## Polarization control of single photon quantum orbital angular momentum states

Optics Express, Vol. 17, Issue 21, pp. 18745-18759 (2009)

http://dx.doi.org/10.1364/OE.17.018745

Acrobat PDF (498 KB)

### Abstract

The orbital angular momentum of photons, being defined in an infinite-dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum of single photons and vice versa. All our schemes exploit a newly developed optical device, the so-called “q-plate”, which enables the manipulation of the photon orbital angular momentum driven by the polarization degree of freedom. By stacking several q-plates in a suitable sequence, one can also have access to higher-order angular momentum subspaces. In particular, we demonstrate the control of the orbital angular momentum *m* degree of freedom within the subspaces of |*m*|=2*ħ* and |*m*|=4*ħ* per photon.

© 2009 Optical Society of America

## 1. Introduction

17. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. **96**, 163905 (2006).
[CrossRef] [PubMed]

18. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. **103**, 013601 (2009).
[CrossRef] [PubMed]

*π*to a OAM subspace or vice versa, thus achieving a polarization-mediated manipulation of the OAM degree of freedom at the single photon level [18

18. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. **103**, 013601 (2009).
[CrossRef] [PubMed]

*m*and -

*m*, where

*m*denotes here the OAM per photon along the beam axis in units of

*ħ*. We will denote such a OAM subspace as

*o*

_{|m|}. In our previous work [18

18. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. **103**, 013601 (2009).
[CrossRef] [PubMed]

*π*) to OAM (

*o*

_{2}) and vice versa, for the simplest single-photon optical schemes based on the q-plate, and for the case of a two-photon state having non-classical correlations. In this paper, we extend our previous work in the following directions: (i) we complete the description and experimental characterization of the probabilistic quantum information transfer schemes

*π*↔

*o*

_{2}already synthetically presented in Ref. [18

**103**, 013601 (2009).
[CrossRef] [PubMed]

*o*

_{2}OAM space of a single photon, respectively from and to the polarization space

*π*that is ultimately used for writing in and reading out the information (i.e., we realize the double transfer

*π*→

*o*

_{2}→

*π*) [19

19. J. B. Gotte, K. OHolleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express **16**, 993–1006 (2008)
[CrossRef] [PubMed]

*π*→

*o*

_{4}(OAM |

*m*|=4) by means of a cascaded transfer

*π*→

*o*

_{2}→

*o*

_{4}, an accomplishment which represents the first step towards achieving control of a higher-dimensional qu-dit space encoded in a OAM subspace spanning several values of |

*m*|.

## 2. The q-plate

17. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. **96**, 163905 (2006).
[CrossRef] [PubMed]

*q*, which is determined by the (fixed) pattern of the optical axis. The birefringent retardation

*δ*must instead be uniform across the device. Q-plates working in the visible or near-infrared domain can be manufactured with nematic liquid crystals, by means of a suitable treatment of the containing substrates [17

17. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. **96**, 163905 (2006).
[CrossRef] [PubMed]

20. L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation,” Appl. Phys. Lett. **88**, 221102 (2006).
[CrossRef]

*δ*can be tuned either by mechanical compression (exploiting the elasticity of the spacers that fix the thickness of the liquid crystal cell) or by temperature control [21

21. E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. **94**, 231124 (2009).
[CrossRef]

*δ*=

*π*, a QP modifies the OAM state

*m*of a light beam crossing it, imposing a variation Δ

*m*=±2

*q*whose sign depends on the input polarization, positive for left-circular and negative for right-circular. The handedness of the output circular polarization is also inverted, i.e. the optical spin is flipped [22

22. G. F. Calvo and A. Picon, “Spin-induced angular momentum switching,” Opt. Lett. **32**, 838–840 (2007)
[CrossRef] [PubMed]

*q*=1 and

*δ*⋍

*π*. Hence, an input TEM

_{00}mode (having

*m*=0) is converted into a beam with

*m*=±2. In a single-photon quantum formalism, the QP implements the following quantum transformations on the single photon state:

*π*and |·〉

_{o}stand for the photon quantum state ‘kets’ in the polarization and OAM degrees of freedom, and

*L*and

*R*denote the left and right circular polarization states, respectively. In the following, whenever there is no risk of ambiguity, the subscripts

*π*and

*o*will be omitted for brevity.

**103**, 013601 (2009).
[CrossRef] [PubMed]

*m*does not completely define the transverse mode of the photon. A radial number is also necessary for spanning a complete basis, such as that of the Laguerre-Gauss modes or an equivalent one. The effect of the QP on this radial state and its role in the quantum information applications which will be considered further below will be now briefly discussed. To be general, let us consider the evolution of a generic photon wave-function (optical field)

*ψ*(

*r,φ,s*), expressed as a function of radial position

*r*, azimuthal angle

*φ*, and spin state

*s*=±1. For an initially azimuthally symmetric function

*ψ*

_{0}=

*u*(

_{s}f*r*) (e.g., a TEM

_{00}mode) with polarization state

*u*, the QP itself, in the limit of small thickness, introduces only a spin-dependent azimuthal phase-factor without altering significantly the radial profile (this is valid except for a very small region around the central optical vortex)[24

_{s}24. E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, “Hypergeometric-Gaussian Modes,” Opt. Lett. **32**, 3053–3055 (2007).
[CrossRef] [PubMed]

23. E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Light propagation in a birefringent plate with topological charge,” Opt. Lett. **34**, 1225–1227 (2009).
[CrossRef] [PubMed]

*m*=2

*sq*=±2

*q*. The phase factor

*e*appearing in this equation is the spatial wave-function associated to the OAM ket |

^{imφ}*m*〉

_{o}, i.e.,

*e*=〈

^{imφ}*φ*|

*m*〉

_{o}. Thus the QP itself introduces no coupling with the radial mode (this is actually valid for ideally thin QPs). However, the subsequent free propagation (in air or any homogeneous medium) generates a coupling between the azimuthal mode

*m*and the radial distribution. In particular, the following equation defines the free propagation effect:

*F*are given by

*A*

_{|m|}(

*k*) given by the standard Hankel transform of order |

*m*| of the initial radial mode

*f*(

*r*), i.e.,

*m*| and the radial profile develops during the propagation. This entanglement is detrimental in the quantum information applications, as it makes it more difficult to preserve a coherent qubit encoded in a OAM sub-space. This problem can be however minimized by introducing suitable imaging optics, so as to invert as much as possible the effect of propagation given in Eq. (4).

*o*

_{|m|}subspace of OAM, however, the above mentioned problem is essentially eliminated. Thanks to the symmetry between

*m*and -

*m*, the radial profile associated to these two states remain identical at all optical planes

*z*. Hence, a qubit superposition suffers no dephasing, as the radial part is identical and factorizes, so that the qubit is fully preserved in the propagation. Explicitly, from Eq. (4) one has

*m*| are manipulated simultaneously, a task which will be addressed in future work.

## 3. Experimental setup

**a, b, c, d**) that will be described in the following Sections, and is concerned with the OAM and polarization manipulations and with the final quantum-state tomography.

*H*〉 polarization state and then coupled to a single-mode fiber, which selects only a pure TEM

_{00}transverse mode, corresponding to OAM

_{m}=0. After the fiber output, two waveplates compensate (C) the polarization rotation introduced by the fiber. Then, a polarizing beams-plitter and a set of wave plates are used for setting the photon polarization to an arbitrary qubit state |

*φ*〉

_{π}. This concludes the first section of the apparatus. The one-photon quantum state at this point can be represented by the ket |

*φ*〉

_{π}|0〉

_{o}.

**a)**Quantum transferrer from polarization to OAM subspace |

*m*|=2, i.e.

*π*→

*o*

_{2}

**b)**Quantum transferrer from OAM subspace |

*m*|=2 to polarization, i.e.

*o*

_{2}→

*π*

**c)**Quantum bidirectional transfer polarization-OAM-polarization, i.e.

*π*→

*o*

_{2}→

*π*

**d)**Quantum transferrer from polarization to OAM subspace |

*m*|=4, i.e.

*π*→

*o*

_{4}

*m*=0 state |0〉

_{o}before detection. After the analysis, the signals have been detected by single photon counters SPCM and then sent to a coincidence box interfaced with a computer, for detecting and counting the coincidences of the photons and the trigger

*D*.

_{T}## 4. Holograms and OAM-polarization correspondence

*m*|, except of course for

*m*=0. This analogy is for example useful for retracing the quantum tomography procedure to the standard one for polarization [26

26. M. J. Padgett and J. Courtial, “New high-intensity source of polarization-entangled photon pairs,” Opt. Lett. **24**, 430 (1999).
[CrossRef]

9. N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Observation of quantum entanglement using spatial light modulators,” Phys. Rev. Lett. **93**, 053601 (2004).
[CrossRef] [PubMed]

*m*|〉 as the analog of the circular polarizations |

*L*〉 and |

*R*〉, as the latter ones are obviously the eigenstates of the spin angular momentum. To make the analogy more apparent, small-letter symbols |

*l*〉=|+|

*m*|〉 and |

*r*〉=|-|

*m*|〉 are introduced to refer to the OAM case, while the capital letters are used for the polarization. Following the same convention, the OAM equivalent of the two basis linear polarizations |

*H*〉 and |

*V*〉 are then defined as

*A*〉=(|

*H*〉+|

*V*〉)/√2 and |

*D*〉=(|

*H*〉-|

*V*〉)/√2, and the corresponding OAM states are defined analogously:

_{00}input mode is sent into the hologram and the first-order diffracted mode is used for output. The input beam must be precisely centered on the hologram pattern center. The output OAM quantum state obtained is shown in the upper corner of each hologram pattern in Fig. 2.

*m*=0 state, before detection. It can be shown that the amplitude of this output is then just proportional to the projection of the input state onto the OAM state shown in the upper corner of each hologram pattern, in Fig. 2 (except, possibly, for a sign inversion of m in the case of the upper row holograms).

## 5. Manipulation of orbital angular momentum in the subspace |m|=2

*q*=1) can be used for coupling the polarization subspace π with the OAM subspace

*o*

_{2}, spanned by the OAM eigenstates {|+2〉

_{o},|-2〉

_{o}}. In this Section, we present a complete detailed description of two optical schemes, which we introduced in [18

**103**, 013601 (2009).
[CrossRef] [PubMed]

**a**, transferrer

*π*→

*o*

_{2}), from OAM to polarization (setup

**b**,

*transferrer o*

_{2}→

*π*). Moreover, we tested also the combination of these two schemes, thus realizing the

*bidirectional transfer*polarization-OAM-polarization (setup c,

*π*→

*o*

_{2}→

*π*). The latter demonstration is equivalent to demonstrating quantum communication using OAM for encoding the message. In other words, the qubit is initially prepared in the polarization space, then passed to OAM in a transmitting unit (Alice), sent to a receiving unit (Bob), where it is transferred back to polarization for further processing or detection.

### 5.1. Transferrer polarization to OAM

_{o}indicates the TEM

_{00}mode. By passing it through a pair of suitably oriented quarter-waveplates (one with the optical axis parallel to the horizontal direction and the other at 45°), the photon state is rotated into the

*L,R*basis:

_{out}is obtained with a probability

*p*=50%, owing to the final polarizing step. Moreover, since we are using the {|

*H*〉, |

*V*〉} basis for the polarization encoding and the {|+2〉,|-2〉}={|

*l*〉, |

*r*〉} for the OAMone, the transfer is associated also with a rotation of the Poincaré sphere. The correspondence of the six orthogonal states on the polarization Poincaré sphere with the six final ones in the OAM sphere is given in Table 1.

*F*=〈

*ψ*|

*ρ*|

_{exp}*ψ*〉, where |

*ψ*〉 is the theoretical state to be compared to the experimental one. Hence in this experiment the average fidelity value between the experimental states and the theoretical predictions is

*F*=(97.7±0.2)%. The fidelities obtained for six different input states are shown in Table 1.

_{00}state can be coherently transferred to the OAM degree of freedom, thanks to the

*π*→

*o*

_{2}converter, giving rise to the preparation of a qubit in the orbital angular momentum. As the initial information has been stored in the orbital part of the qubit wave-function, new information can be stored in the polarization degree of freedom, allowing the transportation in a single photon of a higher amount, at least two qubits, of information.

### 5.2. Transferrer OAM to polarization

*o*

_{2}into the polarization space. We therefore consider as initial quantum state of the photon the following one:

_{in}in the q-plate device, and then rotating the output state by means of a pair of waveplates, we obtain the following state:

*m*=0 that is, the TEM

_{00}modes, will be efficiently transmitted. Of course, this implies that a probabilistic process is obtained again, since we discard all the contributions with

*m*≠0 (ideally, again

*p*=50%). After the fiber, the output state reads:

**b**. The input qubit in OAM is prepared using one of the six holograms shown in Fig. 2 (left box), as explained in the previous Section. The output state is analyzed by a standard polarization-state quantum tomography. The experimental results for three cases are shown in Fig. 4. We find again a good agreement with theory, with an average fidelity

*F*=(97.3±0.2)%, and the specific cases shown in Table 2.

### 5.3. Bidirectional transfer polarization-OAM-polarization

*F*=(95.9±0.2)%. Thus, there seems to be no significant problem to the combined use of many q-plates in a cascaded configuration. After the two q-plates the quantum efficiency of the conversion process, defined as the capability to convert a TEM

_{00}mode in a pure Laguerre-Gauss, is still around 80% (to optimize the efficiency, the q-plate birefringent retardations

*δ*were tuned by mechanical pressure).

### 5.4. Deterministic conversion processes

*deterministic*transferrer for both directions polarization-OAM and backward. This is obtained at the price of a slightly more complex optical layout, based on a q-plate and a Mach-Zehnder interferometer, shown in Fig. 5. The deterministic transferrer is bidirectional, and it converts the polarization in OAM (

*π*→

*o*

_{2}) if crossed in one way and the OAM in polarization (

*o*

_{2}→

*π*) if crossed in the opposite way.

*π*→

*o*

_{2}conversion. The initial state reads:

*L,R*basis, and then the QP is applied, so as to obtain the following state:

*A*〉, |

*D*〉, leading to

*α*|

*A*〉|+2〉+

*β*|

*D*〉|-2〉:

*V*-polarized one, a device acting as a Pauli’s operator

*σ*̃

_{z}is inserted that operates only on the OAM states. This operator can be for example realized by means of a Dove’s prism rotated at a

*π*/8 angle in the lab frame followed by another Dove’s prism rotated at zero angle, eventually with a set of compensating wave-plates for correcting possible polarization variations. Alternatively, one Dove’s prism can be put in one arm and the other in the other arm of the interferometer (to make it more balanced), both rotated by

*π*/16. At each reflection in a mirror or in the PBS (as well as in a Dove’s prism) the OAM is flipped (

*m*→-

*m*). However, the overall number of reflections is even in both paths, so we can ignore this effect (however, some care must be taken for computing the correct phases of each term).

*σ*〉

_{z}device will just change sign to the last term in Eq. (19). Therefore, the state in the interferometer becomes the following:

*H*〉 is also associated with one arm and |

*V*〉 with the other arm of the interferometer. After the exit PBS, these two states are again superimposed in the same mode and provide only a single output on one exit face of the PBS, which is the following:

*H*by a final half-wave plate rotated by 22.5°. Thus, the expected final state

27. We note that, although the optical layout is a Mach-Zehnder interferometer, the optical path phase difference between the two arms of the interferometer is only affecting the polarization state of the single output obtained after the final PBS, while it does not act on the PBS exit mode and on the OAM final state. The final polarization may therefore turn elliptical if this phase difference is not well controlled. However, the H polarization can be easily restored by suitable wave-plates, as long as it is uniform.

*o*

_{2}→

*π*, is obtained by simply reversing the direction of light propagation in the same setup. All the transformations are then reversed and provide the desired information transfer from OAM to polarization, again fully deterministically.

27. We note that, although the optical layout is a Mach-Zehnder interferometer, the optical path phase difference between the two arms of the interferometer is only affecting the polarization state of the single output obtained after the final PBS, while it does not act on the PBS exit mode and on the OAM final state. The final polarization may therefore turn elliptical if this phase difference is not well controlled. However, the H polarization can be easily restored by suitable wave-plates, as long as it is uniform.

28. M. Fiorentino and F. N. C. Wong, “Deterministic Controlled-NOT Gate For Single-Photon Two-Qubit Quantum Logic,” Phys. Rev. Lett. **93**, 070502 (2004).
[CrossRef] [PubMed]

## 6. Manipulation of orbital angular momentum in the subspace |m|=4

20. L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation,” Appl. Phys. Lett. **88**, 221102 (2006).
[CrossRef]

_{1}and QP

_{2}(both with

*q*=1). We demonstrate that it is possible to efficiently encode the quantum information in the OAM basis {|+4〉,|-4〉}, by exploiting the spin-orbit coupling in the q-plates. In order to analyze the orbital angular momentum with |

*m*|=4 we have adopted newly designed holograms, shown in Fig. 2 (box on the right).

_{00}mode and arbitrary polarization |

*φ*〉

_{π}=(

*α*|

*H*〉+

*β*|

*V*〉) is transformed by a pair of quarter-wave plates and QP

_{1}into the following one:

_{1}, so that we get:

_{2}and a polarizer leads to the final state:

## 7. Conclusion

## References and links

1. | L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woederman, “Spin-orbit coupling in free-space Laguerre-Gaussian light beams,” Phys. Rev. A |

2. | G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature Phys. |

3. | A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature(London) |

4. | G. Molina-Terriza, J. P. Torres, and L. Torner, “Orbital angular momentum of photons in noncollinear parametric downconversion,” Opt. Commun. |

5. | A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. |

6. | H. Arnaut and G. A. Barbosa, “Orbital and Intrinsic Angular Momentum of Single Photons and Entangled Pairs of Photons Generated by Parametric Down-Conversion,” Phys. Rev. Lett. |

7. | S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Observation of quantum entanglement using spatial light modulators,” Phys. Rev. A |

8. | M. Stutz, S. Grblacher, T. Jennewein, and A. Zeilinger, “How to create and detect N-dimensional entangled photons with an active phase hologram,” Appl. Phys. Lett. |

9. | N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, “Observation of quantum entanglement using spatial light modulators,” Phys. Rev. Lett. |

10. | A. Vaziri, G. Weihs, and A. Zeilinger, “Superpositions of the Orbital Angular Momentum for Applications in Quantum Experiments,” Phys. Rev. Lett. |

11. | A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A |

12. | S. S. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “Experimental Demonstration of Fractional Orbital Angular Momentum Entanglement of Two Photons,” Phys. Rev. Lett. |

13. | S. S. Oemrawsingh, J. A. de Jong, X. Ma, A. Aiello, E. R. Eliel, G. W. t Hooft, and J. P. Woerdman, “High-dimensional mode analyzers for spatial quantum entanglement,” Phys. Rev. A |

14. | J. T. Barreiro, N. K. Langford, N. A. Peters, and P.G. Kwiat, “Generation of Hyperentangled Photon Pairs,” Phys. Rev. Lett. |

15. | J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nature Phys. |

16. | L. Chen and W. She, “Increasing Shannon dimensionality by hyperentanglement of spin and fractional orbital angular momentum,” Opt. Lett. |

17. | L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. |

18. | E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. |

19. | J. B. Gotte, K. OHolleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express |

20. | L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation,” Appl. Phys. Lett. |

21. | E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. |

22. | G. F. Calvo and A. Picon, “Spin-induced angular momentum switching,” Opt. Lett. |

23. | E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Light propagation in a birefringent plate with topological charge,” Opt. Lett. |

24. | E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, “Hypergeometric-Gaussian Modes,” Opt. Lett. |

25. | P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. |

26. | M. J. Padgett and J. Courtial, “New high-intensity source of polarization-entangled photon pairs,” Opt. Lett. |

27. | We note that, although the optical layout is a Mach-Zehnder interferometer, the optical path phase difference between the two arms of the interferometer is only affecting the polarization state of the single output obtained after the final PBS, while it does not act on the PBS exit mode and on the OAM final state. The final polarization may therefore turn elliptical if this phase difference is not well controlled. However, the H polarization can be easily restored by suitable wave-plates, as long as it is uniform. |

28. | M. Fiorentino and F. N. C. Wong, “Deterministic Controlled-NOT Gate For Single-Photon Two-Qubit Quantum Logic,” Phys. Rev. Lett. |

**OCIS Codes**

(230.3720) Optical devices : Liquid-crystal devices

(270.0270) Quantum optics : Quantum optics

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: July 2, 2009

Revised Manuscript: September 2, 2009

Manuscript Accepted: September 7, 2009

Published: October 2, 2009

**Citation**

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, "Polarization control of single photon quantum orbital angular momentum states," Opt. Express **17**, 18745-18759 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-18745

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### References

- L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woederman, "Spin-orbit coupling in free-space Laguerre-Gaussian light beams," Phys. Rev. A 45, 8185 (1992). [CrossRef] [PubMed]
- G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nature Phys. 3, 305-310 (2007). [CrossRef]
- A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature(London) 412, 313-316 (2001). [CrossRef]
- G. Molina-Terriza, J. P. Torres, and L. Torner, "Orbital angular momentum of photons in noncollinear parametric downconversion," Opt. Commun. 228, 155-160 (2003). [CrossRef]
- A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, "Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum," Phys. Rev. Lett. 91, 227902 (2003). [CrossRef] [PubMed]
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