Macroscopic Quantum Coherence: detection and quantification

What makes the difference between a classical and a quantum system is generally termed quantum coherence. Intuitively, one can say that the characteristic trait of quantum mechanics is the fact that a particle (even massive), e.g., an electron, can be in a ``quantum`` superposition of, e.g., two different rotational states. In a multipartite scenario this translates into a puzzling phenomenon, termed entanglement by Schrodinger back in 1935, that contrasts with classical principles. Astonishingly, this was experimentally confirmed as a physical fact and, even more surprisingly, this has been noticed to lead to a very broad range of technological improvements. Thus, the question arises: How to properly quantify quantum coherence as a resource for different technological tasks? How to relate resources for different tasks to each other? In parallel, the early debate about the foundations of quantum theory that goes back to the fathers is still ongoing: Where is the boundary between the microscopic realm governed by quantum mechanics and the classical macroscopic world? Although this might contrast with our intuition, no fundamental reason, nor any experimental proof, have been found so far of why quantum mechanics should not be valid at macroscopic scales. Nevertheless modifications of quantum mechanics (collapse models) have been proposed trying to explain why quantum coherence is not observed in large massive objects and still wait for experimental test. Thus, for foundational purposes as well as for practical applications, it is important to understand to what extent quantum coherence can be observed at larger and larger scales. Ideally, the scope of the project goes into the direction of addressing such questions. However the main focus is put on a very concrete system: (macroscopic-scale) ensembles of atoms interacting with light, of which the quantum physics community has currently reached a very high level of control and understanding. The output of the action is expected to give important insights on the possible presence and nature of quantum coherence at macroscopic scales and also provide a proper quantification of its presence in different scenarios. On the applied side, this will lead to important links between a resource (for technological purposes) point of view on quantum coherence and its understanding from a foundational point of view.

The notion of entanglement is, according to Schrödinger, the trait of quantum mechanics that makes it radically different from classical physics, challenging our very notion of reality. Due to this phenomenon, correlations can be present between distant particles such that they are seemingly influencing each other at a distance. Even if this influence is just illusive, these quantum correlations have been found useful for information transmission and processing. Nowadays, entangled states are produced routinely in many systems, promising an imminent ``quantum'' technological revolution. At the same time, entangled states are being produced in larger and larger objects, challenging our classical intuition even in our everyday macroscopic world. Similarly, correlations in time have been recently investigated from the point of view of witnessing genuine quantum effects. However, in a sequence of measurements, quantum effects can be always mimicked by a disturbance that uses a certain amount of memory. In our project, we have investigated both these notions of quantum correlations, with particular focus on atomic gases at very low temperatures, or Bose-Einstein Condensates. In particular, we have focused on so-called spin-squeezed states, that are particular entangled states of many atoms that have recently found applications in high-precision measurements, such as magnetometry, atomic clocks or gravitational waves detection. We have derived methods to quantify the amount of entanglement present in spin-squeezed states and have collaborated with experiments to implement our findings. Concerning temporal quantum correlations, we have contributed to clarify the difference between a classical disturbance and a genuine quantum effect. The latter is what can be termed quantum coherence, that manifests itself, for example, in a particle being in a superposition of two different states (e.g., two different positions, or two different velocities) at the same time. Furthermore, we have investigated temporal quantum correlations as a resource, quantified by the memory cost needed to simulate them, and have discovered that such a resource plays a fundamental role for the design of clocks. Finally, we have investigated the role of quantum correlations in thermodynamics, i.e., in systems that are designed to use the energy of thermal baths to perform work. We have studied, on the one hand, the amount of energy that has to be invested to create correlations. On the other hand, we have investigated the ultimate resources needed for certain thermodynamic tasks, like refrigeration, trying to understand whether quantum effects play an important role, or are rather just detrimental effects. Furthermore, we have designed a blueprint for a thermal machine that uses a Bose-Einstein Condensate as the working fluid, i.e., operates in a truly quantum regime, with the idea of implementing this proposal in an experiment in the near-future.