November 2018. The quantum matter team at Institut Polytechnique de Paris has devised a new method to demonstrate the onset of fermionization in a trapped, strongly-correlated Lieb-Liniger (Bose) gas . Using a combination of analytical and numerical calculations, they have shown that the Tan contact, a pivotal quantity in strongly-correlated quantum gases, displays a marked maximum when adjusting the temperature, which pinpoints the crossover to fermionization. It provides a direct signature of this spectacular effect, observable in ultracold-atom quantum simulators.
When confined to a single spatial dimension, a Bose gas with strong repulsive interactions (Lieb-Liniger model) acquires fermionic properties. This dramatic effect, known as fermionization, is due to the strong repulsion between the particles, which produces an effect similar to the Pauli principle in an ideal Fermi gas. At zero temperature, the state of the Bose gas can be then be mapped onto a Fermi sea, characterized by a strong Fermi pressure. The latter can be observed directly on the density profile of the gas when it is confined to a harmonic trap. Fermionization also takes place at finite temperature, but in this case, the Fermi pressure is dominated by the thermal pressure and the density profile is not significantly affected by fermionization.
To find a signature of fermionization at arbitrary temperature, the team performed a systematic study of the Tan contact, which characterizes the state of a strongly-correlated gas, as a function of the temperature and the interaction strength at arbitrary temperature, using a combination of analytical and numerical computations. The analytical calculations are based on the theramal Bethe ansatz (Yang-Yang theory) and a local density approximation. They made it possible to establish a universal scale form of the Tan contact, confirmed with great precision by numerical calculations obtained by path integral quantum Monte Carlo techniques. The results show the onset of fermionization is marked by a maximum of the Tan contact as a function of the temprature, or equivalently, of the entropy as a function of the interaction strength. It provides a clear signature of fermionization.
The team has further shown that this effect is extremely robust in the strongly-correlated regime and that it can be observed in the tails of momentum distributions obtained by standard time-of-flight images.
 H. Yao, D. Clement, A. Minguzzi, P. Vignolo, and L. Sanchez-Palencia, “Tan’s contact for trapped Lieb-Liniger bosons at finite temperature”, Phys. Rev. Lett. 121, 220402 (2018).