Hologram of a Single Photon

Hologram of a single photon: reconstructed from raw measurements (left) and theoretically predicted (right) (Source: FUW)

Hologram of a single photon: reconstructed from raw measurements (left) and theoretically predicted (right) (Source: FUW)

Until quite recently, creating a hologram of a single photon was believed to be impossible due to fundamental laws of physics. However, scientists at the Faculty of Physics, University of Warsaw, have successfully applied concepts of classical holo­graphy to the world of quantum phenomena. A new measurement technique has enabled them to register the first ever hologram of a single light particle, thereby shedding new light on the foundations of quantum mechanics.

“We performed a relatively simple experiment to measure and view something incredibly difficult to observe: the shape of wavefronts of a single photon,” says Radoslaw Chrap­kiewicz. In standard photo­graphy, individual points of an image register light intensity only. In classical holography, the inter­ference phenomenon also registers the phase of the light waves. When a hologram is created, a well-described, un­disturbed reference wave is super­imposed with another wave of the same wavelength but reflected from a three-dimensional object. This results in inter­ference and the phase differences between the two waves create a complex pattern of lines. Such a hologram is then illu­minated with a beam of reference light to recreate the spatial structure of wave­fronts of the light reflected from the object, and as such its 3D shape.

One might think that a similar mechanism would be observed when the number of photons creating the two waves were reduced to a minimum, that is to a single reference photon and a single photon reflected by the object. And yet you’d be wrong! The phase of individual photons continues to fluctuate, which makes classical inter­ference with other photons im­possible. Since the Warsaw physicists were facing a seemingly impossible task, they attempted to tackle the issue dif­ferently: rather than using classical inter­ference of electro­magnetic waves, they tried to register quantum inter­ference in which the wave functions of photons interact.

Wave function is a funda­mental concept in quantum mechanics and the core of its most important equation: the Schrö­dinger equation. The function could be compared to putty in the hands of a sculptor: when expertly shaped, it can be used to mould a model of a quantum particle system. Physicists are always trying to learn about the wave function of a particle in a given system, since the square of its modulus represents the distri­bution of the proba­bility of finding the particle in a particular state, which is highly useful. “All this may sound rather complicated, but in practice our experiment is simple at its core: instead of looking at changing light inten­sity, we look at the changing proba­bility of registering pairs of photons after the quantum inter­ference,” explains doctoral student Michal Jachura.

Scheme of the experimental setup for measuring holograms of single photons (Source: FUW)

Scheme of the experimental setup for measuring holograms of single photons (Source: FUW)

Why pairs of photons? A year ago, Chrap­kiewicz and Jachura used an innovative camera built at the University of Warsaw to film the behaviour of pairs of distin­guishable and non-distin­guishable photons entering a beam splitter. When the photons are distin­guishable, their behaviour at the beam splitter is random: one or both photons can be transmitted or reflected. Non-distinguishable photons exhibit quantum inter­ference, which alters their behaviour: they join into pairs and are always transmitted or reflected together. This is known as two-photon inter­ference or the Hong-Ou-Mandel effect. “Following this experiment, we were inspired to ask whether two-photon quantum inter­ference could be used similarly to classical inter­ference in holography in order to use known-state photons to gain further information about unknown-state photons. Our analysis led us to a surprising conclusion: it turned out that when two photons exhibit quantum inter­ference, the course of this interference depends on the shape of their wavefronts,” says Chrap­kiewicz.

Quantum interference can be observed by regis­tering pairs of photons. The experiment needs to be repeated several times, always with two photons with identical properties. To meet these conditions, each experiment started with a pair of photons with flat wavefronts and perpen­dicular pola­risations; this means that the electrical field of each photon vibrated in a single plane only, and these planes were perpen­dicular for the two photons. The different polari­sation made it possible to separate the photons in a crystal and make one of them unknown by curving their wavefronts using a cylin­drical lens. Once the photons were reflected by mirrors, they were directed towards the beam splitter. The splitter didn’t change the direction of verti­cally-polarised photons, but it did diverge diplace hori­zontally-polarised photons. In order to make each direction equally probable and to make sure the crystal acted as a beam splitter, the planes of photon polari­sation were bent by 45° before the photons entered the splitter. The photons were registered using the state-of-the-art camera designed for the previous experiments. By repeating the measure­ments several times, the researchers obtained an interference image corres­ponding to the hologram of the unknown photon viewed from a single point in space. The image was used to fully reconstruct the amplitude and phase of the wave function of the unknown photon.

The experiment is a major step towards improving our under­standing of the fundamental principles of quantum mechanics. Until now, there has not been a simple experi­mental method of gaining information about the phase of a photon’s wave function. Although quantum mechanics has many applications, and it has been verified many times with a great degree of accuracy over the last century, we are still unable to explain what wave functions actually are: are they simply a handy mathematical tool, or are they something real? “Our experiment is one of the first allowing us to directly observe one of the fundamental parameters of photon’s wave function bringing us a step closer to under­standing what the wave function really is,” explains Jachura.

The Warsaw physicists used quantum holo­graphy to reconstruct wave function of an individual photon. Researchers hope that in the future they will be able to use a similar method to recreate wave functions of more complex quantum objects, such as certain atoms. Will quantum hol­ography find appli­cations beyond the lab to a similar extent as classical holo­graphy, which is routinely used in security, enter­tainment, transport, micro­scopic imaging and optical data storing and processing techno­logies? “It’s difficult to answer this question today. All of us must first get our heads around this new tool. It’s likely that real appli­cations of quantum holography won’t appear for a few decades yet, but if there’s one thing we can be sure of it’s that they will be surprising,” says Konrad Banaszek. (Source: Univ. Warsaw)

Reference: R. Chrapkiewicz et al.: Hologram of a single photon, Nat. Phot., online 18 July 2016, DOI: 10.1038/nphoton.2016.129

Link: Quantum Optics and Atomic Physics, Faculty of Physics, University of Warsaw, Poland

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