Double-slit interference pattern measurement with entangled photons

[DrChinese]

Although it is well known that a series of individual photons will build up an interference pattern in a double slit setup, there have been few (if any) experiments where such a pattern is built up by sending photons through one at a time. Here is a great experiment from one of the top quantum optics teams using entangled* photons:

Time-resolved double-slit interference pattern measurement with entangled photons

Piotr Kolenderski, Carmelo Scarcella, Kelsey D. Johnsen, Deny R. Hamel, Catherine Holloway, Lynden K. Shalm, Simone Tisa, Alberto Tosi, Kevin J. Resch, Thomas Jennewein

Abstract: "The double-slit experiment strikingly demonstrates the wave-particle duality of quantum objects. In this famous experiment, particles pass one-by-one through a pair of slits and are detected on a distant screen. A distinct wave-like pattern emerges after many discrete particle impacts as if each particle is passing through both slits and interfering with itself. While the direct event-by-event buildup of this interference pattern has been observed for massive particles such as electrons, neutrons, atoms and molecules, it has not yet been measured for massless particles like photons. Here we present a temporally- and spatially-resolved measurement of the double-slit interference pattern using single photons. We send single photons through a birefringent double-slit apparatus and use a linear array of single-photon detectors to observe the developing interference pattern. The analysis of the buildup allows us to compare quantum mechanics and the corpuscular model, which aims to explain the mystery of single-particle interference. Finally, we send one photon from an entangled pair through our double-slit setup and show the dependence of the resulting interference pattern on the twin photon's measured state. Our results provide new insight into the dynamics of the buildup process in the double-slit experiment, and can be used as a valuable resource in quantum information applications."

http://arxiv.org/abs/1304.4943

The use of entangled photons allows the photons to be heralded (ie announced in advance). It is therefore clear that the pattern is built from independent photons. Some very interesting work, and a great demonstration of the theory!

* Entangled photons normally do not produce interference patterns. But these have been specifically modified to prevent polarization attributes to allow which-slit information to be obtained. So interference is possible.

 

[San K]

* Entangled photons normally do not produce interference patterns. But these have been specifically modified to prevent polarization attributes to allow which-slit information to be obtained. So interference is possible.

Great paper, DrChinese. Not read it yet but the summary sounds interesting.

Are you, in the above paragraph, saying that, in this paper/experiment, the experimenter was able to which-way and interference at the same time?

I know partial-partial is possible. Is the above different from that?

 

[DrChinese]

Great paper, DrChinese. Not read it yet but the summary sounds interesting.

Are you, in the above paragraph, saying that, in this paper/experiment, the experimenter was able to which-way and interference at the same time?

I know partial-partial is possible. Is the above different from that?

No, this is a standard theoretical treatment so there is no which way information when the interference is obtained. The "extra" entangled particle is used to demonstrate that the pattern is built up one photon at a time. There is no coincidence counting required to see the pattern.

 

[San K]

No, this is a standard theoretical treatment so there is no which way information when the interference is obtained. The "extra" entangled particle is used to demonstrate that the pattern is built up one photon at a time. There is no coincidence counting required to see the pattern.

Is coincidence counting NOT required because "noise" has already been removed? (via use of equipment containing polarizers)

 

[Cthugha]

One should note that the authors do not use what people typically consider a double slit, but rather a polarization based equivalent. They make use of a birefringent calcite crystal which will displace photons of different polarization in a different manner. The difference in displacement is 3.68 mm.

Heralding the single photon obviously requires coincidence counting, but the authors do not use any polarization-resolved or momentum-resolved coincidence counting which would pick only a part of the single photons (at least in the first of the two experiments described here), so it is just used to ensure that indeed only single photons are taken into account (at least in the first of the two experiments described).

One should also note, that the authors use a Sagnac-type photon source. These produce narrow bandwidth polarization entangled photons. This is different from the momentum-entangled light used for many other interference experiments with entangled light.

 

[DrChinese]

One should note that the authors do not use what people typically consider a double slit, but rather a polarization based equivalent. They make use of a birefringent calcite crystal which will displace photons of different polarization in a different manner. The difference in displacement is 3.68 mm.

Heralding the single photon obviously requires coincidence counting, but the authors do not use any polarization-resolved or momentum-resolved coincidence counting which would pick only a part of the single photons (at least in the first of the two experiments described here), so it is just used to ensure that indeed only single photons are taken into account (at least in the first of the two experiments described).

One should also note, that the authors use a Sagnac-type photon source. These produce narrow bandwidth polarization entangled photons. This is different from the momentum-entangled light used for many other interference experiments with entangled light.

Great comments, Cthugha. I missed the points you make above when I read the article. The crystal acts as a double slit by displacing the output beams slightly. There is no physical (traditional) double slit.

I don't follow completely the point about Sagnac photon pairs. I am guessing that we don't want these to be momentum entangled because that would supply which-path information to the heralded side. But I am not sure. Can you explain that to me?

 

[Cthugha]

Well, I am not sure about the authors' motivation to use this kind of source. It might be that they did not want momentum entanglement. It might also be that they needed a rather bright source to overcome the dark count rates of all the avalanche diodes. I am not sure.

I am also not really an expert in entangled sources, so take the following summary with a grain of salt. If someone knows more details, he is free to correct me. The "traditional" entangled light source is a bulk nonlinear crystal like KTP or some similar material. The critical property in realizing entangled photon sources is the phase matching condition. In these bulk crystals you can use the birefringence of the crystal and the angle to get the matching right. However, this usually means that you will get emission on two intersecting cones (the standard momentum spread in two directions) and as the phase matching condition is quite picky, you need high power light sources to get reasonable amounts of light. For pulsed light, this typically means you need to get femtosecond pulses which are spectrally quite broad. Even worse, you also cannot increase efficiency by using longer crystals as you will not be able to get phase matching over the whole length of the crystal.

Over the course of time different strategies of creating entangled photon sources have emerges. One of them lies in using periodically poled (PP) nonlinear crystals like PPKTP or PPLiNb. While you grow these nonlinear crystals, you apply alternating electrical fields. As a consequence, you do not get a simple nonlinearity across the crystal, but effective nonlinearity along the crystal is inverted periodically after a certain distance. The effective period of the crystal is now another degree of freedom in achieving phase matching. It can even be tuned by varying the temperature of the crystal. This has several consequences: phase matching is easier to achieve, one can use longer crystals, one will get higher output intensities and there are collinear solutions of the phase matching condition. So you can generate entangled photons of degenerate wavelength not emitted on some cones in space, but instead rather looking like parallel beams going through the crystal. This gives you modes of good brightness. However, you now need to separate these modes somehow - both output modes of interest are traveling along the same path now. This can be easily done when losing a lot of light is ok, but that somewhat weakens the point of having a bright source.

One way out is the Sagnac interferometer geometry. You have your pump light hit a polarizing beam splitter, which is the entry and exit port of a triangular interferometer. In the middle of the interferometer, you have the nonlinear crystal and at one of the entry ports of the interferometer you have a half wave plate which makes the polarization of the two countercirculating beams indistinguishable and corrects for travel time differences of the two beams. You now get two counterpropagating beams which again will leave the interferometer via the two exit ports formed by the polarizing beam splitter. The exact state created depends on the geometry of the interferometer and the phase of the pump beam. When that phase is chosen right, you will get rather bright Bell states at the output without losing much light.

This is just a very short summary. There are some publications about this kind of light source like "A wavelength-tunable fiber-coupled source of narrowband entangled photons", Alessandro Fedrizzi, Thomas Herbst, Andreas Poppe, Thomas Jennewein, and Anton Zeilinger, Optics Express, Vol. 15, Issue 23, pp. 15377-15386 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?&uri=oe-15-23-15377

or "Pulsed Sagnac source of polarization entangled photon pairs", Ana Predojević, Stephanie Grabher, and Gregor Weihs, Optics Express, Vol. 20, Issue 22, pp. 25022-25029 (2012) http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-20-22-25022

There are more publications, but these two have been published in Optics Express which is open access, so everyone should be able to have access to these articles.

 

[DrChinese]

Well, I am not sure about the authors' motivation to use this kind of source. It might be that they did not want momentum entanglement. It might also be that they needed a rather bright source to overcome the dark count rates of all the avalanche diodes. I am not sure.

I am also not really an expert in entangled sources, so take the following summary with a grain of salt. If someone knows more details, he is free to correct me. The "traditional" entangled light source is a bulk nonlinear crystal like KTP or some similar material. The critical property in realizing entangled photon sources is the phase matching condition. In these bulk crystals you can use the birefringence of the crystal and the angle to get the matching right. However, this usually means that you will get emission on two intersecting cones (the standard momentum spread in two directions) and as the phase matching condition is quite picky, you need high power light sources to get reasonable amounts of light. For pulsed light, this typically means you need to get femtosecond pulses which are spectrally quite broad. Even worse, you also cannot increase efficiency by using longer crystals as you will not be able to get phase matching over the whole length of the crystal.

Over the course of time different strategies of creating entangled photon sources have emerges. One of them lies in using periodically poled (PP) nonlinear crystals like PPKTP or PPLiNb. While you grow these nonlinear crystals, you apply alternating electrical fields. As a consequence, you do not get a simple nonlinearity across the crystal, but effective nonlinearity along the crystal is inverted periodically after a certain distance. The effective period of the crystal is now another degree of freedom in achieving phase matching. It can even be tuned by varying the temperature of the crystal. This has several consequences: phase matching is easier to achieve, one can use longer crystals, one will get higher output intensities and there are collinear solutions of the phase matching condition. So you can generate entangled photons of degenerate wavelength not emitted on some cones in space, but instead rather looking like parallel beams going through the crystal. This gives you modes of good brightness. However, you now need to separate these modes somehow - both output modes of interest are traveling along the same path now. This can be easily done when losing a lot of light is ok, but that somewhat weakens the point of having a bright source.

One way out is the Sagnac interferometer geometry. You have your pump light hit a polarizing beam splitter, which is the entry and exit port of a triangular interferometer. In the middle of the interferometer, you have the nonlinear crystal and at one of the entry ports of the interferometer you have a half wave plate which makes the polarization of the two countercirculating beams indistinguishable and corrects for travel time differences of the two beams. You now get two counterpropagating beams which again will leave the interferometer via the two exit ports formed by the polarizing beam splitter. The exact state created depends on the geometry of the interferometer and the phase of the pump beam. When that phase is chosen right, you will get rather bright Bell states at the output without losing much light.

This is just a very short summary. There are some publications about this kind of light source like "A wavelength-tunable fiber-coupled source of narrowband entangled photons", Alessandro Fedrizzi, Thomas Herbst, Andreas Poppe, Thomas Jennewein, and Anton Zeilinger, Optics Express, Vol. 15, Issue 23, pp. 15377-15386 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?&uri=oe-15-23-15377

or "Pulsed Sagnac source of polarization entangled photon pairs", Ana Predojević, Stephanie Grabher, and Gregor Weihs, Optics Express, Vol. 20, Issue 22, pp. 25022-25029 (2012) http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-20-22-25022

There are more publications, but these two have been published in Optics Express which is open access, so everyone should be able to have access to these articles.

Thanks for the explanation. I will review these excellent references as well.

-DrC

 

[DevilsAvocado]

Very cool!

This looks like the key sentences to me:

“The fringes are complementary because of the phase difference between the states heralded by D1 and D2. If we instead choose to herald using D1 or D2 without distinguishing between the two, there is no interference pattern. This is because we effectively ignore the polarization state of the trigger photon, leaving the signal photon in a mixed state. This can be seen as a nonlocal manifestation of a quantum eraser.”

And the video is of course helpful:

Double-slit interference buildup
https://www.youtube.com/watch?v=H11hJWIcUY0
http://www.youtube.com/watch?v=H11hJWIcUY0

 

[DevilsAvocado]

I am also not really an expert in entangled sources, so take the following summary with a grain of salt.

Sure looks like the ultimate source guru to me (i.e. an Avocado ).

Seriously Cthugha, do you know if there’s any hope of getting (almost) “clean” entangled photons, i.e. without the noise? And if – wouldn’t that be the final 100% closing of “loopholes”?