Table of Contents:

Open questions
The following questions / key words were raised at the organizational get-together on Monday, Nov 7 as a foundation for the discussions and collaborations that are anticipated during the workshop. Please feel free to edit these points with better formulated problem statements, or add to it with new areas of interest.
  • What are the "universalities" in the dynamics of correlated quantum systems? Is every such system different, or can common ground be found in properties such as the relevant time scales, out of equilibrium dynamics (quenches, etc), the few-to-many body physics, etc?
  • How many is "many"? Are there any universal properties that determine when a many-body approach is needed vs a few body approach?
  • Universal properties of relatively simple few body systems have been studied, but what about those of more complicated species such as the lanthanide atoms or molecules?
  • What about universal properties of systems with more complex dispersion relations, like those found in synthetic gauge systems or around Dirac cones. What is the role of topology or geometry, or of low dimensionality, on universal properties for these sorts of systems?
  • What is the role of confinement from external trapping potentials on universal physics in few body systems? What about mixed or quasi-dimensional systems?
  • Is there universality not just in the zeroth order expansion of the system in r/a, the ratio of the range of the interaction to the scattering length? What can be found by exploring the effective range expansion?
  • There is a need for precision in few body studies -- how can precision be maximized for the lowest number of parameters?
  • What about mass-inbalanced systems, such as heteronuclear systems?
  • What is the effect of many-body physics on few-body physics, i.e. can few body systems of quasiparticles or excitations in a many body system be studied?
  • How long does it take to reach universality? What are the relevant time scales, especially in highly correlated quantum systems?
  • Transfer of few-body, particularly two-body parameters, to the control of many body dynamics -- especially relevant to experimental concerns.
  • How can the tools and methods of few body physics be extended to many body applications? Some examples include hyperspherical coordinates, MCDTH methods, etc. What are the problems that have so far been encountered in adapting these approaches?
  • What kinds of experimental probes yield better few body information than just measuring losses?
  • Few body systems are typically highly correlated and entangled - how can this be studied experimentally?

First Week synthesis
At the organizational meeting on November 14, the following points were discussed. These were primarily related to the open questions raised in week 1 as well as the talks and tutorials presented in the first week. Again, researchers are encouraged to edit these notes as desired, either to include additional references, review articles, helpful papers, or to continue the discussion.
1) Cindy Regal presented a system (small array of ultracold atoms that can be manipulated at will) that looks like an ideal prototype system to be modeled by various approaches that we heard about.
2) ML-MCTDHB, and Lindblad approach. For instance, what would reveal the treatment of such a model systems with these approaches, and which kind of experiments could be designed (spontaneous dynamics of atoms around lattice sites, loss of particles and corresponding induced dynamics in the lattice, etc...)
3) It was also mentioned the possible analogy between the example of three particles in three wells given by P. Schmelcher, extended to periodic conditions, and the dynamics of three identical atoms in hyperspherical coordinates.
4) The method presented by Peter Schmelcher relies on a very simple description of the interaction through a single parameter. On the other hand, physical
chemists use MCTDH with high dimensional PES. These are two extreme situations. Could we think about any intermediate step?
5) Clearly several people in the audience were not aware of the QDT, and its connection with scattering length. More generally there is certainly a "universality" amongst most of the approaches to treat quantum dynamical problems: the separation of the space and interactions between short and large distances. It seems that some participants wanted to have more mathematical information (or justifications) about QDT.
6) Also we could come back to E. Braaten's talk, regarding the interpretation in terms of time scale on one hand (for the interparticle correlations to emerge - or for the density matrix to be less diagonal).
7) Also one could revisit the question that arose about the difference between the use of an optical complex potential to account for particle decays, and the Lindblad equation formalism.

Relevant review articles:

D Blume, Few-body physics with ultracold atomic and molecular systems in traps, Rep. Prog. Phys. 75 (2012) 046401
D. S. Petrov, The few-atom problem, Lecture presented at the 2010 Les Houches Summer School "Many-Body Physics with Ultra-Cold Gases", vol. 94, (2012), arXiv:1206.5752

M. J. Seaton, "Quantum defect theory", Reports on Progress in Physics, 46, 167 (1983)
Mireille Aymar, Chris H. Greene, and Eliane Luc-Koenig, "Multichannel Rydberg spectroscopy of complex atoms", Rev. Mod. Phys. 68, 1015 (1996)

*Review article on cold molecules, including universal collisions models:
G. Quéméner and P. S. Julienne, “Ultracold molecules under control,” Chem. Reviews 112, 4949-5011 (2012).

Alan Edelman, N. Raj Rao, "Random matrix theory", Acta Numerica, 1-65 (2005) (General & mathematical, with Matlab code snippets)

P. Naidon, S. Endo, "Efimov Physics: a review", arXiv:1610.09805, to be published in Reports on Progress in Physics

F. F. Bellotti, A. S. Dehkharghani, N. T. Zinner, "Comparing numerical and analytical approaches to strongly interacting Fermi-Fermi and Bose-Fermi mixtures in one dimensional traps" arXiv:1606.09528

Bijaya Acharya, Chen Ji, Lucas Platter, "An effective-field-theory analysis of Efimov physics in heteronuclear mixtures of ultracold atomic gases", arXiv:1606.04508

Ran Qi, "Universal relations of strongly interacting Fermi gases with multiple scattering channels", arXiv:1606.03299

Xingze Qiu, Xiaoling Cui, Wei Yi, " Universal trimers emerging from a spin-orbit coupled Fermi sea", arXiv:1607.03580

Paul M. A. Mestrom, Jia Wang, Chris H. Greene, Jose P. D'Incao, "Efimov universality for ultracold atoms with positive scattering lengths", arXiv:1609.02857

Meera Parish, Jesper Levinsen, "Quantum dynamics of impurities coupled to a Fermi sea", arXiv:1608.00864

K. Kato, Yujun Wang, J. Kobayashi, P. S. Julienne, S. Inouye, "Isotopic shift of atom-dimer Efimov resonances in K-Rb mixtures: Critical effect of multichannel Feshbach physics," arXiv:1610.07900

O. V. Marchukov, A. G. Volosniev, M. Valiente, D. Petrosyan, N. T. Zinner: Quantum spin transistor with a Heisenberg spin chain, arXiv:1610.02938

M. Valiente, P. Ohberg, Few-Body Route to One-Dimensional Quantum Liquids, arXiv:1607.08604

Matthew T. Eiles, Chris H. Greene, A Hamiltonian for the inclusion of spin effects in long-range Rydberg molecules, arXiv:1611.04508

A paper on the few-body scattering with a non-standard dispersion relation, namely that of a flat band can be found here:
Manuel Valiente and Nikolaj Thomas Zinner, 'Quantum collision theory in flat bands', arXiv:1611.05459

Jesper Levinsen, Pietro Massignan, Shimpei Endo, Meera M. Parish, "Universality of the unitary Fermi gas: A few-body perspective", arXiv:1612.02131
(Significant progress made and the work completed during the workshop.)

Material from talks:

Talk of Cindy Regal, Nov 8
I will discuss our experiments with Raman-cooled neutral atoms in sets of optical tweezers. Recent and future work focuses on the Hong-Ou-Mandel effect with atoms, entanglement via spin exchange, microscopic Kondo lattice physics, and measurement-induced entanglement. I will discuss the implications for microscopic control of larger quantum systems and few-body physics.

Brian J. Lester, Niclas Luick, Adam M. Kaufman, Collin M. Reynolds, and Cindy A. Regal, "Rapid Production of Uniformly Filled Arrays of Neutral Atoms" Phys. Rev. Lett. 115, 073003

Talk of Paul Julienne, Nov 9
This talk will cover ideas about universal 2- and 3-body collisions based on quantum defect theory and numerical calculations, illustrated by alkali and lanthanide systems.
Useful references:
P. S. Julienne, "Ultracold molecules from ultracold atoms: a case study with the KRb molecule", Faraday Discuss., 142, 1 (2009)
Yujun Wang, P. S. Julienne, Chris H. Greene, "Few-body physics of ultracold atoms and molecules with long-range interactions", Annual Review of Cold Atoms and Molecules: Volume 3, World Scientific (2015).
P. S. Julienne, "Molecular states near a collision threshold", Cold Molecules: Theory, Experiment, Applications, eds R. Krems, B. Friedrich, W. C. Stwalley, CRC Press (2009), arXiv:0902.1727The QDT formulas are compared to real-world calculations in the Blackley et al paper below.
Some papers on quantum defect theory:
*Mies and PSJ: J. Chem. Phys. 80, 2514 and 2526 (1984).
*Julienne, P. S., and Mies, F., "Collisions of Ultracold Trapped Atoms," J. Op. Soc. Am. B 6, 2257(1989).
Van Der Waals universality in 3-body collisions:
*Experiment: Berninger et al, Phys. Rev. Lett. 107, 120401 (2011)
*Theory: J. Wang et al, Phys. Rev. Lett. 108, 263001 (2012); Naidon et al, Phys. Rev. Lett. 112, 105301 (2014)
Numerical implementation compared to experiment:
*Y. Wang and PSJ, Nat. Phys. 10, 768 (2014)(Cs and Rb85 examples)
Kato et al (K30+2Rb and K40+2Rb examples), arXiv:1610.07900v1
Chaotic collisions:
*Maier et al, Phys. Rev. A 92, 060702 (2015) and Supp. Material for Dy universal state (patterned complexity)
*Frisch et al, Nature 507, 475 (2014), chaos in Er collisions
*Maier et al, Phys. Rev. X 5, 041029 (2015), Dy and Er compared + theory
*Mayle, Ruzic, Bohn, Phys. Rev. A 85, 062712 (2012), random matrix theory for molecular collisions.
Effective range questions:
*C. L. Blackley, P. S. Julienne, and J. M. Hutson, “Effective-range approximations for resonant scattering of cold atoms,” Phys. Rev. A 89, 042701 (2014). See Fig. 2.
*Werner and Castin, Phys. Rev. A 86, 013626 (2012), see Eq. (185) for corrections to the effective range due to a Feshbach resonance (broad or narrow).
*P. Naidon, E. Tiesinga, W. F. Mitchell, and P. S. Julienne, “Effective-range description of a Bose gas under strong one- or two-dimensional confinement,” New J. Phys. 9, 19 (2007). (physics/0607140).
QDT theory of universal molecular reaction rates (not covered in talk):
*Z. Idziaszek and P. S. Julienne, “Universal rate constants for reactive collisions of ultracold molecules,” Phys. Rev. Lett 104, 113202 (2010). See also Bo Gao, PRL 105, 263203(2010).
*S. Ospelkaus, K.-K. Ni, D. Wang, M. H. G. de Miranda, B. Neyenhuis, G. Quéméner, P. S. Julienne, J. L. Bohn, D. S. Jin and J. Ye, “Quantum-State Controlled Reactions of Ultracold KRb Molecules,” Science 327, 853-857 (2010).
*A. Micheli, Z. Idziaszek, G. Pupillo, M. A. Baranov, P. Zoller, and P. S. Julienne, “Universal rates for reactive ultracold polar molecules in reduced dimensions,” Phys. Rev. Lett. 105, 073202 (2010).
*K. Jachymski, M. Krych, P.l S. Julienne, and Zb. Idziaszek, “Quantum defect model of a reactive collision at finite temperature," Phys. Rev. A 90, 042705 (2014).
*Z. Idziaszek, K. Jachymski, and P. S. Julienne, “Reactive collisions in confined geometries,” New. J. Phys. 17, 035007 (2015).
*M. D. Frye, P. S. Julienne, and J. M. Hutson, “Cold atomic and molecular collisions: approaching the universal loss regime,” New J. Phys. 17, 045019 (2015). Nice color graphics

Talk of Peter Schmelcher, Nov 10.

Ultracold bosonic and fermionic gases are ideal laboratories for studying the nonequilibrium quantum dynamics of interacting systems. The latter can be triggered by a sudden quench or a continuous driving of the external trapping potential or of the interaction strength among the atoms. While the mean-field behaviour of such systems is quite well understood, the correlation dynamics is an intriguing open problem. Related to this is the question whether there is any type of universality in these systems, or whether the behaviour could be classified and, as a final aim, whether one can control or steer the correlated dynamics in a desired direction. This talk will address a number of different example cases for the correlated quantum dynamics, focusing on the few-body regime but also bridging between the few- and many-body case, which are meant to be a starting-point for discussions related to the above questions and beyond.
Our computational approach is the multi-layer multi-configuration time-dependent Hartree method for bosons which represents a powerful ab-initio method for the investigation of the non-equilibrium quantum dynamics of single and multi-species bosonic systems in traps and optical lattices [1,2]. After briefly introducing the method we discuss a number of different applications ranging from the correlated quantum dynamics in optical lattices to beyond mean-field behaviour of solitons and collisionally coupled correlated species. Firstly we demonstrate [3] in a `bottom-up approach' the correlated many-particle effects in the collective breathing dynamics for few- to many-boson systems in a harmonic trap. Many-body processes in black and grey matter-wave solitons are explored thereby demonstrating that quantum fluctuations limit the lifetime of the soliton contrast, which increases with increasing soliton velocity [4]. For atomic ensembles in optical lattices we explore the interaction quench induced multimode dynamics leading to the emergence of density-wave tunneling, breathing and cradle-like processes. An avoided-crossing in the respective frequency spectrum provides to a beating dynamics for selective modes [5,6]. A particular far from equilibrium system is then studied at hand of the correlated quantum dynamics of a single atom collisionally coupled to a finite bosonic reservoir [7].
In the last part of the presentation we provide some selective aspects of our recent investigations on atom-ion hybrid systems [8-9] using the same methodology. First the ground state properties of ultracold trapped bosons with an immersed ionic impurity are discussed. Subsequently the capture dynamics of ultracold atoms in the presence of the impurity ion is explored.

[1] L. Cao, S. Krönke, O. Vendrell and P. Schmelcher, NJP 15, 063018 (2013)
[2] L. Cao, S. Krönke, O. Vendrell and P. Schmelcher, JCP 139, 134103 (2013)
[3] R. Schmitz, S. Krönke, L. Cao and P. Schmelcher, PRA 88, 043601 (2013)
[4] S. Krönke and P. Schmelcher, PRA 91, 053614 (2015)
[5] S. Mistakidis, L. Cao and P. Schmelcher, JPB 47, 225303 (2014)
[6] S.I. Mistakidis, L. Cao and P. Schmelcher, PRA 91, 033611 (2015)
[7] S. Krönke, J. Knörzer and P. Schmelcher, NJP 17, 053001 (2015)
[8] J.M. Schurer, P. Schmelcher and A. Negretti, PRA 90, 033601 (2014)
[9] J.M. Schurer, P. Schmelcher and A. Negretti, NJP 17, 083024 (2015)

Talk of Eric Braaten, Nov 11

The loss of ultracold trapped atoms due to deeply inelastic reactions has often been taken into account by adding local anti-Hermitian terms to the effective Hamiltonian. An additional modification is required in the equation governing the density matrix for multi-atom systems. The effective density matrix satisfies the Lindblad equation (which originated in quantum information theory) with local Lindblad operators that are determined by the local anti-Hermitian terms in the effective Hamiltonian. The Lindblad equation can be used to derive universal relations for inelastic loss rates.

Relevant background reading:
Braaten, Hammer, and Lepage, Lindblad Equation for the Inelastic Loss of Ultracold Atoms [arXiv:1607.08084]
Open Effective Field Theories from Deeply Inelastic Reactions [arXiv:1607.02939]

Talk of Johannes Hecker Denschlag, Dec 6

A chemical reaction is a complicated quantum mechanical process between two or more atoms. Already for three atoms a full description of the reaction dynamics is in general not yet fully theoretically tractable. In order to fully understand the reaction path for a given reactant’s quantum state, the final product quantum state has to be determined. I will talk about recent work of my group where we have discovered an experimental method for tracking the chemical reaction paths. In our lab we study three-body recombination of ultracold Rb atoms, where two atoms combine to form a Rb_2 molecule while the third atom carries away part of the released binding energy. In the experiment, we prepare the external and internal degrees of freedom of the reactants in a well-defined quantum state. After the reaction we state-selectively ionize the molecules with such high resolution that the different final quantum states can be distinguished. Our first results allow for extracting some simple propensity rules for the reaction paths.

Additional articles:

The Journal of Physics B: Atomic, Molecular, and Optical Physics is currently compiling a couple relevant special issues:

  • "Few Body Physics with Cold Atoms" The special issue articles can be found here.
  • "Addressing Quantum Many-body Problems with Cold Atoms and Molecules" The special issue articles can be found here.

If you would like to add any additional reference material that would be relevant for the program, please send Matt Eiles an e-mail here