homodyne detection can further surpass the angular rotation shot noise limit 1 2 l N and improve the resolution and sensitivity of angular rotation measurement. Two models are considered, one is that OAM is carried by a probe beam and the other one is a pump beam with the OAM. The sensitivity can be improved by higher OAM and nonlinear process with a large gain. The resolution can be enhanced in the case that the pump beam has OAM. Moreover, we present a brief discussion on the variation of resolution and sensitivity in the presence of photon loss.

Any practical experiment utilizing the innate

D

-dimensional entanglement of the orbital angular momentum (OAM) of photons is subject to the generation capacity of the entangled photon source and the modal capacity of the detection system. We report an experimental spontaneous parametric-down-conversion system able to generate and detect tunable high-dimensional OAM entanglement. By tuning the phase matching, we demonstrate a factor of 2 increase on the half-width of the OAM-correlation spectrum, from 10 to 20. In terms of quantum mutual information capacity, this is an increase from

3.18

to

4.95

bits/photon. Furthermore, we measure correlations in the conjugate variable, angular position, and obtain concurrence values

0.96

and

0.90

. The good entanglement measures in both OAM and angular position bases indicate bipartite,

D

-dimensional entanglement where

D

is tunable.