Physical phenomena occurring on the subatomic scales are described by the laws of quantum physics, which are often in conflict with our everyday "classical" intuition. The paradoxical behavior of quantum matter is revealed primarily when we measure a physical quantity that the laws of quantum mechanics do not allow us to determine with arbitrarily high accuracy at the microscopic level. In such a situation, as a result of a single measurement we obtain an unambiguous, very accurate value of the measured physical quantity, but when the experiment is repeated many times we will get slightly different results each time. And although the first impression is that they are completely random, a closer analysis of the results shows that they are not completely independent from each other but somehow correlated. It turns out that, although these correlations have no counterparts in the classical world, they are very well described and predicted by the laws of quantum physics. Therefore, the study of quantum correlations is an inspiration for physicists who want to better understand the laws that govern the micro-world, because they can allow to harness the behavior of matter at the subatomic level.

Exploring the relationship between non-classical correlations in quantum systems and the parameters of external triggers under experimentalists' control is not just an academic task, but may have practical significance. Indeed, if quantum correlations could be controlled on demand, it would become possible to use them to solve abstract problems whose solution on classical computers is very time-consuming, if feasible at all. This concept is one of the pillars of the upcoming so-called second quantum revolution which aims to use quantum correlations for processing and transmitting digital information.

Depending on the choice of a quantum system and the choice of measurement method, the non-classical correlations existing in the system can manifest themselves in different ways. For example, in a microscopic system consisting of many identical interacting quantum particles (e.g., atoms in a very cold gas, or electrons in a conductor), the internal correlations are preferably measured by making independent measurements on two of its subsystems and then checking how the obtained results are correlated with each other. It is a common belief that in such situations quantum correlations significantly depend not only on how strong and what kind of interactions between the particles are but also on the external forces acting on them. This is because we know, for example, that a sufficiently strong external magnetic field can destroy the quantum correlations responsible for superconductivity, or that the correlations between subsystems in a quantum atomic gas depend on the external forces that hold the gas in a particular region of space. For various many-body quantum systems, however, the relationship between quantum correlations and external control parameters is still not fully known and requires detailed research.

The work of Kościk and Sowiński brings another surprising result in this research. The physicists have analyzed non-classical correlations in a specific quantum system of interacting identical atoms contained in an external trap. In such systems, measurements made on individual subsystems quite naturally depend on the shape of the trap in which they are placed. It is easy to imagine this by focusing, for example, on measuring the position of individual atoms - atoms tend to accumulate at the minima of the trapping potential, so by changing its shape we change the result of the measurements. If atoms interact with each other and are not completely independent, the same will happen with correlations between atoms, because they are directly related to the measurements themselves. However, as the authors have shown, there is an exception to this seemingly obvious rule. If the atoms obey fermionic statistics (see footnote), are placed in a trap that allows motion in only one dimension (the trap in the other two directions is so tight that transverse motion is not possible), and interactions between them are of a short-range and attractive nature, the non-classical correlations between any two subsystems of such a gas (being in the ground state) turn out to be independent of the shape of the trapping potential.

In the precise language of quantum mechanics, this surprising result can be described as follows. The many-body ground-state wave function of such a system does significantly depend on an external trapping potential. However, the reduced density matrix describing any fraction of this system (containing all information about the correlations of the subsystem with the rest of the system) has a spectral distribution (eigenvalues) completely independent of this potential.

Is the quantum system found the only one whose quantum correlations are universal, i.e. insensitive to external potential? We don't know, but the demonstration that at least one such system exists changes the way we think about quantum correlations in many-body systems. An element that enhances this purely theoretical result is that, although such a system seems rather unusual, its experimental realization is possible using present-day techniques for cooling and trapping atomic gases.

FOOTNOTE:

Elementary particles can be divided into two disjoint groups: bosons and fermions. Bosons are particles that carry interactions (such as a photon). The matter is composed of fermions. These include both quarks, of which baryons (e.g., protons and neutrons) and leptons (e.g., the electron) are composed. According to the laws of physics, objects composed of several fermions, as long as their internal structure does not change, should be treated either as bosons (if they consist of an even number of fermions) or as fermions (if they consist of an odd number of fermions). Therefore, protons and neutrons are fermions (composed of three quarks), while, for example, a hydrogen atom is a boson (composed of one proton and one electron). The fermionic atoms discussed here are all those atoms that consist of an odd number of fermions. In experiments with ultracold atoms, the most common is lithium-6 (three protons, three neutrons, three electrons), or potassium-44 (19 protons, 25 neutrons, 19 electrons).

The most important difference between bosons and fermions is that, flowing directly from the laws of relativistic quantum mechanics, fermions are subject to the so-called Pauli rule. It says that no two fermions can be in the same quantum state. Therefore, if we are dealing with identical fermions (i.e., being in exactly the same internal quantum state), they must be in a different spatial state. Thanks to this rule, atoms, chemical molecules, and all other more complex structures of matter exist.