Recent theory has indicated how to emulate tunable models of quantum magnetism with ultracold polar molecules. Here we show that present molecule optical lattice experiments can accomplish three crucial goals for quantum emulation, despite currently being well below unit filling and not quantum degenerate. The first is to verify and benchmark the models proposed to describe these systems. The second is to prepare correlated and possibly useful states in well-understood regimes. The third is to explore many-body physics inaccessible to existing theoretical techniques. Our proposal relies on a nonequilibrium protocol that can be viewed either as Ramsey spectroscopy or an interaction quench. The proposal uses only routine experimental tools available in any ultracold molecule experiment. To obtain a global understanding of the behavior, we treat short times pertubatively, develop analytic techniques to treat the Ising interaction limit, and apply a time-dependent density matrix renormalization group to disordered systems with long range interactions.
Recent theory has indicated how to emulate tunable models of quantum magnetism with ultracold polar molecules. Here we show that present molecule optical lattice experiments can accomplish three crucial goals for quantum emulation, despite currently being well below unit filling and not quantum degenerate. The first is to verify and benchmark the models proposed to describe these systems. The second is to prepare correlated and possibly useful states in well-understood regimes. The third is to explore many-body physics inaccessible to existing theoretical techniques. Our proposal relies on a nonequilibrium protocol that can be viewed either as Ramsey spectroscopy or an interaction quench. The proposal uses only routine experimental tools available in any ultracold molecule experiment. To obtain a global understanding of the behavior, we treat short times pertubatively, develop analytic techniques to treat the Ising interaction limit, and apply a time-dependent density matrix renormalization group to disordered systems with long range interactions.
This article gives an introduction to the realization of effective quantum magnetism with ultracold molecules in an optical lattice, reviews experimental and theoretical progress, and highlights future opportunities opened up by ongoing experiments. Ultracold molecules offer capabilities that are otherwise difficult or impossible to achieve in other effective spin systems, such as long-ranged spin-spin interactions with controllable degrees of spatial and spin anisotropy and favorable energy scales. Realizing quantum magnetism with ultracold molecules provides access to rich many-body behaviors, including many exotic phases of matter and interesting excitations and dynamics. Far-from-equilibrium dynamics plays a key role in our exposition, just as it did in recent ultracold molecule experiments realizing effective quantum magnetism. In particular, we show that dynamical probes allow the observation of correlated many-body spin physics, even in polar molecule gases that are not quantum degenerate. After describing how quantum magnetism arises in ultracold molecules and discussing recent observations of quantum magnetism with polar molecules, we survey prospects for the future, ranging from immediate goals to long-term visions.
We use Ramsey spectroscopy to experimentally probe the quantum dynamics of disordered dipolar-interacting ultracold molecules in a partially filled optical lattice, and we compare the results to theory. We report the capability to control the dipolar interaction strength. We find excellent agreement between our measurements of the spin dynamics and theoretical calculations with no fitting parameters, including the dynamics' dependence on molecule number and on the dipolar interaction strength. This agreement verifies the microscopic model expected to govern the dynamics of dipolar molecules, even in this strongly correlated beyond-mean-field regime, and represents the first step towards using this system to explore many-body dynamics in regimes that are inaccessible to current theoretical techniques.
By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the $t\mathrm{\text{\ensuremath{-}}}J$ model, which we refer to as the $t\mathrm{\text{\ensuremath{-}}}J\mathrm{\text{\ensuremath{-}}}V\mathrm{\text{\ensuremath{-}}}W$ model. In addition to XXZ spin exchange, the model features density-density interactions and density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the $t\mathrm{\text{\ensuremath{-}}}J\mathrm{\text{\ensuremath{-}}}V\mathrm{\text{\ensuremath{-}}}W$ model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally.
Abstract This paper reviews recent advances in the study of strongly interacting systems of dipolar molecules. Heteronuclear molecules feature large and tunable electric dipole moments, which give rise to long-range and anisotropic dipole–dipole interactions. Ultracold samples of dipolar molecules with long-range interactions offer a unique platform for quantum simulations and the study of correlated many-body physics. We provide an introduction to the physics of dipolar quantum gases, both electric and magnetic, and summarize the multipronged efforts to bring dipolar molecules into the quantum regime. We discuss in detail the recent experimental progress in realizing and studying strongly interacting systems of polar molecules trapped in optical lattices, with particular emphasis on the study of interacting spin systems and non-equilibrium quantum magnetism. Finally, we conclude with a brief discussion of the future prospects for studies of strongly interacting dipolar molecules.
Ultracold polar molecules present a rich platform for experimental quantum science leveraging their unique properties. Of particular relevance is the intrinsic electric dipole moment of the molecule, which results in strong coupling to microwave fields and can be used to engineer long-range, anisotropic, and tunable dipole-dipole interactions. Such interactions can generate entanglement between molecules and enable the study of novel quantum many-body phenomena in parameter regimes inaccessible in other systems. Modern experiments in optical tweezers and optical lattices have demonstrated controlled interactions between molecules in coherent quantum states, and recently bulk gases of molecules have been cooled to quantum degeneracy. Motivated by these landmark advances, we present this article to explain many of the key concepts relevant to current research in the field.
Real materials are extremely complicated, and any attempt to understand their bulk properties must begin with the appropriate choice of an idealized model, or Hamiltonian. There are many situations where such models have furnished a decisive understanding of complex quantum phenomena, such as BCS superconductivity and quantum magnetism. There are also cases, for instance the unconventional superconductivity of doped cuprates or heavy-fermion metals, where even the simplest conceivable models are intractable to current theoretical techniques. A promising route toward understanding the physics of such models is to simulate them directly with a highly controlled quantum system. Ultracold neutral atoms, polar molecules, and ions are in many ways ideally suited to this task.\nIn this thesis, we emphasize how the unique features of particular atomic and molecular sys- tems can be leveraged to access interesting physics in experimentally feasible temperature regimes. In chapter 3, we consider prospects for simulation of the Kondo lattice model using alkaline- earth atoms. In particular, we show how groundstate properties--for instance anomalous mass enhancement--can be probed by looking at far-from equilibrium dynamics, which are a standard diagnostic tool in ultracold atom experiments. Chapter 4 describes a realistic implementation of a bosonic version of the Kondo lattice model, and we show how the Kondo interaction qualitatively changes the superfluid to Mott insulator phase transition. Chapters 5, 6, and 7 are unified through an attempt to understand the effects of dissipation in many-body quantum systems. In chapter 5, our goal is mainly to understand the detrimental effects of two-body reactive collisions on dipolar molecules in a 3D optical lattice. Chapter 6 takes a rather different perspective, and shows that this type of loss naturally induces quantum correlations in the steady state of reactive fermionic molecules or alkaline earth atoms. In chapter 7, we develop an exact analytic solution for the non-equilibrium dynamics of long-ranged Ising models with Markovian decoherence. We apply our solution to the benchmarking of dynamics in an existing trapped-ion quantum simulator, which due to its large size and long-ranged, frustrated, interactions is well beyond the reach of a brute force numerical description.