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Resolution in rotation measurements

Stephen M Barnett, Roberta Zambrini

Published Jan 1, 2005• 22 citations
OpenAlex

Abstract

Abstract. The limiting resolution in optical interferometry is set by the number of photons used, with the functional dependence determined by the state of light that is prepared. We consider the problem of measuring the rotation of a beam of light about an optical axis and show how the limiting resolution depends on the total number of quanta of orbital angular momentum carried by the light beam. 1

Related papers

Resolution in rotation measurements

Stephen M. Barnett, Roberta Zambrini

The limiting resolution in optical interferometry is set by the number of photons used, with the functional dependence determined by the state of light that is prepared. We consider the problem of measuring the rotation of a beam of light about an optical axis and show how the limiting resolution depends on the total number of quanta of orbital angular momentum carried by the light beam.

arXiv:quant-ph/0503224•Journal of Modern Optics•Feb 21, 2006•29 citations

Quantum entanglement of orbital angular momentum

Martin P. van Exter, E. R. Eliel, J. P. Woerdman

Introduction In this chapter, we will be concerned with entangled states of light. Historically, quantum states of light, i.e., photons, have played a dominant role in the experimental study of quantum entanglement. For instance, the first Bell tests and the first realizations of quantum teleportation were performed using two-dimensional polarization-entangled twophoton states [3]. From an experimental point of view these states are readily prepared and manipulated using conventional polarization optics. Recently, however, both theoretical and experimental efforts have shifted towards entanglement in more than two modes , which is often referred to as high-dimensional entanglement. This is much richer than two-dimensional entanglement, as is, for instance, reflected in stronger violations of various measures of nonlocality which reveal the complexity of high-dimensional Hilbert spaces [4–7]. Also, from an applications perspective, it promises a larger channel capacity [8, 9] and improved security for quantum communication [10, 11]. There are several ways to implement high-dimensional two-photon entanglement. One can exploit the temporal [12], frequency [13], or spatial [14–18] degrees of freedom of the optical field. A promising way to implement high-dimensional two-photon entanglement is to use the orbital-angular-momentum (OAM) degree of freedom of light. Light beams that carry OAM have a helical wavefront that spirals around the optical axis during propagation [19]. The winding number m , which characterizes the OAM eigenmodes, can adopt any integer value between −∞ and ∞; since all coaxial OAM modes are orthogonal they can thus span a very high-dimensional Hilbert space.

Cambridge University Press eBooks•Nov 8, 2012•2 citations

Ultra-sensitive and super-resolving angular rotation measurement based on photon orbital angular momentum using parity measurement

Zijing Zhang, Tianyuan Qiao, Kun Ma +4 more

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.

Optics Letters•Aug 9, 2016•11 citations

Resolution in image rotation measurements

Roberta Zambrini, Stephen Mark Barnett

Few years ago it was experimentally demonstrated how squeezed light can be used to enhance the resolution of measurements of small displacements in optical images, or beam displacements (Treps et al., 2002). In this work we discuss measurements of beam rotations about the optical axis and identify the factors limiting the resolution (Barnett et al., 2006).

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2007•0 citations

Supersensitive measurement of angular displacements using entangled photons

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

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.

arXiv:1011.2833•Physical Review A•May 20, 2011•85 citations

Experimental test of uncertainty relations for quantum mechanics on a circle

Jaroslav Řeháček, Zdeněk Bouchal, Radek Čelechovský +2 more

We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution. Intelligent states minimizing the uncertainty product under the constraint of a given uncertainty in angle or in angular momentum turn out to be given by Mathieu wave functions. We also discuss a number of physically feasible approximations to these optimal states. The theory is applied to the orbital angular momentum of a beam of photons and verified in an experiment that employs computer-controlled spatial light modulators at both the state preparation and analyzing stages.

arXiv:0712.0230•Physical Review A•Mar 24, 2008•33 citations
Abstract. The limiting resolution in optical interferometry is set by the number of photons used, with the functional dependence determined by the state of light that is prepared. We consider the problem of measuring the rotation of a beam of light about an optical axis and show how the limiting resolution depends on the total number of quanta of orbital angular momentum carried by the light beam. 1
Introduction In this chapter, we will be concerned with entangled states of light. Historically, quantum states of light, i.e., photons, have played a dominant role in the experimental study of quantum entanglement. For instance, the first Bell tests and the first realizations of quantum teleportation were performed using two-dimensional polarization-entangled twophoton states [3]. From an experimental point of view these states are readily prepared and manipulated using conventional polarization optics. Recently, however, both theoretical and experimental efforts have shifted towards entanglement in more than two modes , which is often referred to as high-dimensional entanglement. This is much richer than two-dimensional entanglement, as is, for instance, reflected in stronger violations of various measures of nonlocality which reveal the complexity of high-dimensional Hilbert spaces [4–7]. Also, from an applications perspective, it promises a larger channel capacity [8, 9] and improved security for quantum communication [10, 11]. There are several ways to implement high-dimensional two-photon entanglement. One can exploit the temporal [12], frequency [13], or spatial [14–18] degrees of freedom of the optical field. A promising way to implement high-dimensional two-photon entanglement is to use the orbital-angular-momentum (OAM) degree of freedom of light. Light beams that carry OAM have a helical wavefront that spirals around the optical axis during propagation [19]. The winding number m , which characterizes the OAM eigenmodes, can adopt any integer value between −∞ and ∞; since all coaxial OAM modes are orthogonal they can thus span a very high-dimensional Hilbert space.
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.
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.
We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution. Intelligent states minimizing the uncertainty product under the constraint of a given uncertainty in angle or in angular momentum turn out to be given by Mathieu wave functions. We also discuss a number of physically feasible approximations to these optimal states. The theory is applied to the orbital angular momentum of a beam of photons and verified in an experiment that employs computer-controlled spatial light modulators at both the state preparation and analyzing stages.