Anomalous Expansion of Attractively Interacting Fermionic Atoms in an Optical Lattice

Abstract

Strong correlations can dramatically modify the thermodynamics of a quantum many-particle system. Especially intriguing behaviour can appear when the system adiabatically enters a strongly correlated regime, for the interplay between entropy and strong interactions can lead to counterintuitive effects. A well known example is the so-called Pomeranchuk effect, occurring when liquid 3 He is adiabatically compressed towards its crystalline phase. Here, we report on a novel anomalous, isentropic effect in a spin mixture of attractively interacting fermionic atoms in an optical lattice. As we adiabatically increase the attraction between the atoms we observe that the gas, instead of contracting, anomalously expands. This expansion results from the combination of two effects induced by pair formation in a lattice potential: the suppression of quantum fluctuations as the attraction increases, which leads to a dominant role of entropy, and the progressive loss of the spin degree of freedom, which forces the gas to excite additional orbital degrees of freedom and expand to outer regions of the trap in order to maintain the entropy. The unexpected thermodynamics we observe reveal fundamentally distinctive features of pairing in the fermionic Hubbard model. A. IntroductionThe striking consequences of strong correlations in many-body quantum systems are at the frontier of current research. Typically, interest is devoted to the unusual properties of ground states or low-lying excitations, which range from exotic types of order to unconventional quasiparticle statistics [1,2]. But strong correlations can also severely alter the thermodynamics of a quantum system, leading to fascinating finite temperature effects. Especially surprising behaviour can arise when the system adiabatically enters a strongly correlated phase, as the emerging correlations can imply a substantial redistribution of entropy.A well known example of this type of phenomena is the so-called Pomeranchuk effect [3,4], which occurs in the liquid to solid transition of 3 He. Since the solid, through its randomly oriented spins, is more disordered than the liquid, it turns out that when the liquid is adiabatically squeezed, it freezes into a solid by, astoundingly, absorbing heat.Other examples of anomalous behaviour due to the combination of finite entropy and strong correlations have been rarely observed in nature, usually because interactions in typical strongly correlated systems can hardly be tuned. Recently, the extraordinary progress in the control and manipulation of neutral atoms in optical lattices [5,6,7] has added a valuable degree of freedom to the investigation of strongly correlated systems. By varying a collection of parameters, like the scattering length, the lattice depth or the external confinement, it is possible to adiabatically bring a non-interacting gas of bosonic [8,9,10,11,12,13,14,15,16,17,18] or fermionic atoms [19,20,21,22] into a regime of strong correlations. Here, we report on the experimental observation and the theoretical predi...

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