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Item Accessing Rydberg-dressed interactions using many-body Ramsey dynamics(American Physical Society, 2016) Mukherjee, Rick; Killian, Thomas C.; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsShow more We demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions in a many-body system well within experimentally measured lifetimes, in contrast to previous research, which either focused on interactions near Förster resonances or on few-atom systems. We build a spin-12 from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, which we demonstrate can be used to characterize the Rydberg-dressed interactions. Furthermore, the dynamics can differ significantly from that observed in other spin systems. As one example, spin echo can increase the rate at which coherence decays. The results also apply to bare (undressed) Rydberg states as a special case, for which we quantitatively reproduce recent ultrafast experiments without fitting.Show more Item Analytic ground state wave functions of mean-fieldﾠpx+ipy superconductors with vortices and boundaries(American Physical Society, 2018) Wang, Zhiyuan; Hazzard, Kaden R.A.Show more We study Read and Green's mean-field model of the spinless px+ipy superconductor [N. Read and D. Green, Phys. Rev. B 61, 10267 (2000)] at a special set of parameters where we find the analytic expressions for the topologically degenerate ground states and the Majorana modes, including in finite systems with edges and in the presence of an arbitrary number of vortices. The wave functions of these ground states are similar (but not always identical) to the Moore-Read Pfaffian states proposed for the ν=5/2 fractional quantum Hall system, which are interpreted as the p-wave superconducting states of composite fermions. The similarity in the long-wavelength universal properties is expected from previous work, but at the special point studied herein the wave functions are exact even for short-range, nonuniversal properties. As an application of these results, we show how to obtain the non-Abelian statistics of the vortex Majorana modes by explicitly calculating the analytic continuation of the ground state wave functions when vortices are adiabatically exchanged, an approach different from the previous one based on universal arguments. Our results are also useful for constructing particle-number-conserving (and interacting) Hamiltonians with exact projected mean-field states.Show more Item Bosonic molecules in a lattice: Unusual fluid phase from multichannel interactions(American Physical Society, 2018) Ewart, Kevin D.; Wall, Michael L.; Hazzard, Kaden R.A.Show more We show that multichannel interactions significantly alter the phase diagram of ultracold bosonic molecules in an optical lattice. Most prominently, an unusual fluid region intervenes between the conventional superfluid and the Mott insulator. In it, number fluctuations remain but phase coherence is suppressed by a significant factor. This factor can be made arbitrarily large, at least in a two-site configuration. We calculate the phase diagram using complementary methods, including Gutzwiller mean-field and density-matrix renormalization group calculations. Although we focus on bosonic molecules without dipolar interactions, we expect multichannel interactions to remain important for dipolar interacting and fermionic molecules.Show more Item Bounding the finite-size error of quantum many-body dynamics simulations(American Physical Society, 2021) Wang, Zhiyuan; Foss-Feig, Michael; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsShow more Finite-size errors (FSEs), the discrepancies between an observable in a finite system and in the thermodynamic limit, are ubiquitous in numerical simulations of quantum many-body systems. Although a rough estimate of these errors can be obtained from a sequence of finite-size results, a strict, quantitative bound on the magnitude of FSE is still missing. Here we derive rigorous upper bounds on the FSE of local observables in real-time quantum dynamics simulations initialized from a product state. In d-dimensional locally interacting systems with a finite local Hilbert space, our bound implies ∣∣⟨ˆS(t)⟩L−⟨ˆS(t)⟩∞|≤C(2vt/L)cL−μ, with v, C, c, μ constants independent of L and t, which we compute explicitly. For periodic boundary conditions (PBCs), the constant c is twice as large as that for open boundary conditions (OBCs), suggesting that PBCs have smaller FSEs than OBCs at early times. The bound can be generalized to a large class of correlated initial states as well. As a byproduct, we prove that the FSE of local observables in ground-state simulations decays exponentially with L under a suitable spectral gap condition. Our bounds are practically useful in determining the validity of finite-size results, as we demonstrate in simulations of the one-dimensional (1D) quantum Ising and Fermi-Hubbard models.Show more Item Cooling fermions in an optical lattice by adiabatic demagnetization(American Physical Society, 2018) Mirasola, Anthony E.; Wall, Michael L.; Hazzard, Kaden R.A.Show more The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the Néel temperature. However, reaching this temperature in the laboratory has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the SU(2) symmetry introduces many level crossings that prevent the system from reaching the ground state, even in principle. However, by breaking the SU(2) symmetry with a spin-dependent tunneling, we show that adiabatic demagnetization can achieve low-temperature states. Using density matrix renormalization group (DMRG) calculations in one dimension, we numerically find that demagnetization protocols successfully reach low-temperature states of a spin-anisotropic Hubbard model, and we discuss how to optimize this protocol for experimental viability. By subsequently ramping spin-dependent tunnelings to spin-independent tunnelings, we expect that our protocol can be employed to produce low-temperature states of the Fermi-Hubbard model.Show more Item Correlations and enlarged superconducting phase of t−J⊥ chains of ultracold molecules on optical lattices(American Physical Society, 2017) Manmana, Salvatore R.; Möller, Marcel; Gezzi, Riccardo; Hazzard, Kaden R.A.Show more We compute physical properties across the phase diagram of the t−J⊥ chain with long-range dipolar interactions, which describe ultracold polar molecules on optical lattices. Our results obtained by the density-matrix renormalization group indicate that superconductivity is enhanced when the Ising component Jz of the spin-spin interaction and the charge component V are tuned to zero and even further by the long-range dipolar interactions. At low densities, a substantially larger spin gap is obtained. We provide evidence that long-range interactions lead to algebraically decaying correlation functions despite the presence of a gap. Although this has recently been observed in other long-range interacting spin and fermion models, the correlations in our case have the peculiar property of having a small and continuously varying exponent. We construct simple analytic models and arguments to understand the most salient features.Show more Item Effective many-body parameters for atoms in nonseparable Gaussian optical potentials(American Physical Society, 2015) Wall, Michael L.; Hazzard, Kaden R.A.; Rey, Ana Maria; Rice Center for Quantum MaterialsShow more We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and nonseparability. Although these effects are negligible in more conventional optical lattice experiments, they are essential for emerging ultracold-atom developments. We focus in particular on two potentials utilized in current ultracold-atom experiments: arrays of tightly focused optical tweezers and a one-dimensional optical lattice with transverse Gaussian confinement and highly excited transverse modes. Our main numerical tools are discrete variable representations (DVRs), which combine many favorable features of spectral and grid-based methods, such as the computational advantage of exponential convergence and the convenience of an analytical representation of Hamiltonian matrix elements. Optimizations, such as symmetry adaptations and variational methods built on top of DVR methods, are presented and their convergence properties discussed. We also present a quantitative analysis of the degree of nonseparability of eigenstates, borrowing ideas from the theory of matrix product states, leading to both conceptual and computational gains. Beyond developing numerical methodologies, we present results for construction of optimally localized Wannier functions and tunneling and interaction matrix elements in optical lattices and tweezers relevant for constructing effective models for many-body physics.Show more Item Geometric representation of spin correlations and applications to ultracold systems(American Physical Society, 2018) Mukherjee, Rick; Mirasola, Anthony E.; Hollingsworth, Jacob; White, Ian G.; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsShow more We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics using a Bloch vector—e.g., a magnetic field causes it to precess and dissipation causes it to shrink—one can reason similarly about the shapes we use to visualize correlations. This visualization demonstrates its usefulness by unveiling the hidden structure in the correlations. For example, seemingly complex correlation dynamics can be described as simple motions of the shapes. We demonstrate the simplicity of the dynamics, which is obscured in conventional analyses, by analyzing several physical systems of relevance to cold atoms.Show more Item Model for scattering with proliferating resonances: Many coupled square wells(American Physical Society, 2018) Mehta, Nirav P.; Hazzard, Kaden R.A.; Ticknor, ChristopherShow more We present a multichannel model for elastic interactions, composed of an arbitrary number of coupled finite square-well potentials, and derive semianalytic solutions for its scattering behavior. Despite the model's simplicity, it is flexible enough to include many coupled short-ranged resonances in the vicinity of the collision threshold, as is necessary to describe ongoing experiments in ultracold molecules and lanthanide atoms. We also introduce a simple but physically realistic statistical ensemble for parameters in this model. We compute the resulting probability distributions of nearest-neighbor resonance spacings and analyze them by fitting to the Brody distribution. We quantify the ability of alternative distribution functions, for resonance spacing and resonance number variance, to describe the crossover regime. The analysis demonstrates that the multichannel square-well model with the chosen ensemble of parameters naturally captures the crossover from integrable to chaotic scattering as a function of closed-channel coupling strength.Show more Item Number-conserving interacting fermion models with exact topological superconducting ground states(American Physical Society, 2017) Wang, Zhiyuan; Xu, Youjiang; Pu, Han; Hazzard, Kaden R.A.Show more We present a method to construct number-conserving Hamiltonians whose ground states exactly reproduce an arbitrarily chosen BCS-type mean-field state. Such parent Hamiltonians can be constructed not only for the usual s -wave BCS state, but also for more exotic states of this form, including the ground states of Kitaev wires and two-dimensional topological superconductors. This method leads to infinite families of locally interacting fermion models with exact topological superconducting ground states. After explaining the general technique, we apply this method to construct two specific classes of models. The first one is a one-dimensional double wire lattice model with Majorana-like degenerate ground states. The second one is a two-dimensional p x + i p y superconducting model, where we also obtain analytic expressions for topologically degenerate ground states in the presence of vortices. Our models may provide a deeper conceptual understanding of how Majorana zero modes could emerge in condensed matter systems, as well as inspire novel routes to realize them in experiment.Show more Item Photoassociative spectroscopy of a halo molecule in 86Sr(American Physical Society, 2018) Aman, J.A.; Hill, J.C.; Ding, R.; Hazzard, Kaden R.A.; Killian, T.C.; Kon, W.Y.Show more We present two-photon photoassociation to the least-bound vibrational level of the X1Σ+g electronic ground state of the 86Sr2 dimer and measure a binding energy of Eb=−83.00(7)(20)kHz. Because of the very small binding energy, this is a halo state corresponding to the scattering resonance for two 86Sr atoms at low temperature. The measured binding energy, combined with universal theory for a very weakly bound state on a potential that asymptotes to a van der Waals form, is used to determine an s-wave scattering length a=810.6(3)(9)a0, which is consistent with, but substantially more accurate than, the previously determined a=798(12)a0 found from mass scaling and precision spectroscopy of other Sr isotopes. For the intermediate state, we use a bound level on the metastable 1S0−3P1 potential. Large sensitivity of the dimer binding energy to light near resonant with the bound-bound transition to the intermediate state suggests that 86Sr has great promise for manipulating atom interactions optically and probing naturally occurring Efimov states.Show more Item Quantum Simulators: Architectures and Opportunities(American Physical Society, 2021) Altman, Ehud; Brown, Kenneth R.; Carleo, Giuseppe; Carr, Lincoln D.; Demler, Eugene; Chin, Cheng; DeMarco, Brian; Economou, Sophia E.; Eriksson, Mark A.; Fu, Kai-Mei C.; Greiner, Markus; Hazzard, Kaden R.A.; Hulet, Randall G.; Kollár, Alicia J.; Lev, Benjamin L.; Lukin, Mikhail D.; Ma, Ruichao; Mi, Xiao; Misra, Shashank; Monroe, Christopher; Murch, Kater; Nazario, Zaira; Ni, Kang-Kuen; Potter, Andrew C.; Roushan, Pedram; Saffman, Mark; Schleier-Smith, Monika; Siddiqi, Irfan; Simmonds, Raymond; Singh, Meenakshi; Spielman, I.B.; Temme, Kristan; Weiss, David S.; Vučković, Jelena; Vuletić, Vladan; Ye, Jun; Zwierlein, MartinShow more Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behavior to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the National Science Foundation workshop on “Programmable Quantum Simulators,” that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multidisciplinary collaborations with resources for quantum simulator software, hardware, and education.This document is a summary from a U.S. National Science Foundation supported workshop held on 16–17 September 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum simulators over the next 2–5 years.Show more Item Spin-imbalanced ultracold Fermi gases in a two-dimensional array of tubes(American Physical Society, 2020) Sundar, Bhuvanesh; Fry, Jacob A.; Revelle, Melissa C.; Hulet, Randall G.; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsShow more Motivated by a recent experiment Revelle et al., [Phys. Rev. Lett. 117, 235301 (2016)] that characterized the one- to three-dimensional crossover in a spin-imbalanced ultracold gas of 6Li atoms trapped in a two-dimensional array of tunnel-coupled tubes, we calculate the phase diagram for this system by using Hartree-Fock Bogoliubov-de Gennes mean-field theory and compare the results with experimental data. Mean-field theory predicts fully-spin-polarized normal, partially-spin-polarized normal, spin-polarized superfluid, and spin-balanced superfluid phases in a homogeneous system. We use the local density approximation to obtain density profiles of the gas in a harmonic trap. We compare these calculations with experimental measurements in Revelle et al. as well as previously unpublished data. Our calculations qualitatively agree with experimentally measured densities and coordinates of the phase boundaries in the trap and quantitatively agree with experimental measurements at moderate-to-large polarizations. Our calculations also reproduce the experimentally observed universal scaling of the phase boundaries for different scattering lengths at a fixed value of scaled intertube tunneling. However, our calculations have quantitative differences with experimental measurements at low polarization and fail to capture important features of the one- to three-dimensional crossover observed in experiments. These suggest the important role of physics beyond mean-field theory in the experiments. We expect that our numerical results will aid future experiments in narrowing the search for the Fulde-Ferrell-Larkin-Ovchinnikov phase.Show more Item Synthetic dimensions in ultracold polar molecules(Springer Nature, 2018) Sundar, Bhuvanesh; Gadway, Bryce; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsShow more Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many – potentially hundreds of – synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a membrane, with an emergent condensate that lives on this string or membrane. All these phases can be detected using local measurements of rotational state populations.Show more Item Synthetic-gauge-field stabilization of the chiral-spin-liquid phase(American Physical Society, 2016) Chen, Gang; Hazzard, Kaden R.A.; Rey, Ana Maria; Hermele, Michael; Rice Center for Quantum MaterialsShow more We explore the phase diagram of the SU(N) Hubbard models describing fermionic alkaline-earth-metal atoms in a square optical lattice with, on average, one atom per site, using a slave rotor mean-field approach. We find that the chiral spin liquid (CSL) predicted for N≥5 and large interactions passes through a fractionalized state with a spinon Fermi surface as interactions are decreased before transitioning to a weakly interacting metal. We show that by adding a uniform artificial gauge field with 2π/N flux per plaquette, the CSL becomes the ground state for all N≥3 at intermediate interactions, persists to weaker interactions, and exhibits a larger spin gap. For N≥5 we find the CSL is the ground state everywhere the system is a Mott insulator. The gauge field stabilization of the CSL at lower interactions, and thus at weaker lattice depths, together with the increased spin gap, can relax the temperature constraints required for its experimental realization in ultracold atom systems.Show more Item Thermodynamics and magnetism in the two-dimensional to three-dimensional crossover of the Hubbard model(American Physical Society, 2020) Ibarra-García-Padilla, Eduardo; Mukherjee, Rick; Hulet, Randall G.; Hazzard, Kaden R.A.; Paiva, Thereza; Scalettar, Richard T.; Rice Center for Quantum MaterialsShow more The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using the determinant quantum Monte Carlo method, a simple realization of anisotropy in the three-dimensional (3D) Hubbard model in which the tunneling between planes, t⊥, is unequal to the intraplane tunneling t. This model interpolates between the three-dimensional isotropic (t⊥=t) and two-dimensional (2D; t⊥=0) systems. We show that at fixed interaction strength to tunneling ratio (U/t), anisotropy can enhance the magnetic structure factor relative to both 2D and 3D results. However, this enhancement occurs at interaction strengths below those for which the Néel temperature TNˊeel is largest, in such a way that the structure factor cannot be made to exceed its value in isotropic 3D systems at the optimal U/t. We characterize the 2D-3D crossover in terms of the magnetic structure factor, real space spin correlations, number of doubly occupied sites, and thermodynamic observables. An interesting implication of our results stems from the entropy's dependence on anisotropy. As the system evolves from 3D to 2D, the entropy at a fixed temperature increases. Correspondingly, at fixed entropy, the temperature will decrease going from 3D to 2D. This suggests a cooling protocol in which the dimensionality is adiabatically changed from 3D to 2D.Show more Item Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition(American Physical Society, 2023) Wang, Zhiyuan; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsShow more We study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution [L. Onsager, Phys. Rev. 65, 117 (1944); B. Kaufman, Phys. Rev. 76, 1232 (1949)] of the 2D Ising model and the solution of Kitaev's honeycomb model [A. Kitaev, Ann. Phys, 321, 2 (2006)], leading to a three-parameter phase diagram with a third-order phase transition between two distinct phases. Interestingly, the phases of this model are distinguished by topological features: the expectation value of a certain family of loop observables depend only on the topology of the loop (whether the loop is contractible), and are quantized at rational values that differ in the two phases. We show that a related exactly solvable 3D classical statistical model with real coupling constants also shows the topological features of one of these phases. Furthermore, even in the model with complex parameters, the partition function has some physical relevance, as it can be interpreted as the transition amplitude of a quantum dynamical process and may shed light on dynamical quantum phase transitions.Show more Item Ultracold Nonreactive Molecules in an Optical Lattice: Connecting Chemistry to Many-Body Physics(American Physical Society, 2016) Doçaj, Andris; Wall, Michael L.; Mukherjee, Rick; Hazzard, Kaden R.A.; Rice Center for Quantum MaterialsShow more 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.Show more