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We investigate theoretically the suppression of two-body losses when the on-site loss rate is larger than all other energy scales in a lattice. This work quantitatively explains the recently observed suppression of chemical reactions between two rotational states of fermionic KRb molecules confined in one-dimensional tubes with a weak lattice along the tubes [Yan et al., Nature 501, 521-525 (2013)]. New loss rate measurements performed for different lattice parameters but under controlled initial conditions allow us to show that the loss suppression is a consequence of the combined effects of lattice confinement and the continuous quantum Zeno effect. A key finding, relevant for generic strongly reactive systems, is that while a single-band theory can qualitatively describe the data, a quantitative analysis must include multiband effects. Accounting for these effects reduces the inferred molecule filling fraction by a factor of five. A rate equation can describe much of the data, but to properly reproduce the loss dynamics with a fixed filling fraction for all lattice parameters we develop a mean-field model and benchmark it with numerically exact time-dependent density matrix renormalization group calculations., 4+ pages main text, 4 figures. 3 pages supplementary material, 2 figures

The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics. In a step toward understanding this interplay, we obtain an exact analytic solution for the nonequilibrium dynamics of Ising models with arbitrary couplings (and therefore in arbitrary dimension) and subject to local Markovian decoherence. Our solution shows that decoherence significantly degrades the nonclassical correlations developed during coherent Ising spin dynamics, which relax much faster than predicted by treating decoherence and interactions separately. We also show that the competition of decoherence and interactions induces a transition from oscillatory to overdamped dynamics that is absent at the single-particle or mean-field level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. In particular, we apply our results to the NIST Penning trapped-ion experiment and show that the current experiment is capable of producing entanglement amongst hundreds of quantum spins.

Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations. In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t=0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Ref. [1]. Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g. Bloch vector and spin-squeezing dynamics. In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence of both T_1 (spontaneous spin relaxation/excitation) and T_2 (dephasing) type decoherence processes. Even though the decoherence is local, our solution reveals that the competition between Ising dynamics and T_1 decoherence gives rise to an emergent non-local dephasing effect, thereby drastically amplifying the degradation of quantum correlations. In addition to identifying the mechanism of this deleterious effect, our solution points toward a scheme to eliminate it via measurement-based coherent feedback., Comment: 34 pages, 11 pages

We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole-dipole interactions give rise to interactions between the spins. In particular, we show that, with sufficient microwave control, the interaction between two spins can be written as a sum of five independently controllable Hamiltonian terms proportional to the five rank-2 spherical harmonics Y_{2,q}(theta,phi), where (theta,phi) are the spherical coordinates of the vector connecting the two molecules. To demonstrate the potential of this approach beyond the simplest examples studied in [S. R. Manmana et al., arXiv:1210.5518v2], we focus on the realization of the Kitaev honeycomb model, which can support exotic non-Abelian anyonic excitations. We also discuss the possibility of generating spin Hamiltonians with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry., Comment: 8 pages, 2 figures, submitted to a special issue of Molecular Physics

Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal $\mathrm{SU}(N)$ symmetries, where $N$ can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime of one-dimensional chains, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing $N$. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature $\mathrm{SU}(N)$ magnetism. Our findings are encouraging for the exploration of exotic large-$N$ magnetic states in ongoing experiments.

We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin S >= 1/2 and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases -- previously studied only in the nearest-neighbor case -- survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed., Main text: 4 pages plus references, 3 figures. Supplementary info.: 4+epsilon pages. v2: significantly improved presentation

Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal SU(N) symmetries, where N can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime of one-dimensional chains, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing N. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature SU(N) magnetism. Our findings are encouraging for the exploration of exotic large-N magnetic states in ongoing experiments.

We calculate experimentally relevant properties of trapped fermionic alkaline-earth-metal atoms in an optical lattice, modeled by the SU$(N)$ Hubbard model. We employ a high-temperature expansion that is accurate when the temperature is larger than the tunneling rate, similar to current regimes in ultracold atom experiments. In addition to exploring the Mott insulator-metal crossover, we calculate final temperatures achieved by the standard experimental protocol of adiabatically ramping from a noninteracting gas, as a function of initial gas temperature. Of particular experimental interest, we find that increasing $N$ for fixed particle numbers and initial temperatures gives substantially colder Mott insulators after the adiabatic ramping, up to more than a factor of 5 for relevant parameters. This cooling happens for all $N$, fixing the initial entropy, or for all $N\ensuremath{\lesssim}20$ (the exact value depends on dimensionality), at fixed, experimentally relevant initial temperatures.

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 non-equilibrium protocol that can be viewed either as Ramsey spectroscopy or an interaction quench. It uses only routine experimental tools available in any ultracold molecule experiment., Comment: 6+ pages, 4 figures

lling 1 =N, which is due to the fact that BA improperly treats the triply and higher occupied states. Using the DMRG forN 4 and the BA for large N, we determine the regimes of validity of strong- and weak-coupling perturbation theory for all values of N and in particular, the parameter range in which the system is well described by a SU(N) Heisenberg model at lling 1 =N. We nd this depends only weakly on N. We investigate the Berezinskii-Kosterlitz-Thouless phase transition from a Luttinger liquid to a Mott-insulator by computing the delity susceptibility and the Luttinger parameter K at 1=N lling. The numerical ndings give strong evidence that the delity susceptibility develops a minimum at a critical interaction strength which is found to occur at a nite positive value for N > 2.

Motivated by ongoing measurements at JILA, we calculate the recoil-free spectra of dipolar interacting fermions, for example ultracold heteronuclear molecules, in a one-dimensional lattice of two-dimensional layers or "pancakes," spectroscopically probing transitions between different internal (e.g., rotational) states. We additionally incorporate p-wave interactions and losses, which are important for reactive molecules such as KRb. Moreover, we consider other sources of spectral broadening: interaction-induced quasiparticle lifetimes and the different polarizabilities of the rotational states used for the spectroscopy. Although our main focus is molecules, some of the calculations are also useful for optical lattice atomic clocks. For example, understanding the p-wave shifts between identical fermions and small dipolar interactions coming from the excited clock state is necessary to reach future precision goals. Finally, we consider the spectra in a deep three-dimensional lattice and show how they give a great deal of information about static correlation functions, including all the moments of the density correlations between nearby sites. The range of correlations measurable depends on spectroscopic resolution and the dipole moment.

We study the time scales for adiabaticity of trapped cold bosons subject to a time-varying lattice potential using a dynamic Gutzwiller mean-field theory. We explain apparently contradictory experimental observations by demonstrating a clear separation of time scales for local dynamics ($\ensuremath{\sim}\text{ }\mathrm{ms}$) and global mass redistribution ($\ensuremath{\sim}1\text{ }\text{ }\mathrm{s}$). We provide a simple explanation for the short and fast time scales, finding that while density or energy transport is dominated by low energy phonons, particle-hole excitations set the adiabaticity time for fast ramps. We show how mass transport shuts off within Mott-insulator domains, leading to a chemical potential gradient that fails to equilibrate on experimental time scales.

This chapter will discuss RF spectroscopy of lattice bosons from a point of view complementary to that of Chap. 4. That chapter looked at things from the vantage of sum rules assuming a single, narrow spectral line, one common approach in the literature. This chapter is more closely related to another common approach in the literature: taking the RF spectra to be (convolutions of) the single particle spectral functions, perhaps with shifts of lines due to final state interactions. This naturally leads to a two-peaked structure in the superfluid: there are gapless Goldstone modes (superfluid phonons) and gapped order parameter amplitude modes (Higgs modes). After constructing an approximation sufficient to capture the global physics, we will reconcile the two points of view. In addition to giving a global calculation for the spectrum of bosons in an optical lattice, the reconciliation provides a new general lesson for interpreting RF spectra of many-body systems, showing how standard viewpoints emerge in special limits of the proper calculation.

In this chapter, I further develop the theory necessary to apply RF spectra techniques to overcoming experimental challenges in ultracold atomic systems.

Many of the most important, interesting, and vexing problems we encounter are questions about the behavior of large collections of objects: How do atoms organize themselves to form diverse materials such as plastics, metals, fluids, and magnets? How do connected neurons collectively result in intelligence? How do competing organisms give rise to ecosystems? How do humans organize themselves into groups, economies, and societies? Each of these questions shares the common thread of being a question about how entities come together to give rise to behavior not obviously connected to the underlying entities. In physics, the study of large collections of interacting objects is referred to as “many-body physics.”

I develop a phenomenology of a particular model of disordered supersolidity. It is related to proposals that superflow occurs along defects—dislocations, grain boundaries, and amorphous regions—but develops a picture of the macroscopic, experimental properties of the system starting from these microscopic considerations. The essence of the idea is that superflow may exist in large disordered regions, and that the supersolid feature observed in torsional oscillator experiments corresponds to the point where these become globally phase coherent, even though the superflow \(within\) the domains is already present at higher temperatures. The experimental consequences of this are fleshed out and found to be consistent with the present state of experiments.

We theoretically explore the generation of few-body analogs of fractional quantum Hall states. We consider an array of identical few-atom clusters n = 2,3,4, each cluster trapped at the node of an optical lattice. By temporally varying the amplitude and phase of the trapping lasers, one can introduce a rotating deformation at each site. We analyze protocols for coherently transferring ground state clusters into highly correlated states, producing theoretical fidelities (probability of reaching the target state) in excess of 99%.

In Chapter 9 I described a protocol to efficiently generate small clusters of fractional quantum Hall states at sites of a deep optical lattice, in the limit where particles were unable to tunnel between sites on experimentally relevant timescales. One motivation for this chapter is to construct a theory of deep lattices that are nevertheless weak enough to allow particle tunneling between sites (analogous to the Bose-Hubbard limit of bosons in an optical lattice introduced in Chapter 2.). I construct a theory—specifically an effective lattice model—that captures the dominant behavior for bosons, and essentially identical techniques lead to a description of fermions. In the bosonic case, I construct an analog of the Gutzwiller mean field theory (introduced in Chapter 2) for this generalized model. I show that the resulting model has a phase diagram topologically the same as the Bose-Hubbard model: there are globally insulating phases with fractional quantum Hall puddles at each site and no coherence between them occupying “Mott lobes” in the chemical potential-lattice depth phase diagram, and a superfluid phase with coherence between the fractional quantum Halls states at each site.

The work presented in this chapter gives a mechanism which is expected to reduce, potentially dramatically, the collision probability of two spin-polarized hydrogen atoms adsorbed on a helium film. This was motivated by experiments by Ahokas et al. which observed anomalously small collisional shifts. Refs. [1, 2] revealed that a symmetry missed in the original work is likely responsible for the reduction, however our mechanism is still relevant affects other observable properties: atomic recombination rates, other spectral lines, and suggests that the cloud will collapse at sufficiently low temperatures.

Although rotation and effective magnetic fields have been around essentially since the first observations of Bose–Einstein condensates, they have only more recently become capable of approaching exotic states. The (former) Chu group have created fractional quantum Hall puddles in a lattice, using methods similar to those discussed in Chap. 9 (N. Gemelke, private communication).

Chapter 10 introduced a generalized Bose-Hubbard model that is, under appropriate circumstances, capable of describing experimentally important situations, and which is much more general than the ordinary Bose-Hubbard model. However, while we could deduce the form of the Hamiltonian, quantitatively calculating the model’s parameters is non-trivial.

Although the bulk of this thesis concentrates on cold atomic gases, I have also worked in other areas of condensed matter physics. In graduate school, this has largely been in low temperature fluids and solids. The following chapters discuss some results I’ve obtained on these systems: collisional properties of nearly-degenerate spin-polarized hydrogen adsorbed on helium films (Chap. 16), anomalous behavior of atomic hydrogen defects in molecular hydrogen quantum solids (Chap. 17), and a possible scenario for supersolidity, inspired by experiments on solid hydrogen and helium (Chap. 18).

Summarizing our studies of RF spectroscopy, we have showed that two common but qualitatively distinct pictures of RF spectroscopy—one based on sum rules, and one based on single particle Green’s functions—emerge as special limits of a more complete calculation, depending on the final state interactions through the quantity U ab ? U aa/t a . In the deep Mott and superfluid limits, we have extended our calculations to finite temperature. We have also discussed how RF spectra with interactions beyond on-site may be used to probe full joint number distributions on multiple sites; candidates with appropriate interactions are Rydberg excitations or molecular gases.

We calculate the interaction induced inhomogeneous broadening of spectral lines in a trapped Bose gas as a function of the depth of a three-dimensional cubic optical lattice. As observed in recent experiments, we find that the terraced “wedding-cake" structure of Mott plateaus splits the spectrum into a series of discrete peaks. The spectra are extremely sensitive to density corrugations and trap anharmonicities. For example, even when the majority of the cloud is superfluid the spectrum displays discrete peaks.

We show that the dilute Fermi gas quantum critical universality class quantitatively describes the Mott/metal crossover of the two-dimensional Hubbard model for temperatures somewhat less than (roughly half) the tunneling but much greater than (roughly twice) the superexchange energy. We calculate the observables expected to be universal near the transition --- density and compressibility --- with numerically exact determinantal quantum Monte Carlo. We find they are universal functions of the chemical potential. Despite arising from the strongly correlated regime of the Hubbard model, these functions are given by the weakly interacting, dilute Fermi gas model. These observables and their derivatives are the only expected universal static observables of this universality class, which we also confirm by verifying there is no scaling collapse of the kinetic energy, fraction of doubly occupied sites, and nearest neighbor spin correlations. Our work resolves the universality class of the intermediate temperature Mott/metal crossover, which had alternatively been proposed to be described by more exotic theories. However, in the presence of a Zeeman magnetic field, we find that interplay of spin with itinerant charge can lead to physics beyond the dilute Fermi gas universality class., Comment: Main text: 4 pages, 2 figures (6 panels). Supplementary info.: 2 pages, 3 figures (7 panels)

This chapter contains a number of short notes expanding details mentioned in the previous chapter.

Rotating quantum systems leads to dramatic and exotic phenomena. The first rotational phenomena to be experimentally explored in cold atoms was vortices and vortex lattices in a rotating superfluid. Because a superfluid is irrotational, all rotation is contained in topological defects with circulation quantized in units of \(\hbar\). This is a phenomena that occurs in superfluid \(^{4} {\hbox{He}}\) and \(^{3} {\hbox{He}}\), as well as in type-2 superconductors (superconductors only show vortices in a certain limit, corresponding to type-2 superconductors, because the electromagnetic field energy has to be considered in addition to the electron fluid). Images of vortices in cold gas experiments directly showed this spectacular manifestations of superfluidity.

The first stage of producing an ultracold atomic gas is to vaporize a solid (with an “oven” or other source) to create a hot gas, whose center of mass is then slowed sufficiently to be trapped. The slowing is frequently accomplished by a “Zeeman slower”: a series of current carrying coils that generate magnetic fields, and which decrease in intensity over the length of the slower, to create a magnetic field gradient. Atoms used in this technique possess an electron spin degree of freedom so that the internal energy of the atom depends on the applied magnetic field and thus the magnetic field gradient introduces a potential energy gradient that slows the atoms.

Attempts to understand zero temperature phase transitions have forced physicists to consider a regime where the standard paradigms of condensed matter physics break down [1-4]. These quantum critical systems lack a simple description in terms of weakly interacting quasiparticles, but over the past 20 years physicists have gained deep insights into their properties. Most dramatically, theory predicts that universal scaling relationships describe their finite temperature thermodynamics up to remarkably high temperatures. Unfortunately, these universal functions are hard to calculate: for example there are no reliable general techniques [4,5] to calculate the scaling functions for dynamics. Viewing a cold atom experiment as a quantum simulator [6], we show how to extract universal scaling functions from (non-universal) atomic density profiles or spectroscopic measurements. Such experiments can resolve important open questions about the Mott-Metal crossover [7,8] and the dynamics of the finite density O(2) rotor model [1,9], with direct impact on theories of, for example, high temperature superconducting cuprates [10,11], heavy fermion materials [12], and graphene [13]., 12 double spaced pages (main text), 12 double spaced pages (supplementary information), 4 figures (10 panels)

We analyze a number of proposed explanations for spectroscopic anomalies observed in atomic hydrogen defects embedded in a solid molecular hydrogen matrix. In particular, we critically evaluate the possibility that these anomalies are related to Bose-Einstein condensation (both global and local). For each proposed mechanism we discuss which aspects of the experiment can be explained, and make predictions for future experiments., Comment: 7 pages, 2 figures

We extend the standard Bose-Hubbard model to capture arbitrarily strong on-site correlations. In addition to being important for quantitatively modeling experiments, for example, with Rubidium atoms, these correlations must be included to describe more exotic situations. Two such examples are when the interactions are made large via a Feshbach resonance, or when each site rotates rapidly, making a coupled array of quantum Hall puddles. Remarkably, even the mean field approximation to our model includes all on-site correlations. We describe how these on-site correlations manifest themselves in the system's global properties: modifying the phase diagram and depleting the condensate., Comment: 4 pages, 4 figures

24th European Photovoltaic Solar Energy Conference, 21-25 September 2009, Hamburg, Germany; 251-254, Polycrystalline sulfides of the PbXSn1-XS (0 ≤ X ≤ 0.25) alloys were synthesized by the direct fusion technique. The thin films of these materials were prepared by a hot wall deposition method on glass substrates at Tsub. = 240 - 300 oC and vacuum of about 10-5 Torr. The microstructures of the films were characterized by XRD, SEM, EDX, AES and AFM. The thin film powder patterns matched the powder target patterns satisfactorily and indicated the absence of binary phases like PbS and SnS2. The SEM and AFM analyses show that the films are densely packed with layered crystallites which have good mechanical adhesion to each other. The as-grown PbXSn1-XS films show p-type conductivity. The electrical conductivity decreases with increasing Pb/Sn ratio of the thin film composition. As the Pb/Sn ratio increases, the activation energy increases from 0.121 eV for SnS to 0.264 eV for Pb0.25Sn0.75S.

We calculate the radio-frequency spectrum of a trapped cloud of cold bosonic atoms in an optical lattice. Using random phase and local density approximations we produce both trap averaged and spatially resolved spectra, identifying simple features in the spectra that reveal information about both superfluidity and correlations. Our approach is exact in the deep Mott limit and in the deep superfluid when the hopping rates for the two internal spin states are equal. It contains final state interactions, obeys the Ward identities (and the associated conservation laws), and satisfies the $f$-sum rule. Motivated by earlier work by Sun, Lannert, and Vishveshwara [Phys. Rev. A \textbf{79}, 043422 (2009)], we also discuss the features which arise in a spin-dependent optical lattice., Comment: 6 pages, 4 figures, 13 subfigures

We argue that helium film-mediated hydrogen-hydrogen interactions strongly reduce the magnitude of cold collision shifts in spin-polarized hydrogen adsorbed on a helium film. With plausible assumptions about experimental parameters this can explain (i) the 2 orders of magnitude discrepancy between previous theory and recent experiments and (ii) the anomalous dependence of the cold collision frequency shifts on the film's 3 He covering. The mediated interaction is attractive, suggesting that in current experiments the gas will become unstable before reaching the Kosterlitz-Thouless transition.

We calculate the interaction induced inhomogeneous broadening of spectral lines in a trapped Bose gas as a function of the depth of a three-dimensional cubic optical lattice. As observed in recent experiments, we find that the terraced "wedding-cake" structure of Mott plateaus splits the spectrum into a series of discrete peaks. The spectra are extremely sensitive to density corrugations and trap anharmonicities. For example, even when the majority of the cloud is superfluid the spectrum displays discrete peaks., 7 pages, 5 figures, revtex4