Ana Maria Rey

Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices

Quantum mechanical superexchange interactions form the basis of quantum magnetism in strongly correlated electronic media. We report on the direct measurement of superexchange interactions with ultracold atoms in optical lattices. After preparing a spin-mixture of ultracold atoms in an antiferromagnetically ordered state, we measured coherent superexchange-mediated spin dynamics with coupling energies from 5 hertz up to 1 kilohertz. By dynamically modifying the potential bias between neighboring lattice sites, the magnitude and sign of the superexchange interaction can be controlled, thus allowing the system to be switched between antiferromagnetic and ferromagnetic spin interactions. We compare our findings to predictions of a two-site Bose-Hubbard model and find very good agreement, but are also able to identify corrections that can be explained by the inclusion of direct nearest-neighbor interactions.

Observation of dipolar spin-exchange interactions with lattice-confined polar molecules

With the recent production of polar molecules in the quantum regime [1, 2], long-range dipolar interactions are expected to facilitate the understanding of strongly interacting many-body quantum systems and to realize lattice spin models [3] for exploring quantum magnetism. In atomic systems, where interactions require wave function overlap, effective spin interactions on a lattice can be realized through superexchange; however, the coupling is relatively weak and limited to nearest-neighbor interactions [4–6]. In contrast, dipolar interactions exist even in the absence of tunneling and extend beyond nearest neighbors. This allows coherent spin dynamics to persist even for gases with relatively high entropy and low lattice filling. While measured effects of dipolar interactions in ultracold molecular gases have thus far been limited to the modification of inelastic collisions and chemical reactions [7, 8], we now report the first observation of dipolar interactions of polar molecules pinned in a three-dimensional optical lattice. We realize a lattice spin model where spin is encoded in rotational states of molecules that are prepared and probed by microwaves. This interaction arises from the resonant exchange of rotational angular momentum between two molecules and realizes a spin-exchange interaction. The dipolar interactions are apparent in the evolution of the spin coherence, where we observe clear oscillations in addition to an overall decay of the coherence. The frequency of these oscillations, the strong dependence of the spin coherence time on the lattice filling factor, and the effect of a multi-pulse sequence designed to reverse dynamics due to two-body exchange interactions all provide clear evidence of dipolar interactions. Furthermore, we demonstrate the suppression of loss in weak lattices due to a quantum Zeno mechanism [9]. Measurements of these tunneling-induced losses allow us to independently determine the lattice filling factor. The results reported here comprise an initial exploration of the behavior of many-body spin models with direct, long-range spin interactions and lay the groundwork for future studies of many-body dynamics in spin lattices.With the production of polar molecules in the quantum regime, long-range dipolar interactions are expected to facilitate understanding of strongly interacting many-body quantum systems and to realize lattice spin models for exploring quantum magnetism. In ordinary atomic systems, where contact interactions require wavefunction overlap, effective spin interactions on a lattice can be mediated by tunnelling, through a process referred to as superexchange; however, the coupling is relatively weak and is limited to nearest-neighbour interactions. In contrast, dipolar interactions exist even in the absence of tunnelling and extend beyond nearest neighbours. This allows coherent spin dynamics to persist even for gases with relatively high entropy and low lattice filling. Measured effects of dipolar interactions in ultracold molecular gases have been limited to the modification of inelastic collisions and chemical reactions. Here we use dipolar interactions of polar molecules pinned in a three-dimensional optical lattice to realize a lattice spin model. Spin is encoded in rotational states of molecules that are prepared and probed by microwaves. Resonant exchange of rotational angular momentum between two molecules realizes a spin-exchange interaction. The dipolar interactions are apparent in the evolution of the spin coherence, which shows oscillations in addition to an overall decay of the coherence. The frequency of these oscillations, the strong dependence of the spin coherence time on the lattice filling factor and the effect of a multipulse sequence designed to reverse dynamics due to two-body exchange interactions all provide evidence of dipolar interactions. Furthermore, we demonstrate the suppression of loss in weak lattices due to a continuous quantum Zeno mechanism. Measurements of these tunnelling-induced losses allow us to determine the lattice filling factor independently. Our work constitutes an initial exploration of the behaviour of many-body spin models with direct, long-range spin interactions and lays the groundwork for future studies of many-body dynamics in spin lattices.

A Quantum Many-Body Spin System in an Optical Lattice Clock

Strongly Correlated Clocks Optical lattice clocks with alkaline earth atoms provide one of the most stable time-keeping systems. Such clocks, in general, exhibit shifts in their transition frequencies as a consequence of interactions between atoms. Can this sensitivity be used to explore the dynamics of strongly correlated quantum systems? Martin et al. (p. 632) used a 1-dimensional optical lattice clock to study quantum many-body effects. Whereas the clock shift itself could be modeled within the mean field approximation, quantities such as spin noise required a full many-body treatment. This system may be useful for the quantum simulation of exotic magnetism. A one-dimensional lattice of pancake-shaped clouds of 87Sr atoms is used to realize a strongly correlated system of spins. Strongly interacting quantum many-body systems arise in many areas of physics, but their complexity generally precludes exact solutions to their dynamics. We explored a strongly interacting two-level system formed by the clock states in 87Sr as a laboratory for the study of quantum many-body effects. Our collective spin measurements reveal signatures of the development of many-body correlations during the dynamical evolution. We derived a many-body Hamiltonian that describes the experimental observation of atomic spin coherence decay, density-dependent frequency shifts, severely distorted lineshapes, and correlated spin noise. These investigations open the door to further explorations of quantum many-body effects and entanglement through use of highly coherent and precisely controlled optical lattice clocks.

Suppression of Collisional Shifts in a Strongly Interacting Lattice Clock

Keeping Time Optical lattice clocks are comprised of atoms placed in an optical lattice formed by opposing laser beams and can be more precise than traditional microwave atomic clocks because of the higher frequency at which they operate, and the number of atoms available for interrogation. However, interactions between the atoms may lead to shifts in the frequency of the clock transition, usually proportional to the atomic density. Swallows et al. (p. 1043, published online 3 February) demonstrate an opposite and unexpected effect of interactions: For sufficiently strongly interacting systems, the frequency shift is suppressed. Indeed, in a strontium-based fermionic lattice clock, the shift and its associated spread were reduced by an order of magnitude. Increasing atomic interactions improved the accuracy and precision of a clock formed from atoms trapped in an optical lattice. Optical lattice clocks with extremely stable frequency are possible when many atoms are interrogated simultaneously, but this precision may come at the cost of systematic inaccuracy resulting from atomic interactions. Density-dependent frequency shifts can occur even in a clock that uses fermionic atoms if they are subject to inhomogeneous optical excitation. However, sufficiently strong interactions can suppress collisional shifts in lattice sites containing more than one atom. We demonstrated the effectiveness of this approach with a strontium lattice clock by reducing both the collisional frequency shift and its uncertainty to the level of 10−17. This result eliminates the compromise between precision and accuracy in a many-particle system; both will continue to improve as the number of particles increases.

Collective atomic scattering and motional effects in a dense coherent medium

We investigate collective emission from coherently driven ultracold 88Sr atoms. We perform two sets of experiments using a strong and weak transition that are insensitive and sensitive, respectively, to atomic motion at 1 μK. We observe highly directional forward emission with a peak intensity that is enhanced, for the strong transition, by >103 compared with that in the transverse direction. This is accompanied by substantial broadening of spectral lines. For the weak transition, the forward enhancement is substantially reduced due to motion. Meanwhile, a density-dependent frequency shift of the weak transition (∼10% of the natural linewidth) is observed. In contrast, this shift is suppressed to <1% of the natural linewidth for the strong transition. Along the transverse direction, we observe strong polarization dependences of the fluorescence intensity and line broadening for both transitions. The measurements are reproduced with a theoretical model treating the atoms as coherent, interacting radiating dipoles.

Long-Lived Dipolar Molecules and Feshbach Molecules in a 3D Optical Lattice

We have realized long-lived ground-state polar molecules in a 3D optical lattice, with a lifetime of up to 25 s, which is limited only by off-resonant scattering of the trapping light. Starting from a 2D optical lattice, we observe that the lifetime increases dramatically as a small lattice potential is added along the tube-shaped lattice traps. The 3D optical lattice also dramatically increases the lifetime for weakly bound Feshbach molecules. For a pure gas of Feshbach molecules, we observe a lifetime of greater than 20 s in a 3D optical lattice; this represents a 100-fold improvement over previous results. This lifetime is also limited by off-resonant scattering, the rate of which is related to the size of the Feshbach molecule. Individually trapped Feshbach molecules in the 3D lattice can be converted to pairs of K and Rb atoms and back with nearly 100% efficiency.

Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules

By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t-J model, which we refer to as the t-J-V-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-J-V-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally.

Quantum spin dynamics and entanglement generation with hundreds of trapped ions

Hundreds of ions simulate magnetism Strongly interacting quantum systems present a challenge to computational methods even at a relatively low particle number of a few dozen. Researchers are looking to tackle such problems by simulating them in a well-understood and controllable system. A linear array of ions is one such system; however, assembling a large enough number of ions is tricky. Bohnet et al. show that a two-dimensional “crystal” of around 200 9Be+ ions held together by magnetic and electric fields in a so-called Penning trap can simulate quantum magnetism. The work sets the stage for simulations with more complicated forms of interaction that classical computers would find intractable. Science, this issue p. 1297 A two-dimensional array of around 200 beryllium ions in a Penning trap simulates the quantum dynamics of the homogeneous Ising model. Quantum simulation of spin models can provide insight into problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. We studied quantum spin dynamics arising from an engineered, homogeneous Ising interaction in a two-dimensional array of 9Be+ ions in a Penning trap. We verified entanglement in spin-squeezed states of up to 219 ions, directly observing 4.0 ± 0.9 decibels of spectroscopic enhancement, and observed states with non-Gaussian statistics consistent with oversqueezed states. The good agreement with ab initio theory that includes interactions and decoherence lays the groundwork for simulations of the transverse-field Ising model with variable-range interactions, which are generally intractable with classical methods.

Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid

We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely. In a large-N limit, we find a chiral spin liquid ground state with topological order and Abelian fractional statistics. We discuss its experimental detection. Chiral spin liquids with non-Abelian anyons may also be realizable with alkaline earth atoms.

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet

Characterizing the correlations of quantum many-body systems is known to be hard, but there are ways around: for example, a new method for measuring out-of-time correlations demonstrated in a Penning trap quantum simulator with over 100 ions.