We examine a dipolar-gas model to address fundamental issues regarding the correspondence between classical chaos and quantum observations in ultracold dipolar collisions. The theoretical model consists of a short-range Lennard-Jones potential well with an anisotropic, long-range dipole-dipole interaction between two atoms. Both the classical and quantum dynamics are explored for the same Hamiltonian of the system. The classical chaotic scattering is revealed by the fractals developed in the scattering function (defined as the final atom separation as a function of initial conditions), while the quantum chaotic features lead to the repulsion of the eigenphases from the corresponding quantum S matrix. The nearest-eigenphase-spacing statistics have an intermediate behavior between the Poisson and the Wigner-Dyson distributions. The character of the distribution can be controlled by changing an effective Planck constant or the dipole moment. The degree of quantum chaos shows a good correspondence with the overall average of the classical scattering function. The results presented here also provide helpful insights for understanding the role of the inherent dipole-dipole interaction in the currently ongoing experiments on ultracold collisions of highly magnetic atoms.
We examine a dipolar-gas model to address fundamental issues regarding the correspondence between classical chaos and quantum observations in ultracold dipolar collisions. The theoretical model consists of a short-range Lennard-Jones potential well with an anisotropic, long-range dipole-dipole interaction between two atoms. Both the classical and quantum dynamics are explored for the same Hamiltonian of the system. The classical chaotic scattering is revealed by the fractals developed in the scattering function (defined as the final atom separation as a function of initial conditions), while the quantum chaotic features lead to the repulsion of the eigenphases from the corresponding quantum S matrix. The nearest-eigenphase-spacing statistics have an intermediate behavior between the Poisson and the Wigner-Dyson distributions. The character of the distribution can be controlled by changing an effective Planck constant or the dipole moment. The degree of quantum chaos shows a good correspondence with the overall average of the classical scattering function. The results presented here also provide helpful insights for understanding the role of the inherent dipole-dipole interaction in the currently ongoing experiments on ultracold collisions of highly magnetic atoms.
Abstract we report on signatures of classical chaos in ultracold collisions between a trapped ion and a free atom. Using numerical simulations, we show that the scattering dynamics can be highly sensitive to initial conditions for various mass ratios and trapping frequencies, indicating the onset of chaos. We quantify this chaotic dynamics by calculating its fractal dimension. We show that for a trapped 88 Sr + ion and a free 87 Rb atom chaotic dynamic appears under experimentally relevant conditions, and find its characteristic energy scale. The observation of classical chaos in atom-trapped-ion collisions suggests that signatures of quantum chaos might appear, for example, through a Wigner–Dyson distribution of collisional resonances.
Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.
We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system and argue that it offers lessons for real molecular collisions in three dimensions. We analyze the distribution of the adiabatic potentials in the hyperspherical coordinate representation as well as the distribution of near-threshold four-body bound states, systematically studying the effects of molecular properties, such as interaction strength, interaction range, and atomic mass. It is found that the adiabatic potential's nearest-neighbor energy level distribution transitions from significant level repulsion characteristic of chaos (Brody distribution) to nonchaotic (Poisson distribution) as the two molecules are separated. For the near-threshold four-atom bound states, the case where all atoms have equal masses shows a Poissonian spacing distribution, while the unequal-mass system exhibits significant level repulsion characterized by a nonzero Brody parameter. We derive a semiclassical formula for the density of states and extract from it simple scaling laws with potential depth and range. We find good agreement between the semiclassical predictions for the density of states and the full quantum mechanical calculations.
Interactions between particles play an important role in quantum degenerate gases.\nIn fact, the system’s behavior is usually largely determined by the strength, range, and\nsymmetry of the interactions, even if very weak. For more than two decades after the\nfirst experimental realization of a Bose-Einstein condensate (BEC) in 1995, investigations of ultracold atomic gases have mainly considered contact-type interactions, which\nmodel the short-range van der Waals interactions between the atoms in terms of a single\nparameter, the s-wave scattering length. However, some atomic or molecules species\npossess a magnetic or electric dipole moment and additionally interact among each\nother via the dipole-dipole interaction (DDI), which is long-ranged and anisotropic.\nSignatures of the DDI have been first observed in a BEC of chromium atoms in 2005.\nIn the last several years, a new class of atoms from the lanthanide series, e.g., dysprosium and erbium, with stronger dipolar properties, have come into play. This permits\na more full-fledged study of dipolar effects in BECs. Furthermore, ultracold molecules\nand highly excited Rydberg atoms are other promising examples for futures studies of\nsystems where dipolar interaction will be even more dominant, but they still need experimental efforts to achieve the desired quantum regime. Whereas the weak DDI in a\nchromium BEC is well described with the Gross-Pitaevskii equation, stronger dipolar\ninteractions certainly necessitate a beyond-mean-field description within a Bogoliubov\ntheory.\nIn parallel to research on bosons, cold fermions also trigger great interest because\nthey are actually often found in nature, e.g., within the electron gas of metals, as\nneutrons of heavy stars, or as quarks in plasmas as constituent elements of composite particles. Contrary to Bose systems, quantum degeneracy in experiments is much\nmore difficult to achieve in Fermi systems, since s-wave scattering is absent between\nidentical fermions, due to the Pauli exclusion principle. It was first achieved in 1999\nfor alkali atoms using a technique based on the sympathetic cooling with a second spin\nstate, another species, or a different isotope. For highly magnetic atoms, quantum degeneracy was achieved for dysprosium in 2012 using the standard sympathetic cooling\ntechnique, while in 2014 erbium was cooled deep into the degenerate regime using a\ndirect evaporative cooling mediated by dipolar collisions. This direct cooling scheme\nivallows producing very dense Fermi gas down to 10% of the Fermi temperature.\nFurthermore, a novel kind of strongly dipolar quantum gases became available in\nthe last several years. These are weakly bound polar molecules produced from atoms\nwith large magnetic dipole moments, such as erbium. Only very recently a quantum\ndegenerate dipolar Fermi gas of potassium-rubidium molecules has been experimentally realized. Unlike previously considered magnetic systems, heteronuclear molecules\nsuch as potassium-rubidium possess large electric dipole moments. The next natural\nstep is to polarize this system in a preferential direction by an external electric field,\nsuch that the DDI dominates the behavior of the system, which would open up the\nrealm for experimental investigation of strong dipolar Fermi gases...
We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach-resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory-inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant nonzero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate.
This thesis reports on a variety of calculations on cold and ultracold scattering, with a broad theme of how best to consider and understand complex systems in simple ways. Firstly, we investigate quantum defect theory. We demonstrate that it is not only an excellent model for simple systems, but can also provide simple predictions of the \emph{range} of possible behaviours for complex systems, in particular for a model of collisional losses. These predictions agree well with expensive coupled-channels calculations in cases where the full calculations also predict only the range of possible behaviours. Secondly, we consider effects relating to thermalisation of cold and ultracold gases. We show that considering the correct transport cross section, ση(1), is important for determination of scattering lengths and their signs by interspecies thermalisation. This cross section is also important to the understanding of high-quality simulations of sympathetic cooling in a microwave trap, which suggest Rb is likely to be a good coolant for CaF. We also correct an error in the interpretation of previous results for sympathetic cooling in a magnetic trap, showing this may work from over 100 mK for Li+CaF and many Kelvin when using atomic hydrogen as a coolant. Thirdly, we study quantum chaos in ultracold collisions. We find very clear and strong signs of chaos in Li+CaH. We also show that a more strongly coupled system, Li+CaF, is \emph{not} fully chaotic and that there is unexpected structure in the levels of chaos as the CaF rotational constant is varied. We also show that signatures of chaos can emerge in a very simple atom-atom system, Yb(1S0)+Yb(3P2), which interacts on only two Born-Oppenheimer potentials. Finally, we examine the idea that metastable states in 2-body scattering greatly enhance 3-body recombination at ultracold temperatures. We attempt to put it on a more rigorous theoretical grounding by considering Smith's collision lifetime and related quantities, but those are shown to lack clear interpretations in the ultracold regime. We therefore consider 3-body scattering theory and arrive at some general conclusions about how we expect such 2-body features to appear in 3-body scattering and suggest possible ways forward.