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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 17 — Aug. 13, 2012
  • pp: 18869–18875
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Weak interference in the high-signal regime

Juan P. Torres, Graciana Puentes, Nathaniel Hermosa, and Luis Jose Salazar-Serrano  »View Author Affiliations


Optics Express, Vol. 20, Issue 17, pp. 18869-18875 (2012)
http://dx.doi.org/10.1364/OE.20.018869


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Abstract

Weak amplification is a signal enhancement technique which is used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on: a) the existence of a weak interaction which couples a property of a system (the system) with a separate degree of freedom (the pointer), and b) the measurement of an anomalously large mean value of the pointer state (weak mean value), after appropriate pre-and post-selection of the state of the system. Unfortunately, the weak amplification process is generally accompanied by severe losses of the detected signal, which limits its applicability. However, we will show here that since weak amplification is essentially the result of an interference phenomena, it should be possible to use the degree of interference (weak interference) to get relevant information about the physical system under study in a more general scenario, where the signal is not severely depleted (high-signal regime).

© 2012 OSA

1. Introduction

Weak amplification is a concept first introduced by Aharonov, Albert, and Vaidman [1

1. Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988). [CrossRef] [PubMed]

], which describes a situation where two subsystems interact, even though through a weakly coupling process. Generally, the weak amplification idea is presented in the general framework of Quantum Mechanics, where one of the subsystems is assumed to be the measuring device, whose aim is to unveil the value of a property that characterizes the other interacting subsystem (the system).

The fact that the coupling is weak can be seemingly disadvantageous, since it is expected to produce an uncertainty in the measurement larger than the values that should be differentiated. However, when appropriate initial and final states of the system to be measured are selected, for instance by choosing them to be nearly orthogonal, the mean value of the reading of the measuring system (weak mean value) can yield an unexpectedly large value (weak amplification). Surprisingly, this value can lay outside the range of small displacements of the measurement pointer caused by each one of the possible states of the system. Unfortunately, this is also accompanied by a severe depletion of the intensity of the signal detected, due to the quasi-orthogonality of the input and final states of the system. This prevents the applicability of the weak measurement concept to experiments which are already limited by a low signal-to-noise ratio [2

2. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008). [CrossRef] [PubMed]

], since the intensity of the detected signal is severely decreased.

For instance, when considering the refraction of a light beam in a thin birefringent crystal, the two orthogonal linear polarizations components of the optical beam are displaced a small distance Δ compared with the beam waist [3

3. N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett. 66, 1107–1110 (1991). [CrossRef] [PubMed]

]. For a given initial |Ψin〉 and final |Ψout〉 states of the polarization of the system, so that 〈Ψoutin〉 ∼ ε (ε is small), the mean value of the shift of the position of the light beam is 〈x〉/Δ = 𝔕 (〈Aw), where the weak value 〈Aw is defined as
Aw=Ψout|A|ΨinΨout|Ψin~1ε.
(1)
In this example, the power of the output signal (Pout) is severely reduced, i.e., Pout/Pinε2. The signal enhancement of the position of the beam due to weak amplification can thus be observed only if the input signal intensity (Pin) can be enhanced.

Most experimental realizations of weak amplification up to date take place in this context. This is the case for experiments that use the polarization of a light beam to reveal extremely small spatial displacements [2

2. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008). [CrossRef] [PubMed]

, 3

3. N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett. 66, 1107–1110 (1991). [CrossRef] [PubMed]

], and for experiments that make use of the two counter-propagating paths in a Sagnac interferometer to detect tiny beam deflections [4

4. P. Ben Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009). [CrossRef] [PubMed]

], or tiny frequency shifts [5

5. D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82, 063822 (2010). [CrossRef]

]. Interestingly, weak measurements can have a wider range of applicability than originally conceived, appearing naturally in the context of optical telecom networks [6

6. N. Brunner, A. Acin, D. Collins, N. Gisin, and V. Scarini, “Optical telecom networks as weak quantum measurements with postselection,” Phys. Rev. Lett. 91, 180402 (2003). [CrossRef] [PubMed]

], and the description of the response function of a system [7

7. D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. H. Hickmann, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett. 92, 043601 (2004). [CrossRef] [PubMed]

].

Even though the idea of weak amplification was born in the context of Quantum Mechanics, and is generally formulated in the language of Quantum Mechanics, it can be understood as the consequence of the constructive and destructive interference between the complex amplitudes of different pointer states [8

8. I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a ’weak measurement’ of a spin-1/2 particles’s spin component yields a value of 100,” Phys. Rev. D 40, 2112–2117 (1989). [CrossRef]

]. Each of these correspond to the nearly equal readings of the measuring device for each value of the state of the system. The concept behind weak amplification, can thus be applied to any physical wave phenomena and explained in classical terms as a wave interference process [9

9. J. C. Howell, D. J. Starling, P. B. Dixon, K. P. Vudyasetu, and A. N. Jordan, “Interferometric weak value deflections: quantum and classical treatments,” Phys. Rev. A 81, 033813 (2010). [CrossRef]

]. Notwithstanding, certain experiments which deal with quantum concepts such as entanglement [10

10. G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005). [CrossRef] [PubMed]

] and the violation of Leggett-Garg inequalities [11

11. M. E. Goggin, M. P. Almeida, M. Barbieri, B. P. Lanyon, J. L. O’Brien, A. G. White, and G. J. Pryde, “Violation of the Leggett-Garg inequality with weak measurements of photons,” Proc. Natl. Acad. Sci. U.S.A. 108, 1256–1261 (2011). [CrossRef] [PubMed]

] still require a full quantum formalism for its description.

Here we will show that since the measured value of the weak mean value is the result of an interference phenomenon, the weak interference might be noticeable even in the regime of small losses, where the specific value of weak mean value might not convey any relevant information about the system or the measuring device. This can open new applications based on weak interference, especially for interactions where it is not possible to enhance the signal-to-noise ratio of the measurement. For example, when the intensity of the input signal cannot be increased.

2. Weak interference: general scenario

For the sake of simplicity, let us consider a simple case which shows the full potential of the scheme considered here. A linearly polarized input light beam with polarization |Ψin=1/2[|H+|V] and spatial shape Φ(x) propagates in a medium that couples the polarization and spatial degrees of freedom, thereby generating a polarization-dependent displacement of the photons, Δ1 and Δ2. The input state of the system (polarization) and the measuring device (position of the beam) can be written, up to a normalization constant, as
|in=|ΨindxΦ(x)|x.
(2)
The global state of the system and measuring device after the interaction writes [3

3. N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett. 66, 1107–1110 (1991). [CrossRef] [PubMed]

]
|out=dx{Φ(xΔ1)|H+Φ(xΔ2)exp(iφ)|V}|x,
(3)
where φ stands for any polarization-dependent phase difference that can occur during the interaction. Finally, before being detected, the photons are projected into the polarization state |Ψout〉 = cosα|H〉 + exp()sinα|V〉. The intensity distribution of the output light beam can now be written as
I(x)=|cosαΦ(xΔ1)+sinαΦ(xΔ2)exp(iθ)|2,
(4)
with θ = φξ.

Let us assume that the light beam is Gaussian with beam waist w0. Making use of the product theorem for Gaussian integrals [12

12. E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of frequency lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A 6, 1142–1149 (1989). [CrossRef]

], the mean value of the position of the beam, 〈x〉 = ∫ dxxI(x)/∫ dxI(x) reads
x=Δ+2+Δ2cos2α1+γsin2αcosθ,
(5)
where
γ=exp[(Δ1Δ2)24w02],
(6)
Δ+ = Δ1 + Δ2 and Δ = Δ1 − Δ2. In all cases, Δ1, Δ2w0, so γ ∼ 1.

Inspection of Eq. (5) shows that the value of Δ+ can not be amplified with the present scheme. In many experiments [2

2. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008). [CrossRef] [PubMed]

,3

3. N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett. 66, 1107–1110 (1991). [CrossRef] [PubMed]

], Δ1 = −Δ2, so Δ+ = 0, and as a consequence the weak measurement amplifies all the relevant information. Therefore, the weak amplification happens for Δ, with an amplification factor 𝒜 that reads
𝒜=cos2α1+γsin2αcosθ.
(7)
Figure 1 shows the amplification factor for θ = 0.01°. The maximum amplification takes place for the angle α0 = −1/2 sin−1 (γcosθ), where the factor reaches the value of 𝒜max = (1 − γ2 cos2θ)−1/2.

Fig. 1 Weak amplification of the displacement Δ as a function of the output polarization of the system (angle α). The phase difference is θ = 0.01°. We consider displacements Δ = Δ1 = −Δ2 = 10 nm, and the beam waist is w0 = 10μm.

The loss of the system is given by
PoutPin=12[1+γcosθsin2α],
(8)
where Pin,out is the total input and output power of the optical beam, when integrated over all space. Figure 2 shows the loss in the measurement expressed in dB, as 10 log(Pout/Pin). Even though the enhancement of Δ can be a large staggering value for angles close to −45° (Fig. 1 shows an enhancement close to 103), this is unfortunately accompanied by a severe loss penalty close to 70 dB (Fig. 2). For instance, if the goal of the experiment is to attain a signal-to-noise ratio of 10 dB at the measurement stage, the input signal has to be correspondingly increased 70 dB above this level.

Fig. 2 Signal loss as a function of the angle α of the polarization of the output state. The phase difference is θ = 0.01°, Δ1 = −Δ2 = 10 nm and w0 = 10μm.

As it can be seen in Eq. (7), the level of weak amplification achievable depends on the value of θ, which should be chosen close to zero in order to achieve the maximum amplification. This angle can be modified by choosing the appropriate value ξ of the polarization of the output state of the system. The power of the output signal also depends on this angle. Figure 3 shows the signal loss for a few selected angles: α = −45°, −30°, 0° and 45°. In all cases, the loss goes from log[(1 + sin2α)/2] for θ = 0, to −3 dB for θ = ±π/2, which corresponds to post-selecting polarizations cosα|H〉 +sinα|V〉 and cosα|H〉 +isinα|V〉, respectively. Importantly, the dependence of the losses on the polarization selected at the output for α ≠ 0°, 90° is a consequence of the interference effect which is the essence of the weak measurement concept [8

8. I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a ’weak measurement’ of a spin-1/2 particles’s spin component yields a value of 100,” Phys. Rev. D 40, 2112–2117 (1989). [CrossRef]

].

Fig. 3 Signal loss as a function of the angle θ. The beam waist is w0 = 10μm. Red solid line: α = 45°; Blue dashed line: α = 0°; Black dotted line: α = −30°; Green dotted dashed line: α = −45°.

3. Weak measurement in a high-signal regime

In the low-signal regime, when the input and output polarization states are quasi-orthogonal, the retrieval of information about the value of Δ comes with a severe loss penalty. But since the weak measurement is an interference phenomenon, we should be able, in principle, to observe interference also in the high-signal regime. In order to get information about the value of Δ, we can measure the fractional loss ΔP/Pin, where ΔP = PoutPin. One obtains that
ΔPPin=12[γcosθsin2α1].
(9)
Figure 4 shows the value of ΔP/P as a function of the spatial shift Δ for α = 45° and θ = 0, 0.1°, 0.2° and 0.3°. The dependence of the fractional loss on Δ comes from the relationship between γ and δ, as given in Eq. (6). Notice that in all cases, the total losses of the system are below 3 dB, which is significantly below the loss found in the usual regime of weak amplification, where losses can easily reach tens of dB for large amplifications. Moreover, in all cases shown in Fig. 4, the mean value of the beam position is 〈x〉 = 0, so the weak value concept does not convey any relevant information here.

Fig. 4 Fractional loss ΔP/P as a function of the spatial shift Δ. α = 45° and w0 = 10μm. Red solid line: θ = 0°; Blue dashed line: θ = 0.1°; Black dotted line: θ = 0.2°; Green dot-dashed line: θ = 0.3°.

The important point here is that by measuring the fractional loss, one can determine the value of the displacement Δ. The maximum sensitivity of the scheme proposed is obtained for α = 45° and θ = 0°. By choosing other values for these angles, one can decrease the fractional loss, making its detection easier. However, this would decrease the sensitivity, making the distinction between different spatial shifts Δ more difficult. Note that here we are assuming that there are not other sources of polarization-dependent losses.

What is, in general, the minimum fractional loss measurable? In [13

13. C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857–1861 (2008). [CrossRef] [PubMed]

, 14

14. B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010). [CrossRef] [PubMed]

], a high-frequency detection scheme for the detection of Raman gain in Stimulated Raman Scattering process was able to detect a fractional loss of the order of ΔP/P < 10−7. The key point is to modulate the input signal at MHz rates to remove the low-frequency laser noise, implementing a detection scheme that is effectively shot-noise limited. In this way, one can increase the signal-to-noise ratio in a weak interference configuration, where the sensitivity is now limited by the presence of shot noise [15

15. D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803 (2009). [CrossRef]

, 16

16. A. Nishizawa, K. Nakamura, and M. Fujimoto, “Weak-value amplification in a shot-noise-limited interferometer,” Phys. Rev. A 85, 062108 (2012). [CrossRef]

].

4. Conclusions

In conclusion, we have shown that since the idea of weak amplification can be explained as an interference phenomenon, it is possible to obtain relevant information about the weak interaction of the physical system under study even in a regime where the signal is not depleted, and the specific result of the weak mean value does not convey any relevant information. We demonstrate that we can measure tiny quantities generated during a weak interaction by detecting a measurable interference effect in the high-signal regime, as opposed to the usual case of weak amplification, which suffers from severe losses. Therefore, this widens the applicability of the weak interference concept, allowing its use in a broader range of systems.

In experiments that deal with the detection of single photons in a quantum scenario [10

10. G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005). [CrossRef] [PubMed]

, 11

11. M. E. Goggin, M. P. Almeida, M. Barbieri, B. P. Lanyon, J. L. O’Brien, A. G. White, and G. J. Pryde, “Violation of the Leggett-Garg inequality with weak measurements of photons,” Proc. Natl. Acad. Sci. U.S.A. 108, 1256–1261 (2011). [CrossRef] [PubMed]

], the concepts discussed here should apply as well, as reflected by the fact that we use a full quantum formalism in our analysis, even when a classical formalism would work in certain cases. We should remark that we refer to the high-signal regime as the one with low losses, no low flux rate of photons. The quantity to be measured is now the number of photons detected as a function of the spatial shift (see Fig. 4), instead of the more usual parameters measured in a weak amplification scheme, such as the Stokes parameter [10

10. G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005). [CrossRef] [PubMed]

], or spatial [3

3. N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett. 66, 1107–1110 (1991). [CrossRef] [PubMed]

] and frequency displacements [5

5. D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82, 063822 (2010). [CrossRef]

]. The usefulness of the approach considered in this type of experiments will depend on the flux rate of photons generated, and the capability to generate changes of power above the noise level of the experiment.

Finally, we should mention that even though we have discussed our ideas in the context of the specific case of polarization-dependent spatial shifts of optical beams, the main conclusions applies also to other systems, as well as to other degrees of freedom, i.e., frequency. Our scheme would also apply to systems in a higher-dimensional space, so that the total input state writes
|in=1ni=1n|uidxΦ(x)|x,
(10)
where |ui〉 is a base of the N-dimensional space.

An example of this kind of interaction, where our system could be implemented, is the rotational Doppler frequency shift imparted to a beam with orbital angular momentum (OAM) when it traverses a rotating optical device which introduces a time-varying OAM-dependent phase shift, such as a rotating Dove prism. In this case, the spatial and frequency degrees of freedom are coupled [17

17. J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998). [CrossRef]

, 18

18. M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, “Measurement of orbital angular momentum spectrum of a light beam,” Opt. Lett. 28, 2285–2287 (2003). [CrossRef] [PubMed]

], so that the state of the light beam after traversing the rotating Dove prism is
|out=mdωΦ(ω+2mΩ)|m|ω
(11)
Now, the interaction introduces frequency shifts Δm = 2mΩ, where m is the OAM mode index.

Acknowledgments

This work was supported by the Government of Spain ( FIS2010-14831), by the European project PHORBITECH (FET-Open grant number: 255914), and by Fundacio Privada Cellex Barcelona. GP acknowledges financial support from Marie Curie International Incoming Fellowship COFUND.

References and links

1.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988). [CrossRef] [PubMed]

2.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008). [CrossRef] [PubMed]

3.

N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett. 66, 1107–1110 (1991). [CrossRef] [PubMed]

4.

P. Ben Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009). [CrossRef] [PubMed]

5.

D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82, 063822 (2010). [CrossRef]

6.

N. Brunner, A. Acin, D. Collins, N. Gisin, and V. Scarini, “Optical telecom networks as weak quantum measurements with postselection,” Phys. Rev. Lett. 91, 180402 (2003). [CrossRef] [PubMed]

7.

D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. H. Hickmann, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett. 92, 043601 (2004). [CrossRef] [PubMed]

8.

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a ’weak measurement’ of a spin-1/2 particles’s spin component yields a value of 100,” Phys. Rev. D 40, 2112–2117 (1989). [CrossRef]

9.

J. C. Howell, D. J. Starling, P. B. Dixon, K. P. Vudyasetu, and A. N. Jordan, “Interferometric weak value deflections: quantum and classical treatments,” Phys. Rev. A 81, 033813 (2010). [CrossRef]

10.

G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005). [CrossRef] [PubMed]

11.

M. E. Goggin, M. P. Almeida, M. Barbieri, B. P. Lanyon, J. L. O’Brien, A. G. White, and G. J. Pryde, “Violation of the Leggett-Garg inequality with weak measurements of photons,” Proc. Natl. Acad. Sci. U.S.A. 108, 1256–1261 (2011). [CrossRef] [PubMed]

12.

E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of frequency lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A 6, 1142–1149 (1989). [CrossRef]

13.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857–1861 (2008). [CrossRef] [PubMed]

14.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010). [CrossRef] [PubMed]

15.

D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak values,” Phys. Rev. A 80, 041803 (2009). [CrossRef]

16.

A. Nishizawa, K. Nakamura, and M. Fujimoto, “Weak-value amplification in a shot-noise-limited interferometer,” Phys. Rev. A 85, 062108 (2012). [CrossRef]

17.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998). [CrossRef]

18.

M. V. Vasnetsov, J. P. Torres, D. V. Petrov, and L. Torner, “Measurement of orbital angular momentum spectrum of a light beam,” Opt. Lett. 28, 2285–2287 (2003). [CrossRef] [PubMed]

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(270.0270) Quantum optics : Quantum optics
(350.7420) Other areas of optics : Waves

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: May 1, 2012
Revised Manuscript: June 17, 2012
Manuscript Accepted: June 18, 2012
Published: August 2, 2012

Citation
Juan P. Torres, Graciana Puentes, Nathaniel Hermosa, and Luis Jose Salazar-Serrano, "Weak interference in the high-signal regime," Opt. Express 20, 18869-18875 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-18869


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References

  1. Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett.60, 1351–1354 (1988). [CrossRef] [PubMed]
  2. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319, 787–790 (2008). [CrossRef] [PubMed]
  3. N. W. Ritchie, J. G. Story, and R. G. Hulet, “Realization of a measuremernt of a weak value,”Phys. Rev. Lett.66, 1107–1110 (1991). [CrossRef] [PubMed]
  4. P. Ben Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett.102, 173601 (2009). [CrossRef] [PubMed]
  5. D. J. Starling, P. Ben Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A82, 063822 (2010). [CrossRef]
  6. N. Brunner, A. Acin, D. Collins, N. Gisin, and V. Scarini, “Optical telecom networks as weak quantum measurements with postselection,” Phys. Rev. Lett.91, 180402 (2003). [CrossRef] [PubMed]
  7. D. R. Solli, C. F. McCormick, R. Y. Chiao, S. Popescu, and J. H. Hickmann, “Fast light, slow light, and phase singularities: a connection to generalized weak values,” Phys. Rev. Lett.92, 043601 (2004). [CrossRef] [PubMed]
  8. I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, “The sense in which a ’weak measurement’ of a spin-1/2 particles’s spin component yields a value of 100,” Phys. Rev. D40, 2112–2117 (1989). [CrossRef]
  9. J. C. Howell, D. J. Starling, P. B. Dixon, K. P. Vudyasetu, and A. N. Jordan, “Interferometric weak value deflections: quantum and classical treatments,” Phys. Rev. A81, 033813 (2010). [CrossRef]
  10. G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett.94, 220405 (2005). [CrossRef] [PubMed]
  11. M. E. Goggin, M. P. Almeida, M. Barbieri, B. P. Lanyon, J. L. O’Brien, A. G. White, and G. J. Pryde, “Violation of the Leggett-Garg inequality with weak measurements of photons,” Proc. Natl. Acad. Sci. U.S.A.108, 1256–1261 (2011). [CrossRef] [PubMed]
  12. E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of frequency lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A6, 1142–1149 (1989). [CrossRef]
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