Oh what an entangled web we weave...

(Above: The nerdy license plate of fellow Augustana College physics professor Cecilia Vogel, referencing the famous 1935 Phys. Rev. paper by Einstein, Podolsky, and Rosen which introduced the idea of entanglement and questioned the completeness of a quantum mechanical description of reality)

Looking back through some of the literature in photonics and optics published this summer, I was most fascinated by three experiments concerning reliable generation of entangled photons. Two groups, one from China¹ and another from Vienna², showed independent reports of heralded generation of entangled photon pairs. Another, from Toshiba of Europe , demonstrated 'on-demand' entangled photons from a quantum dot embedded inside an LED, making an entangled-LED or more simply, ELED³. These works have been nicely summarized in the News and Views section in the August issue of Nature Photonics: “Entangled photons report for duty,” by Pieter Kok⁴ and “A spooky light-emitting diode” by Val Zwiller⁵ .

For me, quantum entanglement may be one of the coolest and weirdest properties of light. Entanglement ‘spooked’ Einstein and led to a paradigm shift in our fundamental understanding of the nature of measurement and reality. Particles of matter or light don’t live in well defined states until we force them to by a measurement. This is already weird, but now if they are entangled, the measuring process is shown to be nonlocal–a measurement on one particle simultaneously determines the state of the other.

As a young graduate student, I found myself filling up conference itineraries with talks on quantum computing, cryptography, and key distribution. My head spun with trying to understand all the bras and kets that accompanied explanations of quantum information protocols. Admittedly, I should have paid better attention in modern physics and quantum mechanics when I was a student (sorry professors Vogel, Coppersmith, and Drell!). However, frustrated with Alice, Bob, and that pesky Eve, my reaction was to give up, and since my research dealt with large numbers of photons, I decided to happily and naïvely live in a classical world.

The recent News and Views articles by Kok and Zwiller stirred the inner physicist within me, and sent me down a path of literature searching too detailed, too mathy , and too long for a blog post. However, I’ve attempted to give my own understanding of how the exciting work of heralded and on-demand entangled photon sources can be put into a broader context. If you’re a beginner like me and want more information on the fundamentals of quantum information, I recommend Kok’s website and review article⁶, Gisin’s review⁷, and Dehlinger’s article geared for setting up entanglement experiments for the advanced undergraduate laboratory curriculum⁸.

Whether or not you’re a practicing quantum mechanic, you likely know that entanglement is a crucial ingredient for quantum information processing. Entanglement using photons may be the best method for practically achieving quantum computing and for quantum communication due to their coherence, low transmission loss, and ease of manipulation. The most widely used method for generating entangled photon-pairs is through spontaneous parametric down-conversion in a nonlinear crystal (SPDC). This technique is so robust that it has recently been employed in a number of undergraduate teaching labs to help physics students understand the photonic nature of light and the non-intuitive implications of quantum mechanics^8,9,10.

Beating the odds

The problem with SPDC is that the process of pair generation is probabilistic. More often than not, zero or multiple pairs are generated, see Fig 1 (a). Like a game of black-jack at a Vegas card table, more often than not you don’t get the cards want, and so more often than not, the house wins. However, if you are clever and can count cards, you can guarantee a win even though the odds are against you. You aren’t changing the probability distribution of what is being dealt, you are just predicting what will be played. You can select which cards you want and pass on others without having to see their face values. In the language of quantum entanglement, you would be 'heralding' or announcing the cards you want before they are dealt.
Figure 1. reproduced and adapted from ref. 4. Creating entangled photon pairs. (a) In normal operation, a parametric down-converter (PDC) produces an unknown number of entangled photon pairs in each pulse. Detectors must then ‘post-select’ the correct events that contain exactly one pair. (b) The basic setup used by Pan and Walther's lab; a particular four-photon detection event can occur only when three pairs are present, with the remaining two entangled photons propagating freely. This creates precisely one ‘heralded’ entangled photon pair.

The heralded entangled photon source produced by Jian-Wie Pan’s lab in China¹ and Philip Walther’s lab in Vienna² was done through clever counting. Both groups used a setup similar to Fig 1. (b) such that when three photon pairs were generated simultaneously by SPDC, two of the pairs would be ‘peeled off’⁴ by the beam splitters, and remaining would be guaranteed to be a single entangled pair. Essentially, the simultaneous firing of four detectors at the outputs of the ‘peel off’- beam splitter herald a single remaining entangled photon pair. You have to wait for a three-photon pair event, but you can be guaranteed an entangled output.

Fig. 2 (a) Reproduced and adapted from from ref. 3. Schematic of the active region of the ELED, showing the emission of a polarization entangled photon pair through the biexciton cascade. (b) reproduced from ref. 5. Optical microscope image of the from Toshiba Europe.

Another way to beat the house is to change the probability of cards drawn- use your own deck. Salter et al.³ from the Shileds group of Toshiba Europe essentially took this approach to creating entangled photon pairs by using an entirely different physical mechanism than SPDC. Using the radiative decay of the biexciton state in a quantum dot Fig. 2 (a) , the Toshiba group created an ‘on-demand’ entangled source. The biexciton state is created by the capture of two electrons and two holes. So long as the two excitons are degenerate in energy (no fine structure splitting) the output will be entangled. In fact, one of the experimental hurdles overcome by the Tohsiba group was to grow quantum dots emitting photons of the right energy, near 1.4 eV (887 nm), in order to have very small fine-structure splitting. Because the source is not probabilistic and no clever counting setups are needed, it is referred to as ‘sub-Poissonian’⁵. What makes Salter’s work so hot is that the on-demand source is driven electrically. No bulky pump lasers are needed like they are for an SPDC source. The entangled-LED, or ELED, could possibly be scaled down to submicron sizes for on-chip integration⁵, see the microscope image in Fig. 2 (b).

Limitations

Though each technique is a groundbreaking achievement, there are a number of practical limitations to be overcome. The rate at which either gives entangled pairs is quite low. For heralded pair generation using a typical SPDC setup, the rate of three-photon events, from which you cleverly select a single pair, ranges from 0.001 to 0.1 Hz². Cranking up the pump laser power can give you more three-pair events, but then it will start to give you four-pair events as well, which will trigger your detectors and give a false-positive.

For the ELED, the Toshiba group showed an entangled pair rate of 3.0 Hz. This can be improved by increasing the coupling efficiency as well as increasing the injection current. Intrinsically, this device shows better promise as an ‘on-demand’ source since the probability of generating and entangled pair per voltage pulse is 3%³ - about 10,000 times more probable than generating a three-photon pair in SPDC⁴.

Both techniques show an entanglement fidelity of more than 80%. The primary reason that heralded generation using SPDC comes up short of perfect entanglement is due to the nonzero probability of the creation of simultaneous four-photon pairs. As mentioned above, four-photon events will also simultaneously trigger your detectors and give you a two-pair output instead of the single pair you expect. The imperfect entanglement in the ELED made by Toshiba primarily comes from unentangled background light from the surrounding diode structure. Eighty percent fidelity may not be useful for all quantum information protocols but is high enough for important components of quantum computing like teleportation and entanglement swapping³.

Finally, both techniques are not quite ready to be integrated on-chip. Walther et al.² made their pump source with a frequency doubled Ti:Sapphire laser Though Ti:Sapphs are the workhorses of ultrafast optics and are very robust (See earlier post for more details), they currently require a good amount of space on an optics table(roughly four feet long and 1 foot wide), expert knowledge of ultrafast optics to troubleshoot, and a good amount of money (~$100k). The ELED beats SPDC in this regard since it is compact and requires a simple low-voltage electrical pulse. Unfortunately, successful operation requires near-liquid helium temperatures. Salter et al.³ showed operation at a chilly 5 K.

Despite such hang-ups, one has to keep in mind the practicality of early computing and information processing. Could Mauchly and Eckert, the inventors of the ENIAC (which consumed 150 kW of power, used 18,000 vacuum tubes, and was so big that it needed to be housed in a 30 x 50 foot room) ever envisioned an iPod Touch? And even if the quantum version of the iPod Touch never materializes, perhaps this cool physics is just worth doing for its own sake.

References

1. C. Wagenknecht et al., "Experimental demonstration of a heralded entanglement source," Nature Photonics, 4, 549-552, (2010).

2. S. Barz et al., "Heralded generation of entangled photon pairs," Nature Photonics, 4, 553-556, (2010).

3. C. L. Salter et al., “An entangled-light-emitting diode,” Nature, 465, 594-597, (2010).

4. P. Kok, “Entangled photons report for duty,” Nature Photonics, 4, 504-505, (2010).

5. V. Zwiller, “A spooky light-emitting diode,” Nature Photonics, 4, 508-509, (2010).

6. P. Kok et al., “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys., 79, 135-174, (2007).

7. N. Gisin et al., “Quantum Cryptography,” Rev. Mod. Phys., 74, 145-195, (2002).

8. D. Dehlinger and W. M. Mitchell, “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” Am. J. Phys, 70, 903-910, (2002).

9. E. J. Galvez et al., “Interference with correlated photons: five quantum mechanics experiments for undergraduates,” Am. J. Phys, 73, 127-140, (2005).

10. J.J. Thorn et al., “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys, 72, 1210-1219, (2004).