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Register a new userSqueezing the Efimov effect
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Added by
Nikolaj Thomas Zinner
Publication date
2017
fields
Physics
and research's language is
English
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The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of identical bosons can arise at the threshold where the two-body problem has zero binding energy. An important aspect of the Efimov effect is the effect of spatial dimensionality; it has been observed in three dimensional systems, yet it is believed to be impossible in two dimensions. Using modern experimental techniques, it is possible to engineer trap geometry and thus address the intricate nature of quantum few-body physics as function of dimensionality. Here we present a framework for studying the three-body problem as one (continuously) changes the dimensionality of the system all the way from three, through two, and down to a single dimension. This is done by considering the Efimov favorable case of a mass-imbalanced system and with an external confinement provided by a typical experimental case with a (deformed) harmonic trap.
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Universal behaviour has been found inside the window of Efimov physics for systems with $N=4,5,6$ particles. Efimov physics refers to the emergence of a number of three-body states in systems of identical bosons interacting {it via} a short-range interaction becoming infinite at the verge of binding two particles. These Efimov states display a discrete scale invariance symmetry, with the scaling factor independent of the microscopic interaction. Their energies in the limit of zero-range interaction can be parametrized, as a function of the scattering length, by a universal function. We have found, using a particular form of finite-range scaling, that the same universal function can be used to parametrize the energies of $Nle6$ systems inside the Efimov-physics window. Moreover, we show that the same finite-scale analysis reconciles experimental measurements of three-body binding energies with the universal theory.
Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is much larger than the range of the interaction. The binding energies of these states are described as a function of the scattering length and one three-body parameter by a transcendental equation involving a universal function of one angular variable. We provide an accurate and convenient parametrization of this function. Moreover, we discuss the effective treatment of range corrections in the universal equation and compare with a strictly perturbative scheme.
We show that four heavy fermions interacting resonantly with a lighter atom (4+1 system) become Efimovian at mass ratio 13.279(2), which is smaller than the corresponding 2+1 and 3+1 thresholds. We thus predict the five-body Efimov effect for this system in the regime where any of its subsystem is non- Efimovian. For smaller mass ratios we show the existence and calculate the energy of a universal 4+1 pentamer state, which continues the series of the 2+1 trimer predicted by Kartavtsev and Malykh and 3+1 tetramer discovered by Blume. We also show that the effective-range correction for the light-heavy interaction has a strong effect on all these states and larger effective ranges increase their tendency to bind.
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.
It is well-known that three-boson systems show the Efimov effect when the two-body scattering length $a$ is large with respect to the range of the two-body interaction. This effect is a manifestation of a discrete scaling invariance (DSI). In this work we study DSI in the $N$-body system by analysing the spectrum of $N$ identical bosons obtained with a pairwise gaussian interaction close to the unitary limit. We consider different universal ratios such as $E_N^0/E_3^0$ and $E_N^1/E_N^0$, with $E_N^i$ being the energy of the ground ($i=0$) and first-excited ($i=1$) state of the system, for $Nle16$. We discuss the extension of the Efimov radial law, derived by Efimov for $N=3$, to general $N$.
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