Abstract

We examine experimentally how the degree of position-momentum entanglement of photon pairs depends on the transverse coherence of the pump beam that excites them in a process of spontaneous parametric down-conversion. Using spatially incoherent light from a light-emitting diode, we obtain strong position correlation of the photons, but we find that transverse momentum correlation, and thus entanglement, is entirely absent. When we continuously vary the degree of spatial coherence on the pump beam, we observe the emergence of stronger momentum correlations and entanglement. We present theoretical arguments that explain our experimental results. Our results shed light on entanglement generation and can be applied to control entanglement for quantum information applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

H. Defienne and S. Gigan, “Spatially entangled photon-pair generation using a partial spatially coherent pump beam,” Phys. Rev. A 99, 053831 (2019).
[Crossref]

2018 (5)

F. Flamini, N. Spagnolo, and F. Sciarrino, “Photonic quantum information processing: a review,” Rep. Prog. Phys. 82, 016001 (2018).
[Crossref] [PubMed]

J.-P. W. MacLean, J. M. Donohue, and K. J. Resch, “Direct Characterization of Ultrafast Energy-Time Entangled Photon Pairs,” Phys. Rev. Lett. 120, 053601 (2018).
[Crossref] [PubMed]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photons: new quantum perspectives in high dimensions,” Light: Sci. Appl. 7, 17146 (2018).
[Crossref]

E. Giese, R. Fickler, W. Zhang, L. Chen, and R. W. Boyd, “Influence of pump coherence on the quantum properties of spontaneous parametric down-conversion,” Phys. Scr. 93, 084001 (2018).
[Crossref]

2017 (1)

2016 (1)

J. Schneeloch and J. C. Howell, “Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone,” J. Opt. 18, 053501 (2016).
[Crossref]

2015 (3)

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong Loophole-Free Test of Local Realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Z. Xie, T. Zhong, S. Shrestha, X. Xu, J. Liang, Y.-X. Gong, J. C. Bienfang, A. Restelli, J. H. Shapiro, F. N. C. Wong, and C. Wei Wong, “Harnessing high-dimensional hyperentanglement through a biphoton frequency comb,” Nat. Photonics 9, 536 (2015).
[Crossref]

2014 (2)

G. Gbur, “Partially coherent beam propagation in atmospheric turbulence [Invited],” J. Opt. Soc. Am. A 31, 2038–2045 (2014).
[Crossref]

M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, “Generation and confirmation of a (100 × 100)-dimensional entangled quantum system,” Proc. Natl. Acad. Sci. U. S. A. 111, 6243–6247 (2014).
[Crossref] [PubMed]

2011 (2)

J. Galinis, M. Karpiński, G. Tamošauskas, K. Dobek, and A. Piskarskas, “Photon coincidences in spontaneous parametric down-converted radiation excited by a blue LED in bulk LiIO 3 crystal,” Opt. Express 19, 10351–10358 (2011).
[Crossref] [PubMed]

H. Di Lorenzo Pires, F. M. G. J. Coppens, and M. P. van Exter, “Type-I spontaneous parametric down-conversion with a strongly focused pump,” Phys. Rev. A 83, 033837 (2011).
[Crossref]

2010 (4)

G. Tamošauskas, J. Galinis, A. Dubietis, and A. Piskarskas, “Observation of spontaneous parametric down-conversion excited by high brightness blue LED,” Opt. Express 18, 4310–4315 (2010).
[Crossref]

A. K. Jha and R. W. Boyd, “Spatial two-photon coherence of the entangled field produced by down-conversion using a partially spatially coherent pump beam,” Phys. Rev. A 81, 013828 (2010).
[Crossref]

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87 – 139 (2010).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum Correlations in Optical Angle–Orbital Angular Momentum Variables,” Science 329, 662–665 (2010).
[Crossref] [PubMed]

2009 (2)

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

R. M. Gomes, A. Salles, F. Toscano, P. H. S. Ribeiro, and S. P. Walborn, “Observation of a Nonlocal Optical Vortex,” Phys. Rev. Lett. 103, 033602 (2009).
[Crossref] [PubMed]

2008 (2)

A. K. Jha, M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, “Temporal coherence and indistinguishability in two-photon interference effects,” Phys. Rev. A 77, 021801 (2008).
[Crossref]

B. Hage, A. Samblowski, J. DiGuglielmo, A. Franzen, J. Fiurášek, and R. Schnabel, “Preparation of distilled and purified continuous-variable entangled states,” Nat. Phys. 4, 915–918 (2008).
[Crossref]

2007 (1)

K. W. Chan, J. P. Torres, and J. H. Eberly, “Transverse entanglement migration in Hilbert space,” Phys. Rev. A 75, 050101 (2007).
[Crossref]

2005 (1)

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A: Pure Appl. Opt. 7, 232 (2005).
[Crossref]

2004 (3)

C. K. Law and J. H. Eberly, “Analysis and Interpretation of High Transverse Entanglement in Optical Parametric Down Conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[Crossref] [PubMed]

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

M. D’Angelo, Y.-H. Kim, S. P. Kulik, and Y. Shih, “Identifying Entanglement Using Quantum Ghost Interference and Imaging,” Phys. Rev. Lett. 92, 233601 (2004).
[Crossref]

2001 (2)

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]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Biphoton interference with a multimode pump,” Phys. Rev. A 63, 053801 (2001).
[Crossref]

1998 (1)

C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

1993 (1)

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993).
[Crossref] [PubMed]

1989 (1)

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62, 2205–2208 (1989).
[Crossref] [PubMed]

1972 (1)

S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Phys. Rev. Lett. 28, 938–941 (1972).
[Crossref]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Abellán, C.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong Loophole-Free Test of Local Realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Acín, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Allman, M. S.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong Loophole-Free Test of Local Realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Amaya, W.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong Loophole-Free Test of Local Realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Andersen, U. L.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Augusiak, R.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Bacco, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Bachor, H. A.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Barnett, S. M.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum Correlations in Optical Angle–Orbital Angular Momentum Variables,” Science 329, 662–665 (2010).
[Crossref] [PubMed]

Bennink, R. S.

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref] [PubMed]

Bentley, S. J.

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J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Light: Sci. Appl. (1)

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Nat. Photonics (1)

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Nat. Phys. (1)

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Opt. Express (2)

Phys. Rep. (1)

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Phys. Rev. (1)

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Phys. Rev. A (8)

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Figures (4)

Fig. 1
Fig. 1 Schematic of the experimental setup. Photon pairs are generated by pumping a type-II nonlinear crystal (ppKTP) with either a laser beam with adjustable transverse coherence (red shaded beam path) or a beam derived from an LED that is spatially incoherent (blue shaded beam path). The coherence of the laser is tuned by modulating the transverse phase profile with a spatial light modulator (SLM). A polarizing beam splitter (PBS) splits the pairs and their joint spatial distributions are measured by independently movable slits in each arm. They are followed by bucket detector systems consisting of microscope objectives, multimode fibers, single-photon detectors. Position correlations are registered by a coincidence measurement in the image plane (f1 and f2), while momentum correlations are observed in the focal plane of a lens f3 (Fourier transform plane, or momentum space).
Fig. 2
Fig. 2 Position correlations and momentum anti-correlations of SPDC pumped by a laser and an LED. We obtain the coincidence rates in (a,c) by moving the two slits in opposite directions in the near field (measuring the distribution of x) and in (b,c) by moving them in the same directions in the far field (measuring the distribution of p+). The acquisition time of each data point is 1 min for the laser pump (a,b) and 15 min for the LED pump (c,d); the error bars are obtained by averaging over five such measurements. To demonstrate the correlation strength graphically, we show the average rate of singles counts (gray distributions in the back; scale on the right side of each plot).
Fig. 3
Fig. 3 Effect of coherence on joint probability distributions of generated photon pairs. Parts (a) and (b) show the joint position and momentum distributions when pumped with a laser (red), parts (c) and (d) show the respective distributions when pumped with an LED (blue). Horizontal axes denote the position or momentum of the signal; vertical axes denote the position or momentum of the idler. The joint distributions show the number of coincidence counts accumulated in 1 min for the laser (a, b) and in 15 min for the LED (c, d). The pairs are strongly correlated in position when pumped with either the laser or the LED, while strong anti-correlation of their momenta occurs only for a transverse coherent pump beam. The black areas depict parts that have not been measured, since nearly no counts were expected.
Fig. 4
Fig. 4 Momentum anti-correlation, position correlation, and the entanglement criterion for pseudo-thermal pump beams with different coherence lengths. Part (a) shows that Δ x 2 (green) is independent of the coherence length, whereas Δ p + 2 (purple) follows Eq. (4), as highlighted by the fit. The product Δ x 2 Δ p + 2 in part (b) increases for decreasing coherence and therefore makes a transition from entangled to classically correlated photon pairs. The red star represents this product for the (coherent) laser and the blue star represents this product for the (incoherent) LED whose coherence length has been extrapolated from a fit.

Equations (4)

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Δ x 2 Δ p + 2 2 / 4 ,
Δ x 2 Δ p + 2 | laser = ( 0.0112 ± 0.0005 ) 2
Δ x 2 Δ p + 2 | LED = ( 4.62 ± 0.93 ) 2 ,
Δ p + 2 = 2 / ( 8 w 2 ) + 2 w 2 k p 2 / ( 2 R 2 ) + 2 / ( 2 l c 2 )

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