Carmen Rubio Verdú – Columbia University Postdoc Society Blog

Author: Carmen Rubio Verdú

Carmen obtained her PhD in experimental condensed matter physics at CIC nanoGUNE in San Sebastián (Spain). She is currently a Postdoctoral Research Fellow in the Physics Department. Her research focuses on quantum phenomena that emerge in materials that are one atom thick. At Columbia she uses a technique called Scanning Tunneling Microscopy that allows for the study of the electronic properties of materials at the atomic scale at cryogenic temperatures (that is, at -269 °C). During her PhD she was already involved in outreach activities related to science communication and very often with the focus on gender equality. As a Postdoc representative of the Climate, Diversity & Inclusion committee she is committed to foster an inclusive climate in the Physics Department.

Brute force is usually not the best approach when trying to understand physical phenomena. Physical systems are nothing but a collection of particles. In order to study how these particles interact with each other, theorists calculate the time-evolution of the whole ensemble. As the number of particles increases, calculations become not plausible. In this context, defining clever shortcuts may be the only way to study real systems. Columbia researchers have established a new theoretical framework that calculates the conditions under which a light burst is emitted by an array of atoms – a structure used in quantum computers. They found that they can predict whether the high intensity light pulse will be emitted by looking at the first moments, thus circumventing the need of solving for the whole time evolution.

Spontaneous light emission is responsible for most of the light that we see. Examples of spontaneous emission are fireflies and the bioluminiscent bay in Puerto Rico. The physical mechanism responsible for spontaneous emission is sketched in Fig. 1a: the emitter (an atom that can be in two different energy states) is excited to a higher energy state, for example by external light. From that excited state, it spontaneously decays to a lower energy level, releasing the energy difference between the two states as a photon, i.e., as light. This is a purely quantum-mechanical process that cannot be explained by classical physics.

If multiple atoms are placed far away from each other, they act as independent units. When relaxing, they emit photons at an intensity that is proportional to the number of atoms present in the system. However, if the distance between the atoms is very small, a phenomenon called Dicke superradiance occurs.

When the atoms are very close, they interact with each other. As a result, the system as a whole cannot be regarded as the sum of many individual entities but rather as a collective system. Imagine many atoms close together forming an array, an ordered structure. External light will excite one of them, but there is no way to determine which atom within the array is the one that is excited. Effectively, all atoms are excited and not excited at the same time, the same way that Schrödinger’s cat is dead and alive at the same time. In quantum mechanics this phenomenon is called superposition. When one of the atoms relaxes, the full atomic array decays as a whole and a photon is emitted in a particular direction.

If an excited atom is isolated, there is no reason why it should emit a photon in a particular direction. However, in a coupled atomic array, constructive and destructive interference creates what are called bright and dark channels. To understand this concept, we only need a lake and a handful of rocks. When a rock is thrown into a lake, it creates a circular pattern around it by emitting a wave that travels in all the possible directions. However, if one throws many rocks close to each other into the lake, the resulting wave does not travel in all possible directions: the waves from the individual rocks interfere. Some directions will not have waves due to individual waves traveling in opposite directions (destructive interference) and the wave pattern will result from the constructive interference of the individual waves (see Fig. 1c,d). That’s exactly what happens in the atomic array: a photon – which is a quantum object and therefore can behave as a particle as well as a wave – is emitted from each atom in all possible directions, but most of those photons interfere destructively and only a few of them survive, and those constitute bright channels.

**Figure 1. a.** Schematic representation of spontaneous emission. Left: the atom is in an excited state. Right: the atom relaxes to the ground state and emits light (a photon). b. A chain and a ring of atoms. c. Interference created by multiple initial wave fronts originated from the individual objects. d. Interference pattern created by two rocks thrown into the water.

Now let’s think about the second event of photon emission. When the atoms are far away from each other, each photon would be emitted in a random direction. Nevertheless, in an atomic array, the fact that the first photon is radiated along a particular direction makes it more likely for the second photon to be radiated in that same direction. It’s like an avalanche: once the first snow has started moving down along a path, the rest of the snow follows. Once the first photon is emitted along a particular direction, the next photons follow. And that creates the superradiant burst, a high intensity pulse of light.

Theoretical calculations of superradiance in systems of many atoms are not possible due to the complexity of the calculation – the computer memory and time needed are both prohibitive. What Masson and colleagues found is that, by looking at the first two photons, one can already know if there is going to be a superradiant burst. They can anticipate if the avalanche is going to happen. This means that the early dynamics define the nature of the light emission, and a calculation of the whole time-evolution is not necessary.

Since the distance between the atoms dictates the emergence of superradiance, one may ask whether the arrangement of the atoms plays any role. Before Masson’s work, the understanding in the field was that atomic chains and rings behave differently. In an atomic chain, the two atoms at the end are different from those in the middle, since the atom at the edge has only one partner whereas the one in the middle has two. On the other hand, in a ring, all the atoms have the same environment (see Fig. 1b). And this is certainly true for a system with very few atoms. But thanks to the authors’ theoretical approach, it is now possible to include many atoms in the calculation. And they found that, despite the atoms’ arrangement, superradiance occurs equally in chains and rings when the number of atoms is very high. The reason is that, for structures with several atoms, the influence of the two placed at the end of the chain is washed out by the effect of the many atoms located in the middle. Moreover, they also found that atoms can exhibit superradiance at much larger distances than expected.

Atomic arrays are used in atomic clocks, in GPS technology, and quantum computers. In quantum technologies, each atom is used as a bit, the unit of information – it represents a 1 or a 0 depending on if it is excited or relaxed. A byte contains eight bits. As a reference, Figure 1 contains 6000000 bytes. The common belief is that interactions between the atoms and the environment produce information loss with respect to a pure, isolated system. However, Masson and Asenjo-Garcia show that interactions between the atoms results in their synchronization, producing a coherent, high intensity light burst.

Researchers design an accessible, straightforward technique to characterize moiré systems – a class of materials built by placing slightly misaligned atomic monolayers on top of each other. Under certain conditions, such moiré structures exhibit exotic physical phenomena absent in the individual units that conform them.

A moiré pattern is an interference effect that arises when two grids are superimposed. It can be observed in the wrinkles of a mesh shirt and it is responsible for the fringes that appear when taking a picture of a computer screen. Moiré patterns are present in art and fashion, and in the last few years their effect in two-dimensional materials has entailed a revolution in physics.

Two-dimensional materials are those that are less than a nanometer thick. The first one to be isolated was graphene, a single-layer of carbon atoms (see Fig. 1a). Such discovery opened a whole new field of research and many labs around the world started making their own stacks – structures with two-dimensional materials placed on top of each other. If one were to place one of those layers slightly misaligned with the one below, a moiré pattern would emerge. This interference effect can be visualized in Fig. 1b. The small circles represent the carbon atoms that form a crystalline lattice (an ordered structure) on each graphene layer. The top layer is rotated with respect to the bottom one and, as a consequence, a periodicity larger than the atomic lattice emerges as highlighted in Fig. 1b.

In 2018, the field of condensed matter physics was stirred up: such moiré materials, at a very specific misalignment value called the magic angle, exhibit electronic states of matter that are not present in the individual layers, such as superconductivity or magnetism. The emergence of those electronic phases is a consequence of the moiré pattern and its direct visualization is critical for their understanding. There are a few techniques, including transmission electron microscopy and scanning tunneling microscopy that allow for this, but they require complex setups that do not necessarily work for any material, which has significantly slowed down the progress in the field. McGilly and colleagues show a new and simple technique based on piezoresponse force microscopy to visualize moiré patterns.

A piezoresponse force microscope consists of a sharp metallic tip brought into contact with the material under study – in this case, the moiré system (see Fig. 1c). Piezoresponsive materials are those that undergo a mechanical deformation in the presence of an electric field. In the microscope, the sample moves a small amount when a voltage is applied across it and the tip follows the motion. Such tip motion is measured as a voltage which is amplified to detectable values. The tip is then moved around the sample and the process is repeated on every pixel of a selected region, producing a map of the sample’s deformation.

a. Graphene atomic lattice. Each ball represents a carbon atom. b. Twisted graphene bilayers. The three main stacking configurations are shown (AA, AB and domain wall). The moiré unit cell is highlighted. c. Microscope tip in contact with the graphene bilayer d. The strain on the graphene layer bends the chemical bonds between the atoms from in-plane (left) to a mixed in-plane/out-of-plane character (right).

In principle, it was not obvious that a moiré pattern would be detectable with the microscope. When moiré patterns form, it creates a repetitive set of individual units that are called unit cells (highlighted region in Fig. 1b). Each unit cell is formed by regions with different atomic three-dimensional configurations, called sites. In the case of graphene, those sites are called AA and AB which stands for how the atoms from each layer lie on top of each other (see insets in Fig. 1b). The AB regions (also called domains) are separated by domain walls, as highlighted in Fig. 1b. McGilly and colleagues show that the voltage signal detected with the microscope is localized on the domain walls.

When the moiré pattern forms, the atomic layers relax to accommodate it and the layer wrinkles along the domain wall (see right panel in Fig. 1d). Since the microscope is not sensitive to such small deformation, the origin of the detected signal must be electronic. Flat graphene layers have planar bonds, as shown in the left panel of Fig. 1d. However, the curvature of the wrinkle bends the atomic bonds on the graphene layer, which in turn causes an asymmetric distribution of the charge in the vertical direction and gives rise to an out-of-plane polarization (P), which is responsible for the signal measured in the microscope.

The technique designed by McGilly and colleagues has been proven extremely useful for the advancement of the field due to the simplicity of the method and the fact that it allows imaging of any moiré pattern, independently of the nature of the individual units that conform it – that is, whether they are metals, semiconductors or insulators. Being able to image moiré patterns with such an accessible technique will help improve the fabrication process, and having uniform samples is critical since strain gradients can significantly alter the states of matter that emerge in moiré materials.

Dr. Leo McGilly is a Postdoctoral Research Fellow in the Physics Department at Columbia University.

Author: Carmen Rubio Verdú

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