Characterizing spontaneous quantum synchronization

The spontaneous synchronization between different interacting units is a paradigmatic example of a collective phenomenon. In the last decade there has been a growing interest among the scientific community to investigate this phenomenon in the context of quantum systems, in which it is not possible to observe their temporal trajectory. This has led to a great variety of ways to approach the study of spontaneous quantum synchronization.

In this context, a study carried out by researchers at the Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, UIB-CSIC) and published in the journal Physical Review Letters has studied the properties of a spontaneously synchronized quantum system in a one-dimensional network.

The system proposed by the researchers consists of a laser potential that couples quantum elements in the form of a one-dimensional chain. Each of the elements has two energy levels available, so due to its quantum character it can be found in one of them or in a superposition of both.

Spontaneously, the environment in which a quantum system is found acts as a dissipater and takes the system to its lowest energy state, increasing its decoherence. In this way it reduces its superposition, which is a purely quantum phenomenon. In the case in which an element is in a certain level (and not in a superposition of both), it is considered that the quantum element has suffered decoherence and is in a classic regime. The rate at which each of the elements of the quantum system decays into a classical regime, that is, the rate at which its decoherence increases, is called "decay rate" and depends on the characteristics of the element itself.

In the system proposed by the researchers, four of these two level quantum elements were connected in the form of a one-dimensional chain. Due to the interaction that exists between the elements when connected, several collective excitations are produced that can show synchronization. This synchronization is most evident when one of these collective excitations dominates the rest, i.e. it is less affected by the dissipative environment. This spontaneous phenomenon can be seen in the observables of the connected elements, which begin to oscillate in a coherent manner.

The researchers found that the greater the difference in the decay rate, the more dominant is one of the collective excitations and therefore greater synchronization appears in the system. In other words, the synchronization between quantum units is greater the greater the differences between their characteristic decay rates.

One of the most remarkable aspects of the study is its universality. The properties found are extensible to any two-level quantum system, such as a set of cold atoms, i.e. low energy.

Cabot, Albert; Giorgi, Gian Luca; Galve, Fernando; Zambrini, Roberta 
Physical Review Letters 123, 023604 (1-6) (2019). DOI: 10.1103/PhysRevLett.123.023604