Can we observe a single photon

Crystallizing photons - when light becomes matter

Research Report 2017 - Max Planck Institute for the Physics of Complex Systems

Max Planck Institute for the Physics of Complex Systems, Dresden
The interaction between atoms and photons (light particles) has been researched for a long time. But it has only been possible to control this very precisely for a few years. The results are fascinating. In particular, atoms can be used to create a strong interaction between photons. As a many-body system, a collection of interacting photons is a highly interesting research object, the investigation of which only scratches the surface of a complex and new phenomenology. And indeed: under certain conditions, photons crystallize - light becomes, so to speak, matter.


Albert Einstein explained the photoelectric effect in 1905: light consists of individual corpuscles (so-called photons), each of which collides with individual electrons and stimulates them in stages. Light, i.e. electromagnetic waves, can therefore also behave like particles. The wave-particle dualism started here and was only resolved much later by quantum theory.

If you want to create matter out of light, you are faced with two obstacles: 1. The photons have no mass and can disappear, that is, their number is not preserved even with the lowest energies. 2. The photons do not interact with each other.

The possibility of providing light particles with these two properties is extremely interesting both for the investigation of fundamental questions in many-body physics and for the development of (quantum) technologies, especially in the field of communication and signal processing [1].

Non-linear media

In practice, the crucial step is to let the light propagate through certain media. On the one hand, the photons can be confined in such a way that they move as if they had a mass. This is done, for example, through mirrors or materials that have a higher refractive index than air, such as dielectrics. On the other hand, the photons should interact with one another. For this, the medium through which the photons propagate must react non-linearly to light excitation, so the change in the medium generated by the light must grow faster than linear with the light intensity, i.e. with the number of photons. This leads to an effective interaction between photons, because one photon then feels every movement of another photon across the medium.

This article deals with the exciting properties of interacting photons as a many-body system and, in particular, with the possibility that a crystal can even form as a result of the interaction between the photons. In the following we will explain this phenomenon - based on a certain realization in a medium of ultra-cold, neutral atoms.

Photons in neutrals, atomic media

At the level of elementary particles, photons only interact with charged particles, such as electrons. Photons can also interact with neutral (i.e. not charged) particles if such particles consist of several charged elementary particles.

This is the case, for example, with an atom that contains the same number of positively charged protons and negatively charged electrons. If the frequency of the light, i.e. the energy of the photons, is not so high that they can excite a proton from the atomic nucleus, photons then only interact effectively with the outer electrons. The latter are excited or de-excited by absorption or emission of photons between different “paths” around the core - quantum mechanically actually between quantized energy levels.

Using a cloud of such neutral atoms as a nonlinear medium for light is very practical because control over the interaction between photons and atoms has made tremendous advances over the past 30 years. Experimenters can now prepare the internal, electronic excitations as well as the position and temperature of atoms very precisely [2,3].

If the frequency of the incident light is far enough below the next, electronic excitation energy within an atom, the atom-photon interaction is in the so-called “dispersive regime”: Here the atomic cloud acts like a density-dependent refractive index for the light and, conversely, an atom senses one Attraction in the direction in which the light intensity (photon density) is higher.

Under these conditions, a spatially homogeneous cloud of atoms can generate an interaction between photons, which can cause the photons to crystallize.

Crystallizing light

Particles form a crystal by arranging themselves in space in such a way that their density is periodically modulated. The spontaneous refraction of the spatial translational invariance of the system is essential for the process of crystallization. Applied to our system, this means that an initially spatially homogeneous distribution of photons (and atoms) crystallizes by adopting a periodic arrangement in which the particle density oscillates at regular intervals between a minimum and a maximum value. The breaking of the translation invariance is spontaneous insofar as the position of the periodically repeating maximum values ​​is not fixed, but arises randomly.

Why do photons crystallize? As already explained, in the dispersive regime the atoms act as a medium with a refractive index that is proportional to the local atomic density. A spatial variation of the refractive index produces a backscattering of the light, according to which the photon density is periodically modulated with the light wavelength. Again we know that atoms are drawn to exactly where the density of photons is highest. This means that the interaction between two photons brought about by atoms favors the configuration in which they are separated by an integral multiple of the wavelength of light - a crystalline arrangement!

Based on such considerations, we proposed an experiment in which a homogeneous atomic cloud is irradiated by two oppositely propagating lasers so that the light intensity is initially homogeneous [4]. Although the interaction between photons favors a crystalline arrangement, this is not always adopted, but only when the intensity of the laser exceeds a certain threshold. This threshold is proportional to the typical kinetic energy of an atom and in particular to the temperature of the atomic cloud.

Fortunately, the group of Nobel Prize winner Prof. Wolfgang Ketterle at the Massachusetts Institute of Technology (MIT) in Boston implemented our proposal a few months later and was able to observe the crystallization of the photons in the laboratory [5]. This discovery, intriguing in itself, raises many more fundamental questions and opens up new avenues for studying the properties of this new type of many-body system.


Chang, D .; Vuletic, V .; Lukin, M. D .:
Quantum nonlinear optics - photon by photon.
Nature Photonics 8, 685 (2014)
Dalfovo, F .; Giorgini, S .; Pitaevskii, L. P .; Stringari, S:
Theory of Bose-Einstein condensation in trapped gases
Rev. Mod. Phys. 71, 463 (1999)
Bloch, I .; Dalibard, J .; Zwerger, W .:
Many-body physics with ultra-cold gases.
Rev. Mod. Phys. 80, 885 (2008)
Ostermann, S .; Piazza, F .; Ritsch, H .:
Spontaneous crystallization of light and ultracold atoms.
Phys. Rev. X 6, 021026 (2016)
Dimitrova, I .; Lunden, W .; Amato-Grill, J .; Jepsen, N .; Yu, Y .; Messer, M .; Rigaldo, T .; Puentes, G .; Weld, D .; Ketterle, W .:
Observation of New Superradiant Regimes in a Bose-Einstein Condensate.