Scale invariance emerges and plays an important role in strongly correlated many-body systems such as critical regimes nearby phase transitions and the unitary Fermi gases. Discrete scaling symmetry also manifests itself in quantum few-body systems such as the Efimov effect. Here we report both theoretical predication and experimental observation of a novel type expansion dynamics for scale invariant quantum gases. When the frequency of the harmonic trap holding the gas decreases continuously as the inverse of time t, surprisingly, the expansion of cloud size exhibits a sequence of plateaus. Remarkably, the locations of these plateaus obey a discrete geometric scaling law with a controllable scale factor and the entire expansion dynamics is governed by a log-periodic function. This striking expansion of quantum Fermi gases shares similar scaling laws and same mathematical description as the Efimov effect. Our work demonstrates the first expansion dynamics of a quantum many-body system with the temporal discrete scaling symmetry, which reveals the underlying spatial continuous scaling symmetry of the many-body system.Interaction between dilute ultracold atoms is described by the s-wave scattering length. For a spin-1/2 Fermi gas, when the scattering length diverges at a Feshbach resonance, there is no length scale other than the interparticle spacing in this many-body system, and therefore the system, known as the unitary Fermi gas, becomes scale invariant. The spatial scale invariance leads to universal thermodynamics and transport properties as revealed by many experiments [1][2][3][4][5][6][7][8][9][10][11][12][13]. On the other hand, in a boson system with an infinite scattering length, threebody bound state can form, where an extra length scale of the three-body parameter sets a short-range boundary condition for all three bosons being very close. It turns the continuous scaling symmetry into a discrete scaling symmetry, and gives rise to infinite number of three-body bound states whose energies obey a geometric scaling symmetry. This is well known as the Efimov effect [14,15], which has been observed in quite a few cold atom experiments [16][17][18][19][20][21][22][23][24], and recent experiments have also confirmed the geometric scaling of the energy spectrum [25][26][27][28]. Both the continuous and the discrete scaling symmetry are interesting emergent phenomena in a strongly interacting system. For a harmonic trapped gas, the expansion dynamics offers great insight to the property of the gas. Well known example is the anisotropic expansion that proves hydrodynamics behavior due to the Bose condensation [29,30] or strong interactions of Fermi gas [31]. Other examples are, for instance, slowing down of expansion in a disorder potential provides evidence for localization behaviors [32,33] and expansion in the presence of optical lattice reveals correlation effects [34]. In this work, we ask a question that, considering a scale invariant quantum gas hold by a harmonic trap, when the trap is gradually opened...

Shortcut to adiabaticity (STA) guides the nonadiabatic dynamics of a quantum system towards an equilibrium state without the requirement of slow driving. We report the first demonstration of a STA in a strongly-coupled system, i.e., a 3D anisotropic Fermi gas at unitarity. Exploiting the emergent conformal symmetry, the time-dependence of the trap frequencies is engineered so that the final state in a nonadiabatic expansion or compression is stationary and free from residual excitations. The universal scaling dynamics is verified both in the non-interacting limit and at unitarity.

We achieve a highly degenerate and strongly interacting Fermi gas in a mixture of the two lowest hyperfine states of 6 Li by direct evaporative cooling in a high power crossed optical dipole trap. The trap is loaded from a large atom number magneto-optical trap (MOT) which is realized by a laser system of 2.5-watts intracavity-frequency-doubled light output at 671 nm. With this system, we also demonstrate the production of a molecular Bose-Einstein condensates (mBEC), and observe the anisotropic expansion of Fermi gases in the so-called BEC-BCS crossover regime.

We report an observation of a dynamical super Efimovian expansion in a strongly interacting Fermi gas by engineering time dependent external harmonic trap frequencies. When the trap frequency is tailored as [1/4t^{2}+1/t^{2}λlog^{2}(t/t_{*})]^{1/2}, where t_{*} and λ are two controllable parameters, and the change is faster than a critical value, the expansion of such a quantum gas shows novel dynamics that share the same characteristics as the super Efimov effect. A clear double-log periodicity with discrete geometric scaling emerges for the cloud size in the expansion. The universality of such scaling dynamics is verified both in the noninteracting and in the unitarity limit of Fermi gas. Moreover, the measured energy scaling reveals that the potential and internal energy also show double-log periodicity with a π/2 phase difference, but the total energy is monotonically decreased. Observing super Efimovian evolution represents a paradigm in probing universal properties and allows us in a new way to study many-body nonequilibrium dynamics with experiments.