## A compact orbital angular momentum spectrometer using quantum zeno interrogation |

Optics Express, Vol. 19, Issue 12, pp. 11615-11622 (2011)

http://dx.doi.org/10.1364/OE.19.011615

Acrobat PDF (1304 KB)

### Abstract

We present a scheme to measure the orbital angular momentum spectrum of light using a precisely timed optical loop and quantum non-demolition measurements. We also discuss the influence of imperfect optical components.

© 2011 OSA

*lh̄*per photon when the electric field has an overall azimuthal dependence on phase,

*e*

^{−ilϕ}, where

*ϕ*is the azimuthal angle about the beam propagation axis [1

1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A **45**, 8185–8189 (1992). [CrossRef] [PubMed]

3. S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. **2**, 299–313 (2008). [CrossRef]

*l*takes integer values from −∞ to +∞. With an infinite number of states available, OAM can be utilized for qudit (

*d*-dimensional,

*d*> 2) systems [4

4. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. **88**, 013601 (2001). [CrossRef]

5. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature **412**, 313–316 (2001). [CrossRef] [PubMed]

6. G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. **94**, 040501 (2005). [CrossRef] [PubMed]

7. D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. **85**, 4418–4421 (2000). [CrossRef] [PubMed]

8. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. **88**, 127902 (2002). [CrossRef] [PubMed]

9. B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. **5**, 134–140 (2009). [CrossRef]

10. J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. **4**, 282–286 (2008). [CrossRef]

11. J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. **105**, 053904 (2010). [CrossRef] [PubMed]

12. Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. **11**, 085702 (2009). [CrossRef]

*l*-fold fork diffraction grating [13–15

15. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. **45**, 1231–1237 (1998). [CrossRef]

*l*-dependent phase shift, can separate different OAM components of light into different output ports of the interferometers, even at the single-photon level [16

16. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. **92**, 013601 (2004). [CrossRef] [PubMed]

*N*– 1 mutually stabilized interferometers to detect

*N*OAM-modes. A recently proposed scheme [17

17. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. **105**, 153601 (2010). [CrossRef]

18. A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. **48**, 931–932 (1980). [CrossRef]

20. P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. **83**, 4725–4728 (1999). [CrossRef]

*l*=

*l*

_{0}≥ 0, noted as |

*ψ*

^{(0)}〉 = |

*H*,

*l*

_{0}〉. The input pulse first transmits through optical switches S0 and S1 [21

21. S0 and S1 are optical switches that can be switched from been transmittive to reflective. S0 needs to transmit the initial incident light, and be switched to be reflective by the end of the first outer-loop cycle. A high repetition rate is not required and it can be implemeted either mechanically or opto-electrically. Alternatively it could also be a static high-reflectance mirror, if the one-time transmission loss at the very beginning can be tolerated. S1 needs to be switched every QZI loop cycle (Δ*T*) and need to be polarization insensitive. The fastest switches are Pockels cells, which can operate at 10–100 GHz with 99% transmission. One scheme, similar to the one implemented in Ref. [20], is to an interferometer with Pockels cells in one of the arms. The Pockels cells introduce *π* phase shift in the arm when activated, and thus switch the beam between two output ports of the interferometer. Using two Pockels cells rotated relative to each other will cancel the birefringent effect.

*θ*=

*π*/(2

*N*), and the state becomes

*l*= 0, the horizontal and vertical components of

*θ*=

*π/*(2

*N*) each loop. After

*N*loops, the light becomes vertically polarized and enters only the upper path of the interferometer. At this point, the polarization switch P1 is activated and switches the polarization into horizontal. Hence the light transmits through both PBS2 and PBS3, and arrives at the detector at time

*T*

_{0}.

*l*

_{0}≠ 0, however, the vertical component is sent to the upper path at PBS1, and is then blocked by the OAM filter. Only the horizontal component emerges after PBS2, the state collapses into |

*H*,

*l*

_{0}〉 with a probability

*N*loops, a fraction

*p*= cos(

*π/*(2

*N*))

^{2}

*of the light remains in the horizontal polarization in the lower arm of the interferometer, while a fraction 1 –*

^{N}*p*of the light is lost (blocked by OAM filter). At this point, the polarization switch P2 is activated and switches the polarization to vertical, and the light reflects off both PBS2 and PBS3, and enters the outer loop. By this time, S0 is switched to be reflective. As the light cycles in the outer loop, the polarization in rotated back to horizontal by R2, and the OAM value is decreased by Δ

*l*= 1 per cycle by a vortex phase plate (VPP) [22

22. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. **112**, 321–327 (1994). [CrossRef]

*l*

_{0}cycles,

*l*= 0. When the light enters the QZI again, it will exit the spectrometer to the detector, at a time

*T*(

*l*

_{0}) =

*T*

_{0}+

*l*

_{0}(

*NL*+

_{QZI}*L*)

_{out}*/c*. Here

*L*and

_{QZI}*L*are the optical path lengths of the QZI loop (from S1 to PBS2 back to S1) and the outer-loop (from S1 to PBS2, to PBS3, to S0, back to S1). The detected fraction of the light intensity is

_{out}*T*= (

*NL*+

_{QZI}*L*)

_{out}*/c*with a

*perfect*extinction ratio. The total transmission efficiency of the spectrometer is

*P*(

*l*

_{0}) for the component with OAM of

*l*

_{0}

*h̄. P*(

*l*

_{0}) → 1 for all

*l*

_{0}as

*N →*∞ due to the quantum Zeno effect [23

23. B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. **18**, 756–763 (1977). [CrossRef]

*α*|

^{2}∼ 0.96 [24

24. Technically, each |*α*|^{2} is slightly different, but the difference is well within 1%. The |*α*|^{2} that matters most is the one corresponding to the QZI loop (including S1), which, without any optimization, consists of 4 beam splitters, 5 mirrors, 1 waveplate and up to three Pockels cells. Assuming all optics are anti-reflection coated so that loss is 1% at each Pockels cell and 0.1% at each other component, we have |*α*|^{2} = 0.96.

*α*), the QZI loop (

_{out}*α*) and initial and final optics (

_{QZI}*α*). Hence the total transmission efficiency of the OAM spectrometer becomes

_{init, final}*l*

_{0}-th order OAM component. We plot in Fig. 2(b) the

*P*(

*l*

_{0}) vs.

*N*for OAM components

*l*

_{0}= 0 – 10. With increasing

*N*, the quantum Zeno effect leads to an increase in

*P*(

*l*

_{0}), while loss leads to a decrease in

*P*(

*l*

_{0}). As a result, an optimal

*N*is found at about 7 – 8 for high order OAM components. Note that the extinction ratio between different OAM states remains infinite even in the presence of loss. Crosstalk would only take place when the OAM filter is not completely opaque to nonzero OAM states.

*N*and optical loss. We consider the OAM filter having a complex transmission coefficient

*l*th OAM component. If the state |

*ψ*〉 = |

*H*,

*l*

_{0}〉 enters the QZI, after

*N*cycles, it exits the QZI loop in a polarization superposition state

*p*|

_{H}*H*〉 +

*p*|

_{V}*V*〉 [25

25. J. Jang, “Optical interaction-free measurement of semitransparent objects,” Phys. Rev. A **59**, 2322–2329 (1999). [CrossRef]

*p*and

_{H}*p*are given by: The pulse re-enters the outer loop at PBS3 with probability |

_{V}*p*|

_{H}^{2}, corresponding to a successful interrogation by the QZI (if

*l*

_{0}≠ = 0). With probably |

*p*|

_{V}^{2}, the pulse exits toward the detector, corresponding to an error (if

*l*

_{0}≠ 0). The total loss of this QZI interrogation is |

*loss*|

^{2}= 1 – |

*p*|

_{H}^{2}– |

*p*|

_{V}^{2}. In the outer loop, the OAM value of the pulse is lowered by 1 via the VPP, and the intensity of the pulse is reduced by a factor |

*α*|

_{out}^{2}per loop. Therefore, the probability of detecting the OAM eigenstate

*l*

_{0}in the

*l*th time interval (or, measured as with OAM

*lh̄*) is given by: And we define the extinction ratio

*η*as:

*N*th QZI-loop. It will then be switched to horizontal polarization by P1 and exit at a time interval corresponding to components with a lower OAM. Consequently, the extinction ratio is reduced. If the light is transmitted through the filter before the

*N*th loop, it will results in a larger loss. An imperfect OAM filter may also partially block light with zero OAM, which which also results in loss.

*lh̄*, the probabilities of the light exiting toward the detector (|

*p*|

_{V}^{2}), re-entering the outer-loop (|

*p*|

_{H}^{2}) and being lost (1 – |

*p*|

_{V}^{2}– |

*p*|

_{H}^{2}). These probabilities are plotted as a function of transmission

*T*(

*l, a*

_{0}) and

*N*. The crossing of |

*p*|

_{H}^{2}and |

*p*|

_{V}^{2}separates the regimes when the interrogation result is more likely (to the right side) or less likely (to the left side) to be correct than incorrect.

*lh̄*≠ 0 has zero intensity at the center of the beam, while light without OAM has maximum intensity at the center. Hence a very simple pinhole efficiently distinguishes light with and without OAM. The intensity distribution of a Laguerre-Gaussian beam, a paraxial beam possessing OAM

*lh̄*, is given by [1

1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A **45**, 8185–8189 (1992). [CrossRef] [PubMed]

*L*(

_{l}*x*) is the

*l*th order Laguerre Polynomial. Thus the transmission

*T*(

*l*) through a pinhole with a radius

*a*

_{0}(normalized by the waist of the

*l*

_{0}= 0 Gaussian beam) is:

*T*(

*l*,

*a*

_{0}) vs.

*a*

_{0}for

*l*= 0 – 3. The transmission decreases sharply with increasing

*l*when

*a*

_{0}is smaller than ∼ 0.8. Choosing

*a*

_{0}= 0.8, we show in Fig. 4(b) the nearly exponential decrease of

*T*(

*l*,

*a*

_{0}) with

*l*. These values are also marked by the red vertical lines in Fig. 3(a). Due to the fast decrease of

*T*(

*l*,

*a*

_{0}) from

*l*= 0 to

*l*≥ 1, a large extinction ratio is readily achieved, which is very well approximated by:

*η*is essentially the same for all OAM components, and it is mainly determined by how well the QZI can distinguish between states with OAM values

*l*

_{0}= 0 and

*l*

_{0}= 1. We plot in Fig. 5(a)

*η*vs.

*N*for |

*α*|

^{2}= 0.9 – 1. In general,

*η*increases with

*N*but decreases with |

*α*|

^{2}, resulting in an optimal

*N*for each |

*α*|

^{2}< 1. Even for |

*α*|

^{2}= 0.9,

*η*> 70 can be reached with

*N*= 7. For |

*α*|

^{2}= 0.96,

*η*peaks at ∼ 180.

4. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. **88**, 013601 (2001). [CrossRef]

*l*by Δ

*l*= 2 or 3 per passing. A smaller aperture size also introduces extra loss, but only in the final QZI on the zero OAM state, and thus only decreases the detection probability by about a factor of two.

*P*(

*l; l*

_{0}) vs.

*l*and

*l*

_{0}on the log scale, including loss and misalignment. The diagonal elements

*P*(

*l*

_{0};

*l*

_{0}) correspond to correctly detecting an OAM component. They are two orders of magnitude higher than neighboring off diagonal elements, consistent with the high extinction ratios calculated before. In Fig. 6(b), we show

*P*(

*l*

_{0};

*l*

_{0}) as a function of

*N*for different

*l*

_{0}.

*N*∼ 8 gives the highest probability for detecting high order OAM components, while still maintaining an extinction ratio of above 100.

## References and links

1. | L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A |

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

3. | S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. |

4. | G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. |

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

6. | G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. |

7. | D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. |

8. | N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. |

9. | B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. |

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

11. | J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. |

12. | Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. |

13. | V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. |

14. | N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. |

15. | J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. |

16. | J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. |

17. | G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. |

18. | A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. |

19. | A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. |

20. | P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. |

21. | S0 and S1 are optical switches that can be switched from been transmittive to reflective. S0 needs to transmit the initial incident light, and be switched to be reflective by the end of the first outer-loop cycle. A high repetition rate is not required and it can be implemeted either mechanically or opto-electrically. Alternatively it could also be a static high-reflectance mirror, if the one-time transmission loss at the very beginning can be tolerated. S1 needs to be switched every QZI loop cycle (Δ |

22. | M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. |

23. | B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. |

24. | Technically, each | |

25. | J. Jang, “Optical interaction-free measurement of semitransparent objects,” Phys. Rev. A |

**OCIS Codes**

(120.4290) Instrumentation, measurement, and metrology : Nondestructive testing

(050.4865) Diffraction and gratings : Optical vortices

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: April 18, 2011

Revised Manuscript: May 19, 2011

Manuscript Accepted: May 26, 2011

Published: June 1, 2011

**Citation**

Paul Bierdz and Hui Deng, "A compact orbital angular momentum spectrometer using quantum zeno interrogation," Opt. Express **19**, 11615-11622 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11615

Sort: Year | Journal | Reset

### References

- L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef] [PubMed]
- G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007). [CrossRef]
- S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008). [CrossRef]
- G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001). [CrossRef]
- A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001). [CrossRef] [PubMed]
- G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005). [CrossRef] [PubMed]
- D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000). [CrossRef] [PubMed]
- N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002). [CrossRef] [PubMed]
- B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009). [CrossRef]
- J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008). [CrossRef]
- J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010). [CrossRef] [PubMed]
- Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009). [CrossRef]
- V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).
- N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef] [PubMed]
- J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998). [CrossRef]
- J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004). [CrossRef] [PubMed]
- G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010). [CrossRef]
- A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. 48, 931–932 (1980). [CrossRef]
- A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993). [CrossRef]
- P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999). [CrossRef]
- S0 and S1 are optical switches that can be switched from been transmittive to reflective. S0 needs to transmit the initial incident light, and be switched to be reflective by the end of the first outer-loop cycle. A high repetition rate is not required and it can be implemeted either mechanically or opto-electrically. Alternatively it could also be a static high-reflectance mirror, if the one-time transmission loss at the very beginning can be tolerated. S1 needs to be switched every QZI loop cycle (ΔT) and need to be polarization insensitive. The fastest switches are Pockels cells, which can operate at 10–100 GHz with 99% transmission. One scheme, similar to the one implemented in Ref. [20], is to an interferometer with Pockels cells in one of the arms. The Pockels cells introduce π phase shift in the arm when activated, and thus switch the beam between two output ports of the interferometer. Using two Pockels cells rotated relative to each other will cancel the birefringent effect.
- M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994). [CrossRef]
- B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977). [CrossRef]
- Technically, each |α|2 is slightly different, but the difference is well within 1%. The |α|2 that matters most is the one corresponding to the QZI loop (including S1), which, without any optimization, consists of 4 beam splitters, 5 mirrors, 1 waveplate and up to three Pockels cells. Assuming all optics are anti-reflection coated so that loss is 1% at each Pockels cell and 0.1% at each other component, we have |α|2 = 0.96.
- J. Jang, “Optical interaction-free measurement of semitransparent objects,” Phys. Rev. A 59, 2322–2329 (1999). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.