Shallow Dimer Research Articles

Asymmetric Lineshapes of Efimov Resonances in Mass-Imbalanced Ultracold Gases

The resonant profile of the rate coefficient for three-body recombination into a shallow dimer is investigated for mass-imbalanced systems. In the low-energy limit, three atoms collide with zero-range interactions, in a regime where the scattering lengths of the heavy–heavy and the heavy–light subsystems are positive and negative, respectively. For this physical system, the adiabatic hyperspherical representation is combined with a fully semi-classical method and we show that the shallow dimer recombination spectra display an asymmetric lineshape that originates from the coexistence of Efimov resonances with Stückelberg interference minima. These asymmetric lineshapes are quantified utilizing the Fano profile formula. In particular, a closed-form expression is derived that describes the width of the corresponding Efimov resonances and the Fano lineshape asymmetry parameter q. The profile of Efimov resonances exhibits a q-reversal effect as the inter- and intra-species scattering lengths vary. In the case of a diverging asymmetry parameter, i.e., |q|→∞, we show that the Efimov resonances possess zero width and are fully decoupled from the three-body and atom–dimer continua, and the corresponding Efimov metastable states behave as bound levels.

Lattice calculations for two-component fermion systems with unequal masses: one dimension

We consider systems of two-component fermions with unequal masses and interacting via a short-range attractive potential. We discuss the case where the two-component fermions form a shallow dimer with large scattering length. The three-fermion and four-fermion systems with such properties are universal and characterized by the twofermion scattering length a ff and the ratio of the mass of spin-↑ fermion to the mass of spin-↓ fermion, m ↑ /m ↓ . In this study, using lattice effective field theory, we analyze fermion-dimer and dimer-dimer systems and calculate the universal fermion-dimer and dimer-dimer scattering lengths for various values of the mass ratio m ↑ /m ↓ . We find that these universal scattering lengths increase logarithmically with the mass ratio m ↑ /m ↓ .

Atom-dimer scattering in a heteronuclear mixture with a finite intraspecies scattering length

We study the three-body problem of two ultracold identical bosonic atoms (denoted by $B$) and one extra atom (denoted by $X$), where the scattering length $a_{BX}$ between each bosonic atom and atom $X$ is resonantly large and positive. We calculate the scattering length $a_{{\rm ad}}$ between one bosonic atom and the shallow dimer formed by the other bosonic atom and atom $X$, and investigate the effect induced by the interaction between the two bosonic atoms. We find that even if this interaction is weak (i.e., the corresponding scattering length $a_{BB}$ is of the same order of the van der Waals length $r_{{\rm vdW}}$ or even smaller), it can still induce a significant effect for the atom--dimer scattering length $a_{{\rm ad}}$. Explicitly, an atom--dimer scattering resonance can always occur when the value of $a_{BB}$ varies in the region with $|a_{BB}|\lesssim r_{{\rm vdW}}$. As a result, both the sign and the absolute value of $a_{{\rm ad}}$, as well as the behavior of the $a_{{\rm ad}}$-$a_{BX}$ function, depends sensitively on the exact value of $a_{BB}$. Our results show that, for a good quantitative theory, the intra-species interaction is required to be taken into account for this heteronuclear system, even if this interaction is weak.

Ultracold Heteronuclear Three-Body Systems: How Diabaticity Limits the Universality of Recombination into Shallow Dimers.

The mass-imbalanced three-body recombination process that forms a shallow dimer is shown to possess a rich Efimov-Stückelberg landscape, with corresponding spectra that differ fundamentally from the homonuclear case. A semianalytical treatment of the three-body recombination predicts unusual spectra with intertwined resonance peaks and minima and yields in-depth insight into the behavior of the corresponding Efimov spectra. In particular, the patterns of the Efimov-Stückelberg landscape are shown to depend inherently on the degree of diabaticity of the three-body collisions, which strongly affects the universality of the heteronuclear Efimov states.

Atom Loss Resonances in a Bose-Einstein Condensate

Atom loss resonances in ultracold trapped atoms have been observed at scattering lengths near atom-dimer resonances, at which Efimov trimers cross the atom-dimer threshold, and near two-dimer resonances, at which universal tetramers cross the dimer-dimer threshold. We propose a new mechanism for these loss resonances in a Bose-Einstein condensate of atoms. As the scattering length is ramped to the large final value at which the atom loss rate is measured, the time-dependent scattering length generates a small condensate of shallow dimers coherently from the atom condensate. The coexisting atom and dimer condensates can be described by a low-energy effective field theory with universal coefficients that are determined by matching exact results from few-body physics. The classical field equations for the atom and dimer condensates predict narrow enhancements in the atom loss rate near atom-dimer resonances and near two-dimer resonances due to inelastic dimer collisions.

Effective field theory for bound state reflection

Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.

Three-Body Recombination Rates Near a Feshbach Resonance within a Two-Channel Contact Interaction Model

We calculate the three-body recombination rate into a shallow dimer in a gas of cold bosonic atoms near a Feshbach resonance using a two-channel contact interaction model. The two-channel model naturally describes the variation of the scattering length through the Feshbach resonance and has a finite effective range. We confront the theory with the available experimental data and show that the two-channel model is able to quantitatively describe the existing data. The finite effective range leads to a reduction of the scaling factor between the recombination minima from the universal value of 22.7. The reduction is larger for larger effective ranges or, correspondingly, for narrower Feshbach resonances.

Ultracold bosons in the vicinity of a narrow resonance: Shallow dimer and recombination

The different resonant regimes that can be achieved by using a magnetic Feshbach resonance are analyzed with a separable two-channel model. Emphasis is put on the case of narrow resonances in a region of intermediate detuning where a shallow dimer exists and an approximate law including the background scattering length for the three-body recombination rate is derived.

Atom loss maximum in ultra-cold Fermi gases

Recent experiments on atom loss in ultra-cold Fermi gases all show a maximum at a magnetic field below Feshbach resonance, where the s-wave scattering length is large (comparable to inter-particle distance) and positive. These experiments have been performed over a wide range of conditions, with temperatures and trap depths spanning three decades. Different groups have come up with different explanations, including the emergence of Stoner ferromagnetism. Here, we show that this maximum is a consequence of two major steps. The first is the establishment of a population of shallow dimers, which is the combined effect of dimer formation through three-body recombination, and the dissociation of shallow dimers back to atoms through collisions. The dissociation process will be temperature dependent and is affected by Pauli blocking at low temperatures. The second is the relaxation of shallow dimers into tightly bound dimers through atom–dimer and dimer–dimer collisions. In these collisions, a significant amount of energy is released. The reaction products leave the trap, leading to trap loss. We have constructed a simple set of rate equations describing these processes. Remarkably, even with only a few parameters, these equations reproduce the loss rate observed in all recent experiments, despite their widely different experimental conditions. Our studies show that the location of the maximum loss rate depends crucially on experimental parameters such as trap depth and temperature. These extrinsic characters show that this maximum is not a reliable probe of the nature of the underlying quantum states. The physics of our equations also explains some general trends found in current experiments.

Exact solution of the three-boson problem at vanishing energy

A zero range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parametrizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted.

Effective-range corrections to three-body recombination for atoms with large scattering length

Few-body systems with large scattering length $a$ have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass $m$ into a shallow dimer scales as $\ensuremath{\hbar}{a}^{4}∕m$ times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant, which are due to the effective range of the atoms, and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to $^{4}\mathrm{He}$ atoms as a test case.

Enhanced dimer relaxation in an atomic and molecular Bose-Einstein condensate

We derive a universal formula for the rate constant \beta for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length a. We show that \beta is determined by a and by two 3-body parameters that also determine the binding energies and widths of Efimov states. The rate constant \beta scales like \hbar a/m near the resonance, but the coefficient is a periodic function of ln(a) that may have resonant enhancement at values of a that differ by multiples of 22.7.

Fermi Liquid Theory of Dilute Submonolayer 3He on Thin 4He II Film: Dimer Bound State and Cooper Pairs

A degenerate dilute Fermi system, with a shallow dimer bound state, is discussed with attention to the possibility of Fermi superfluidity. (Necessary information on interaction is expressed through the bound state energy of the dimer.) A relevant system may be dilute submonolayer 3He on a thin 4He II film just above the onset of the apparent gas-liquid phase separation of 3He.