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...

In this letter we address the issue how synthetic spin-orbit (SO) coupling can strongly affect three-body physics in ultracold atomic gases. We consider a system which consists of three fermionic atoms, including two spinless heavy atoms and one spin-1/2 light atom subjected to an isotropic SO coupling. We find that SO coupling can induce universal three-body bound states with negative s-wave scattering length at a smaller mass ratio, where no trimer bound state can exist if in the absence of SO coupling. The energies of these trimers are independent of high-energy cutoff, and therefore they are universal ones. Moreover, the resulting atom-dimer resonance can be effectively controlled by SO coupling strength. Our results can be applied to systems like 6 Li and 40 K mixture."Universal phenomenon" refers to observations independent of short-range or high energy details, which is one of the most beautiful and charming parts of physics. Universal physics not only emerges in interacting manybody systems but also exists in quantum mechanical fewbody problems. Cold atoms system, because of its diluteness, is an ideal platform to investigate various intriguing phenomena of few-body systems. For instance, Efimov trimer with universal scaling factor [1, 2] has been extensively studied experimentally [3][4][5][6][7][8][9][10]. Another type of trimer whose energy is universal has also been predicted by Kartavtsev and Malykh [11].On the other hand, thanks to fast experimental developments [12][13][14][15][16][17][18][19][20][21][22], synthetic spin-orbit (SO) coupling recently emerges as one of the most exciting research directions in cold atom physics [23]. Among many profound effects of SO coupling, one distinct factor is that certain types of SO coupling can dramatically change the two-body physics. For instance, with Rashba-type SO coupling, because the low-energy density-of-state is enhanced to a finite constant, any small attractive interaction between atoms can support a two-body bound state in three-dimension, and the binding energy increases with the strength of SO coupling [24]. Consequently, this twobody result dramatically changes many-body physics in the scenario of BEC-BCS crossover for spin-1/2 fermions [25][26][27], where the superfluidity is greatly enhanced by SO coupling even in the far BCS side [25].The dramatic effect of SO coupling in two-body problem and its profound consequence naturally raises the question whether similar significant manifestation also exists in a three-body problem. However, so far threebody problems with SO coupling have not been studied in cold atom content, though historically there were some related studies in investigating nucleus [28][29][30]. In this work we study a three-fermion problem which consists of two heavy fermionic α-atoms with mass M and one light fermionic β-atom with mass m, and α-and β-atom interact via a zero-range s-wave interaction in the vicinity of two-body scattering resonances. α-atom is spinless and β-atom is spin-1/2. As the first attempt to demonstrate...

We conduct a theoretical study of SU(N ) fermions confined by a one-dimensional harmonic potential. Firstly, we introduce a numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU(N ) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz − derived for a Heisenberg SU(2) spin chain − is extendable to these N -component systems. Lastly, we consider balanced SU(N ) Fermi gases that have an equal number of particles in each spin state for N = 2, 3, 4. In the weak-and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N -component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles. arXiv:1707.07781v2 [cond-mat.quant-gas] 1 May 2018

We investigate the problem of N identical bosons that are coupled to an impurity particle with infinite mass. For non-interacting bosons, we show that a dynamical impurity-boson interaction, mediated by a closed-channel dimer, can induce an effective boson-boson repulsion which strongly modifies the bound states consisting of the impurity and N bosons. In particular, we demonstrate the existence of two universal "multi-body" resonances, where all multi-body bound states involving any N emerge and disappear. The first multi-body resonance corresponds to infinite impurity-boson scattering length, a → +∞, while the second corresponds to the critical scattering length a * > 0 beyond which the trimer (N = 2 bound state) ceases to exist. Crucially, we show that the existence of a * ensures that the ground-state energy in the multi-body bound-state region, ∞ > a > a * , is bounded from below, with a bound that is independent of N . Thus, even though the impurity can support multi-body bound states, they become increasingly fragile beyond the dimer state. This has implications for the nature of the Bose polaron currently being studied in cold-atom experiments. arXiv:1807.09948v1 [cond-mat.quant-gas]

It is known from the solution of the two-body problem that an anisotropic dipolar interaction can give rise to s-wave scattering resonances, which are named dipolar interaction induced resonances (DIIR). In this Letter, we study the zero-temperature many-body physics of a two-component Fermi gas across a DIIR. In the low-density regime, it is very striking that the resulting pairing order parameter is a nearly isotropic singlet pairing and the physics can be well described by an s-wave resonant interaction potential with finite range conditions, despite the anisotropic nature of the dipolar interaction. The pairing energy is as strong as a unitary Fermi gas near a magnetic Feshbach resonance. In the high-density regime, the anisotropic effect plays an important role. We find phase transitions from singlet pairing to a state with mixed singlet and triplet pairing and then from mixed pairing to pure triplet pairing. The state with mixed pairing spontaneously breaks the time-reversal symmetry.