Dynamic super Efimov effect

Abstract

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 1970, V. Efimov proposed a remarkable phenomenon which is now known as "the Efimov effect" [1]. He showed that, for three identical bosons in the three dimensions, when the pairwise interaction between the bosons is short-ranged and in the vicinity of an swave scattering resonance, there are an infinite number of three-body bound states, whose binding energies E n obey a discrete geometric scaling withwheres 0 1.006 is a universal constant [1, 2]. The Efimov effect attracts great interests both from the nuclear physics and the cold atom physics communities. In 2005, the first evidence of the Efimov effect was observed in a ultracold Cs gas [3], and later on more details of the effect were revealed in a series of experiments [4][5][6]. Recently, the Efimov effect has also been detected in the nuclear physics systems [7]. What lies at the heart of the Efimov effect is the geometric scaling behavior. However, ifs 0 is small, the exponential dependence makes the geometric scaling difficult to observe, since the next bound state would be very shallow in energy and very large in size. Fortunately, thes 0 parameter can be tuned by the atomic mass ratio in an unequal mass atomic mixture, and it becomes larger for larger mass ratio. Therefore, recently the geometric scaling has been observed in the Li and Cs mixture [8,9]. In 2013, a profound new theoretical development is put forward by Nishida, Moroz and Son [10]. They showed that, for three identical fermions confined in two dimensions, when the pairwise interaction is at the vicinity of a p-wave resonance, the fermions can also form an infinite number of three-body bound states [10], called super Efimov states, since the binding energies follow a fascinating double exponential scaling where the hyper-radius ρ quantifies the linear size of the super Efimov bound states, and ρ * is another parameter. From the effective potential Eq. (3), it becomes clear that the double exponential scaling of the binding energies corresponds to a double-log periodicity of the bound state wave-functions in space [13,14]. In a recent separate development, a dynamic Efimov effect for a scale invariant many-body quantum gas has been proposed [15], in which we considered the situation that the trap frequency ω(t) decreases as 1/( √ λt) with time t. We have shown that the expanding cloud size as a function of time bears the same geometric scaling behavior as the three-body Efimov effect. This aliken...

Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory

“…Furthermore, the recognition of the SLð2; RÞ structure in the problem also has an interesting consequence in the ultracold quantum gases; e.g., see Refs. [52,53]. For the quadratic Hamiltonian, the Heisenberg operators ½xðtÞ; pðtÞ evolve under a SLð2; RÞ transformation that preserves the commutation relation ½x; p ¼ i, [54] Therefore, the stroboscopic evolution of ðx; pÞ is represented by a SLð2; RÞ transformation F ðx;pÞ , whose classification determines the stroboscopic trajectory of ½xðnTÞ; pðnTÞ.…”

Periodically and quasi-periodically driven dynamics of Bose-Einstein condensates

“…As a side note, we would like to point out that the present discussion can be directly applied to specific dynamics of scale-invariant atomic gases in a trap [33,34]. To see the connection, let us consider a single harmonic oscillator 6 with the trapping frequency ω = 1 and a = 1 2 (x+i p).…”

“…In the CFT case, the system has the Virasoro symmetry and for specific driving Hamiltonians, one could focus on the SL(2, ) ∼ = SU(1, 1) subgroup. Another analogy is the dynamics of the scale-invariant gases in the harmonic trap [33,34], as would be discussed in more detail later.…”

Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry

“…This phenomenon is quite counterintuitive as the initial state of a manybody system usually does not revive. For Fermi gas in a harmonic trapping potential with unitary or without interaction, the system size shows a discrete scaling law as the trapping frequency changes in a proper way, which is also named as "Efimovian expansion" [10][11][12]. These experiments are quite different from each other in the aspect of statistics, dimensionality, and extra confinement.…”