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arXiv:1512.06177 · Physical Review Letters

Ultracold Nonreactive Molecules in an Optical Lattice: Connecting Chemistry to Many-Body Physics

Andris Doçaj, Michael L. Wall, Rick Mukherjee, Kaden R. A. Hazzard

Published Mar 30, 2016• 26 citations
arXivHTMLPDF

Abstract

We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter U is replaced by a multichannel interaction, whose properties we elucidate. Because this arises from complex short-range collisional physics, it requires no dipolar interactions and thus occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which, consequently, measure molecular collision dynamics with a vastly sharper energy resolution than experiments in a free-space ultracold gas.

DOI
10.1103/physrevlett.116.135301

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We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter U is replaced by a multichannel interaction, whose properties we elucidate. Because this arises from complex short-range collisional physics, it requires no dipolar interactions and thus occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which, consequently, measure molecular collision dynamics with a vastly sharper energy resolution than experiments in a free-space ultracold gas.
Recent experimental advances in the cooling and manipulation of bialkali-metal dimer molecules have enabled the production of gases of ultracold molecules that are not chemically reactive. It has been presumed in the literature that in the absence of an electric field the low-energy scattering of such nonreactive molecules (NRMs) will be similar to atoms, in which a single sss-wave scattering length governs the collisional physics. However, Do\ifmmode \mbox{\c{c}}\else \c{c}\fi{}aj et al. [Phys. Rev. Lett. 116, 135301 (2016)] argued that the short-range collisional physics of NRMs is much more complex than for atoms and that this leads to a many-body description in terms of a multichannel Hubbard model. In this work we show that this multichannel Hubbard model description of NRMs in an optical lattice is robust against the approximations employed by Do\ifmmode \mbox{\c{c}}\else \c{c}\fi{}aj et al. to estimate its parameters. We do so via an exact, albeit formal, derivation of a multichannel resonance model for two NRMs from an ab initio description of the molecules in terms of their constituent atoms. We discuss the regularization of this two-body multichannel resonance model in the presence of a harmonic trap and how its solutions form the basis for the many-body model of Do\ifmmode \mbox{\c{c}}\else \c{c}\fi{}aj et al.. We also generalize the derivation of the effective lattice model to include multiple internal states (e.g., rotational or hyperfine). We end with an outlook to future research.
We calculate the parameters of the recently derived many-channel Hubbard model that is predicted to describe ultracold nonreactive molecules in an optical lattice, going beyond the approximations used by Do\ifmmode \mbox{\c{c}}\else \c{c}\fi{}aj et al. [A. Do\ifmmode \mbox{\c{c}}\else \c{c}\fi{}aj et al., Phys. Rev. Lett. 116, 135301 (2016)]. Although those approximations are expected to capture the qualitative structure of the model parameters, finer details and quantitative values are less certain. To set expectations for experiments, whose results depend on the model parameters, we describe the approximations' regime of validity and the likelihood that experiments will be in this regime, discuss the impact that the failure of these approximations would have on the predicted model, and develop theories going beyond these approximations. Not only is it necessary to know the model parameters in order to describe experiments, but the connection that we elucidate between these parameters and the underlying assumptions that are used to derive them will allow molecule experiments to probe new physics. For example, transition state theory, which is used across chemistry and chemical physics, plays a key role in our determination of lattice parameters, thus connecting its physical assumptions to highly accurate experimental investigation.
We show that, in appropriate regimes, ultracold collisionally shielded molecules in an optical lattice realize a controlled extended Hubbard model, despite their large-radius hard-core repulsion. We compute the Hubbard parameters and show lattice depth and microwave-induced dipolar interactions provide flexible, independent control of on- and off-site interactions. This makes shielded molecules a powerful platform for extended Hubbard models and enables an interaction microscope that can distinguish inter-hole interactions in doped Mott insulators - crucial to superconductivity and strange metallicity - that are indistinguishable with quantum gas microscopy alone.
We present a theory for ultracold atomic gases in an optical lattice near a Feshbach resonance. In the single-band approximation the theory describes atoms and molecules that can both tunnel through the lattice. Moreover, an avoided crossing between the two-atom and the molecular states occurs at every site. We determine the microscopic parameters of the generalized Hubbard model that describes this physics, using the experimentally known parameters of the Feshbach resonance in the absence of the optical lattice. As an application we also calculate the zero-temperature phase diagram of an atomic Bose gas in an optical lattice.
One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.
One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.