In this letter we study how fast the energy density of a quantum gas can increase in time, when the inter-atomic interaction characterized by the $s$-wave scattering length $a_text{s}$ is increased from zero with arbitrary time dependence. We show th
at, at short time, the energy density can at most increase as $sqrt{t}$, which can be achieved when the time dependence of $a_text{s}$ is also proportional to $sqrt{t}$, and especially, a universal maximum energy growth rate can be reached when $a_text{s}$ varies as $2sqrt{hbar t/(pi m)}$. If $a_text{s}$ varies faster or slower than $sqrt{t}$, it is respectively proximate to the quench process and the adiabatic process, and both result in a slower energy growth rate. These results are obtained by analyzing the short time dynamics of the short-range behavior of the many-body wave function characterized by the contact, and are also confirmed by numerical solving an example of interacting bosons with time-dependent Bogoliubov theory. These results can also be verified experimentally in ultracold atomic gases.
Transport is one of the most important physical processes in all energy and length scales. The non-interacting Boltzmann equation and the hydrodynamic equations respectively describe two opposite limits of transport. Here we present an unexpected mat
hematical connection between these two limits, named textit{idealized hydrodynamics}, which refers to the situation where the solution to the hydrodynamic equations of an interacting system can be exactly constructed from the solutions of a non-interacting Boltzmann equation. We analytically provide three examples of such idealized hydrodynamics. These examples respectively recover the dark soliton solution in a one-dimensional superfluid, generalize fermionization to the hydrodynamics of strongly interacting systems, and determine specific initial conditions for perfect density oscillations in a harmonic trap. They can be used, for instance, to explain a recent puzzling experimental observation in ultracold atomic gases by the Paris group, and to make further predictions for future experiments. We envision that extensive examples of such idealized hydrodynamics can be found by systematical numerical search, which can find broad applications in different problems in various subfields of physics.
We investigate the radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. In the limit of a single impurity, we show using Fermis golden rule that introducing (or injecting) an impurity into the medium is equ
ivalent to ejecting an impurity that is initially interacting with the medium, since the injection and ejection spectral responses are simply related to each other by an exponential function of frequency. Thus, the full spectral information for the quantum impurity is contained in the injection spectral response, which can be determined using a range of theoretical methods, including variational approaches. We use this property to compute the finite-temperature equation of state and Tan contact of the Fermi polaron. Our results for the contact of a mobile impurity are in excellent agreement with recent experiments and we find that the finite-temperature behavior is qualitatively different compared to the case of infinite impurity mass.
We present a theory of radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. By working in the canonical ensemble of a single impurity, we show that the impurity spectral response is directly connected to th
e finite-temperature equation of state (free energy) of the impurity. We consider two different response protocols: injection, where the impurity is introduced into the medium from an initially non-interacting state; and ejection, where the impurity is ejected from an initially interacting state with the medium. We show that there is a simple mapping between injection and ejection spectra, which is connected to the detailed balance condition in thermal equilibrium. To illustrate the power of our approach, we specialize to the case of the Fermi polaron, corresponding to an impurity atom that is immersed in a non-interacting Fermi gas. For a mobile impurity with a mass equal to the fermion mass, we employ a finite-temperature variational approach to obtain the impurity spectral response. We find a striking non-monotonic dependence on temperature in the impurity free energy, the contact, and the radio-frequency spectra. For the case of an infinitely heavy Fermi polaron, we derive exact results for the finite-temperature free energy, thus generalizing Fumis theorem to arbitrary temperature. We also determine the exact dynamics of the contact after a quench of the impurity-fermion interactions. Finally, we show that the injection and ejection spectra obtained from the variational approach compare well with the exact spectra, thus demonstrating the accuracy of our approximate method.
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 effecti
ve 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, $ato +infty$, 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, $infty>a> a^*$, 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.
Super Efimov effect is a recently proposed three-body effect characterized by a double-exponential scaling, which has not been observed experimentally yet. Here, we present the general dynamic equations determining the cloud size of a scale invariant
quantum gas in a time dependent harmonic trap. We show that a double-log periodicity as the hallmark of the super Efimov effect emerges when the trap frequency is decreased with a specially designed time-dependence. We also demonstrate that this dynamic super Efimov effect can be realized with realistic choices of parameters in current experiments.
In this letter we show that the vortex lattice structure in the Bose-Fermi superfluid mixture can undergo a sequence of structure transitions when the Fermi superfluid is tuned from the BCS regime to the BEC regime. This is due to different vortex co
re structure of the Fermi superfluid in the BCS regime and in the BEC regime. In the former the vortex core is nearly filled, while the density at the vortex core gradually decreases until it empties out at the BEC regime. Therefore, with the density-density interaction between the Bose and the Fermi superfluids, the two sets of vortex lattices interact stronger in the BEC regime that yields the structure transition of vortex lattices. In view of recent realization of this superfluid mixture and vortices therein, our theoretical predication can be verified experimentally in near future.
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 s
uch 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.
We study the two-body and three-body bound states in ultracold atomic mixtures with one of the atoms subjected to an isotropic spin-orbit (SO) coupling. We consider a system of two identical fermions interacting with one SO coupled atom. It is found
that there can exist two types of three-body bound states, Efimov trimers and universal trimers. The Efimov trimers are energetically less favored by the SO coupling, which will finally merge into the atom-dimer threshold as increasing the SO coupling strength. Nevertheless, these trimers exhibit a new kind of discrete scaling law incorporating the SO coupling effect. On the other hand, the universal trimers are more favored by the SO coupling. They can be induced at negative s-wave scattering lengths and with smaller mass ratios than those without SO coupling. These results are obtained by both the Born-Oppenheimer approximation and exact solutions from three-body equations.
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.
