Watching Atoms Make Waves
When light hits an atom, it exerts a force on the atom. As weak as these light-induced forces may be, understanding them allows scientists to levitate particles, create the coldest atomic gases in the Universe, operate solar sails, and observe gravitational waves. More exotic phenomena occur when light is confined between a pair of mirrors known as an optical cavity. When a gas of atoms is placed inside such a cavity, light emitted by one atom can be absorbed by another atom. Through the exchange of photons, each atom simultaneously tugs on all the other atoms, causing the ensemble to autonomously rearrange itself into a periodic pattern called a density wave. Now Jean-Philippe Brantut and his colleagues at the Swiss Federal Institute of Technology in Lausanne (EPFL) have built a microscope to, for the first time, image this light-induced density wave in an ultracold atomic gas [1]. The team’s work tests the foundations of light-induced spatial ordering and uncovers microscopic details about phases of matter displaying collective interactions.
The density wave formed by an atomic gas in an optical cavity varies depending on the spatial structure of the light hitting the atoms. In their experiments, Brantut and his colleagues placed an ultracold gas of lithium atoms in a cavity (Fig. 1). They then illuminated the gas with a “pump” laser beam that was tilted at an angle from the cavity axis and that formed a standing electromagnetic wave within the cavity. The atoms began to scatter light into the cavity as the researchers increased the pump power beyond a certain threshold, crossing what is known as a superradiant phase transition [2–4]. The light inside the cavity, which also formed a standing wave, then interfered with the pump light to create a 2D lattice potential into which the atoms settled.
The superradiance harnessed by the researchers refers to an effect in which constructive interference causes the intensity of light generated by multiple emitters to scale as the square of the number of emitters. In the original formulation of superradiance, Robert Dicke considered N excited molecules confined to a space much smaller than the emitted light’s wavelength, so that photons from different molecules are indistinguishable [5]. This indistinguishability leads to constructive interference in the produced light, whose maximal electromagnetic-field amplitude scales as N and whose intensity scales as N2. In the current setup, there is no need to pack atoms within a single wavelength of light. That is because the amplitude and phase of the light emitted by an atom depend on the atom’s position with respect to the periodic pump–cavity lattice. Above the critical pump power, inherent density fluctuations in the gas result in atoms emitting in phase with one another. This light pulls the atoms collectively into a density wave, which encourages their superradiant emission.
Spatial self-organization of the atoms is thus intertwined with the intensity of light inside the cavity. For many years, scientists have focused on measuring the number of cavity photons and other global observables [2]. Until now, local structures have been hidden from view. To directly image density waves, Brantut and his colleagues constructed a microscope with a spatial resolution of 1.7 µm, which is small enough to resolve the large-scale structure of the waves. They then applied a technique called absorption imaging, which involved looking at the shadow formed by the atoms on a beam of light sent through the microscope. Doing so, they saw density ripples emerge in their atom snapshots and confirmed that the periodicity of these ripples matched that of the large-scale structure of the pump–cavity lattice.
The researchers then confirmed that the onset of spatial ordering coincided with the superradiant emission of cavity photons. They examined the correlations between the amplitude of the cavity’s electric field and the amplitude of the density wave’s spatial modulation, finding that these two quantities track each other. Leveraging their ability to study these correlations, the researchers set out to test a long-standing theory of cavity-mediated self-organization: that the cavity field instantaneously adjusts to the atomic motion when the pump frequency is detuned far from cavity resonance. The team saw this effect play out in large, correlated fluctuations between the density modulation and the cavity field. These large fluctuations show that the cavity field cannot be described as a single coherent state and instead behaves like a statistical mixture of different coherent states [6, 7].
The team’s microscope can also resolve more complex spatial structures, which were previously impossible to observe. The phase of the density wave depends on the phase of the transverse electromagnetic mode of the cavity. Previous experiments were conducted with the pump frequency near the resonance of the fundamental mode, which has a uniform phase profile. Brantut and his colleagues instead investigated what happens with a nonuniform phase profile, which they achieved by setting the pump frequency in the vicinity of a first-order mode’s resonance. They saw distinct features of this mode replicated in their density-wave images. Using this technique, they were thus able to study the effects of higher-order cavity modes on spatial self-organization.
Having validated a long-standing theory behind cavity-mediated self-ordering, this work offers a new paradigm for studying systems involving cavity-induced, long-range interactions. For instance, the microscopy technique could be extended to phase-contrast microscopy of spin magnetization patterns [8, 9]. One could also explore the effects of competing phase patterns on spatial ordering. That task might be achieved by coupling atoms to many transverse electromagnetic modes simultaneously or by imposing different spatial patterns onto the pump beam. By combining the microscopy approach with various other tools in the atomic-physics toolbox, scientists could soon be taking pictures of new phases of matter exhibiting exotic spatial order.
References
- T. Bühler et al., “Microscopy of cavity-induced density-wave ordering in ultracold gases,” Phys. Rev. Lett. 136, 143401 (2026).
- K. Baumann et al., “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301 (2010).
- P. Kirton et al., “Introduction to the Dicke model: From equilibrium to nonequilibrium, and vice versa,” Adv. Quantum Tech. 2, 1800043 (2018).
- F. Mivehvar et al., “Cavity QED with quantum gases: New paradigms in many-body physics,” Adv. Phys. 70, 1 (2021).
- R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99 (1954).
- C.-M. Halati et al., “Numerically exact treatment of many-body self-organization in a cavity,” Phys. Rev. Lett. 125, 093604 (2020).
- C.-M. Halati et al., “Theoretical methods to treat a single dissipative bosonic mode coupled globally to an interacting many-body system,” Phys. Rev. Res. 2, 043255 (2020).
- G. B. Partridge et al., “Pairing and phase separation in a polarized Fermi gas,” Science 311, 503 (2006).
- Y. Shin et al., “Observation of phase separation in a strongly interacting imbalanced Fermi gas,” Phys. Rev. Lett. 97, 030401 (2006).