Whether magnets or superconductors: materials are known for their diverse properties. However, these properties can change spontaneously under extreme conditions. Researchers from Technische Universität Dresden (TUD) and Technische Universität München (TUM) have discovered an entirely new type of such phase transitions. They exhibit the phenomenon of quantum entanglement involving many atoms, which was previously observed only in the domain of a few atoms. The results were recently published in the scientific journal Nature.
In physics, Schroedinger’s cat is an allegory of two of the most impressive effects of quantum mechanics: entanglement and superposition. Researchers in Dresden and Munich have now observed these behaviors on a scale much larger than that of the smallest particle. Until now, materials that display properties such as, for example, magnetism, were known to have so-called domains – islands in which material properties are homogeneous either of one type or of a different type (imagine them being either black or white, for example). Looking at lithium holmium fluoride (LiHoF4), physicists have now discovered a whole new phase transition, during which domains surprisingly exhibit quantum mechanical characteristics, resulting in their properties becoming entangled (being black and white at the same time). “Our quantum cat now has new fur because we discovered a new quantum phase transition in LiHoF4 whose existence was not previously known,” comments Matthias Vojta, Chair of Theoretical Solid State Physics at TUD.
Phase transitions and entanglement
We can easily observe the spontaneously changing properties of a substance if we look at water: at 100 degrees Celsius it evaporates into a gas, at zero degrees Celsius it freezes into ice. In both cases, these new states of matter are formed as a result of a phase transition where water molecules rearrange themselves, thus changing the characteristics of matter. Properties such as magnetism or superconductivity emerge as a result of phase transitions of electrons in crystals. For phase transitions at temperatures approaching absolute zero at -273.15 degrees Celsius, quantum mechanical effects such as entanglement come into play, and these are referred to as quantum phase transitions. “Even though there are more than 30 years of extensive research devoted to phase transitions in quantum materials, we had previously assumed that the phenomenon of entanglement only plays a role at the microscopic scale, where it does not involved only a few atoms at a time.« , explains Christian Pfleiderer, professor of topology of correlated systems at the TUM.
Quantum entanglement is one of the most amazing phenomena in physics, where entangled quantum particles exist in a shared state of superposition that allows usually mutually exclusive properties (eg, black and white) to occur simultaneously. As a general rule, the laws of quantum mechanics only apply to microscopic particles. Research teams from Munich and Dresden have now succeeded in observing the effects of quantum entanglement on a much larger scale, that of thousands of atoms. For this, they chose to work with the well-known compound LiHoF4.
Spherical specimens enable precision measurements
At very low temperature, LiHoF4 acts as a ferromagnet where all magnetic moments spontaneously point in the same direction. If you then apply a magnetic field exactly vertically to the preferred magnetic direction, the magnetic moments will change direction, which are called fluctuations. The higher the magnetic field strength, the stronger these fluctuations become, until eventually the ferromagnetism disappears completely in a quantum phase transition. This leads to the entanglement of neighboring magnetic moments. “If you are holding a LiHoF4 sample to a very powerful magnet, it suddenly ceases to be magnetic spontaneously. It’s been known for 25 years,” summarizes Vojta.
What’s new is what happens when you change the direction of the magnetic field. “We discovered that the quantum phase transition continues to occur, whereas it was previously believed that even the smallest tilt of the magnetic field would immediately suppress it,” says Pfleiderer. Under these conditions, however, it is not individual magnetic moments but rather extended magnetic areas, called ferromagnetic domains, that undergo these quantum phase transitions. The domains constitute entire islands of magnetic moments pointing in the same direction. “We used spherical samples for our precision measurements. This allowed us to precisely study the behavior during small changes in direction of the magnetic field,” adds Andreas Wendl, who conducted the experiments as part of his doctoral thesis.
From fundamental physics to applications
“We discovered an entirely new kind of quantum phase transitions where entanglement takes place on the scale of many thousands of atoms instead of just a few in the microcosm,” says Vojta. “If you imagine the magnetic domains as a black and white pattern, the new phase transition leads to the white or black areas becoming infinitely small, i.e., they create a quantum pattern, before completely dissolve. A newly developed theoretical model successfully explains the data obtained from the experiments. “For our analysis, we generalized existing microscopic models and also took into account the feedback of large ferromagnetic domains on microscopic properties,” explains Heike Eisenlohr, who performed the calculations as part of his doctoral thesis.
The discovery of new quantum phase transitions is important as a foundation and general frame of reference for the search for quantum phenomena in materials, as well as for new applications. “Quantum entanglement is applied and used in technologies such as quantum sensors and quantum computers, among others,” says Vojta. Pfleiderer adds: “Our work falls into the realm of basic research, which can however have a direct impact on the development of practical applications, if you use the properties of materials in a controlled way. »
The research was financially supported by the Excellence Strategy of the German federal and state governments within the cluster of excellence Würzburg-Dresden Complexity and Topology in Quantum Matter (ct.qmat) and the cluster of Excellence Munich Center for Quantum Science and Technology (MCQST). In addition, the work was supported by the European Research Council (ERC) through the Advanced Grant ExQuiSid and by the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Centers (SFB) 1143 and TRR80.