Special issue on addressing many-body problems with cold atoms and molecules

A generic feature of AMO systems is the far slower time-scale on which many-body physics evolves: typically micro- to milli-seconds, compared to the typical attosecond- to femtosecond-scale for electronic dynamics in solids. This temporal magnification is a consequence of the low density and high mass of gaseous samples, since the frequency scales affected by quantum degeneracy scales roughly as ${n}^{2/3}/M$, where n is density and M is particle mass [19]. Combined with the isolation of trapped systems from the environment, this opens up new prospects for the study of coherent many-body quantum dynamics [20]. This is the theme of several contributions here [4, 6, 8, 11, 18]. Lee and Proukakis model the non-equilibrium dynamics of Bose condensates [4]. Bulgac et al discuss quantum turbulence in strongly interacting Fermi superfluids [6]. Mumford et al discuss catastrophes in non-equilibrium many-body wave functions [11]. Quench dynamics in a spinor Bose gas are also discussed in analogy to vacuum decay by Fialko et al [8]. Demler et al discuss universal features of the dynamical phase diagram of the Heisenberg model [18]. Many-body dynamics is the indirect subject of several other works here: species-selective manipulation [15] will be an initialisation tool to study superfluid dynamics; non-destructive Faraday imaging [10] is promising to follow a single dynamical time series, and a simple witness for non-classical spin correlations [5] enables the study of entanglement dynamics in Fermi gases.

A behaviour that transcends the details (such as the constituent, or the density) of a physical situation can reveal a limit, or symmetry, of deep significance. Finding these 'universalities' in AMO systems is a theme shared by many of the contributions in this issue. Fermions in the unitary limit are known to have a universal equation of state (for a review, see [21] and references therein). The extent to which these universal features can be reproduced by a few-body calculation is explored by Levinsen et al [13]. For bosons, on the other hand, the question of universality is open, as reviewed by Chevy and Salomon [1]. Universality might also be found in quench dynamics, as discussed by Mumford et al [11], in quantum turbulence as discussed by Bugac et al [6], and nonlinear spin dynamics as discussed by Demler et al [18].

Collisions between neutral alkali atoms are usually dominated by s-wave interactions, since the centrifugal barrier in the centre-of-mass frame is typically 0.1 mK or higher, while typical collision energies are sub-μK. However, several contributions consider situations in which other types of inter-particle interactions are significant or even dominant. Waseem et al [2] report on short-range p-wave interactions in a spin-polarised lithium Fermi gas, in which s-wave collisions are suppressed at low energy. Using a p-wave Feshbach resonance, they demonstrate that the p-wave molecule formation can be controlled by the relative orientation of a Feshbach field and a one-dimensional optical lattice.

Successful strategies to enhance long-range interactions between atoms are magnetic dipole–dipole interactions (in elements such as chromium, erbium, and dysprosium), electric dipole–dipole interactions (in dipolar molecules [22]), cavity-mediated interactions, and Rydberg excited states [23]. In this issue, Ferrier-Barbut et al [7] present a new state of matter, droplets, that exists when repulsive s-wave interactions are cancelled by attractive magnetic dipole–dipole interactions between dysprosium atoms. Whitlock et al [14] propose to use the long-range nature of Rydberg interactions to engineer spin models (discussed further below). Kiffner et al [3] take on the issue of stability in Rydberg systems, by calculating the autoionization rates of two nearby rubidium Rydbergs, suggesting a possibility to realise electron-electron interactions in a cold-atom system instead of mimicking them. Further activity in Rydberg physics is captured in another recent special issue in this journal [23].

In the early years of ultracold atoms, experimental research was dominated by single-component Bose gases and spin-balanced Fermi gases. However, even in spin-balanced Fermi gases, spin degrees of freedom remain active in insulating phases where density degrees of freedom are frozen out. In either the hard-core boson case, or low-temperature fermion Mott insulators, one can describe the remaining degrees of freedom with a Heisenberg model. The phase diagram of semiclassical dynamics of an XXY Heisenberg model is discussed by Demler et al [18]. They characterise different regimes by the solitonic excitations, and discuss the effect of interaction anisotropy. An experimental realisation of a 2D Heisenberg spin model is proposed by Whitlock et al [14], using Rydberg atoms individually trapped in a magnetic lattice. Spin correlations are also important in systems without a lattice, and due to interactions can contain entanglement. Thekkadath et al [5] discuss how spin entanglement dynamics might be observed in Fermi gases by measuring two collective degrees of freedom: the magnetisation and the singlet fraction.

A distinction of AMO systems, compared to materials and nuclei, is that massive bosons are elemental (i.e., not emergent) at ultracold energy scales. Indeed, among the submissions received for this special issue, the majority discuss bosons [1, 3, 4, 7–11, 15, 16]. Among the questions addressed in this issue are whether Efimov physics breaks universality of near-unitary Bosons [1]; how to understand the formation of condensates at finite temperature [4] and in low dimensionality [9, 16]; the superfluid-insulator transition in lattices [17]; and double-well dynamics [9, 11, 15], as discussed below. This strong level of activitiy reflect both the experimental origins of the field (Bose–Einstein condensation was observed four years before Fermi degeneracy) and the enduring interest in superfluidity, as the archetypal example of a macroscopic quantum phenomenon.

Atomic constituents are exquisitely well understood and controlled on the single-particle level. Thus, ab initio calculations have become a more powerful way in which to test the understanding of many-body physics, especially when all terms in the governing hamiltonian are known. This gives rise to a stronger connection between theory and experiment, stimulating both higher-accuracy measurements of many-body phenomena, and the development and benchmarking of new theoretical approaches.

Within the contributions to this issue, we find a wide diversity of theoretical approaches. Many contributions offer an insightful and critical evaluation. Time-dependent density functional theory is used by Bulgac et al to treat quantum turbulence [6]. Exact diagonalization is used by Raventós et al to treat the Bose–Hubbard model [17]. They suggest ways in which quite small ensembles can be compared to phase transitions expected in the thermodynamic limit. With a similar message in a different context, Levinsen et al find that few-body calculations of a unitary Fermi gas compare well to quantum Monte Carlo calculations and to experiments [13]. A path-integral approach is used by Fialko et al, and compared to prior work with other methods. Bolsinger et al review approaches to interacting bosons, and discuss the strength of multi-layer multi-configurational time-dependent Hartree method [9]. Henkel et al provide a 'critical assessment' of mean-field approaches to low-dimensional systems of bosons [16]. Plantz et al discuss the successes and shortcomings of the holographic approach to unitary Fermi gases [12], whose strong correlations poses a challenge to many approaches. The Zaremba–Nikuni–Griffin approach to finite-temperature dynamics of Bose condensates is discussed by Lee and Proukakis [4], who find two-stage dynamics in thermalisation, and indicate the need for further experiments to test the accuracy of the approach.