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Register a new userTopological Floquet engineering of a 1D optical lattice via resonantly shaking with two harmonic frequencies
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We investigate the topological properties of a resonantly shaken one-dimensional optical lattice system, where the lattice position is periodically driven with two harmonic frequencies to generate one- and two-photon couplings between the two lowest orbitals. In a two-band approximation, we numerically show that degenerate edge states appear under a certain driving condition and that the corresponding topological phase is protected by the chiral symmetry of the periodically driven system. The systems micromotion is characterized with oscillating Zak phases and we find that the Zak phases are quantized only at the time when the chiral symmetry condition is explicitly satisfied. Finally, we describe the topological charge pumping effect which arises when the driving parameters are slowly modulated around a critical point, and investigate its adiabaticity for increasing the modulation frequency.
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We report the experimental realization of a topological Creutz ladder for ultracold fermionic atoms in a resonantly driven 1D optical lattice. The two-leg ladder consists of the two lowest orbital states of the optical lattice and the cross inter-leg links are generated via two-photon resonant coupling between the orbitals by periodic lattice shaking. The characteristic pseudo-spin winding in the topologically non-trivial bands of the ladder system is demonstrated using momentum-resolved Ramsey-type interferometric measurements. We discuss a two-tone driving method to extend the inter-leg link control and propose a topological charge pumping scheme for the Creutz ladder system.
Two-component coupled Bose gas in a 1D optical lattice is examined. In addition to the postulated Mott insulator and Superfluid phases, multiple bosonic components manifest spin degrees of freedom. Coupling of the components in the Bose gas within same site and neighboring sites leads to substantial change in the previously observed spin phases revealing fascinating remarkable spin correlations. In the presence of strong interactions it gives rise to unconventional effective ordering of the spins leading to unprecedented spin phases: site-dependent $ztextsf{-}x$ spin configuration with tunable (by hopping parameter) proclivity of spin alignment along $z$. Exact analysis and Variational Monte Carlo (VMC) along with stochastic minimization on Entangled Plaquette State (EPS) bestow a unique and enhanced perspective into the system beyond the scope of mean-field treatment. The physics of complex intra-component tunneling and inter-component coupling and filling factor greater than unity are discussed.
We present a quantitative, near-term experimental blueprint for the quantum simulation of topological insulators using lattice-trapped ultracold polar molecules. In particular, we focus on the so-called Hopf insulator, which represents a three-dimensional topological state of matter existing outside the conventional tenfold way and crystalline-symmetry-based classifications of topological insulators. Its topology is protected by a emph{linking number} invariant, which necessitates long-range spin-orbit coupled hoppings for its realization. While these ingredients have so far precluded its realization in solid state systems and other quantum simulation architectures, in a companion manuscript [1901.08597] we predict that Hopf insulators can in fact arise naturally in dipolar interacting systems. Here, we investigate a specific such architecture in lattices of polar molecules, where the effective `spin is formed from sublattice degrees of freedom. We introduce two techniques that allow one to optimize dipolar Hopf insulators with large band gaps, and which should also be readily applicable to the simulation of other exotic bandstructures. First, we describe the use of Floquet engineering to control the range and functional form of dipolar hoppings and second, we demonstrate that molecular AC polarizabilities (under circularly polarized light) can be used to precisely tune the resonance condition between different rotational states. To verify that this latter technique is amenable to current generation experiments, we calculate from first principles the AC polarizability for $sigma^+$ light for ${}^{40}$K$^{87}$Rb. Finally, we show that experiments are capable of detecting the unconventional topology of the Hopf insulator by varying the termination of the lattice at its edges, which gives rise to three distinct classes of edge mode spectra.
Coupling electronic and vibrational degrees of freedom of Rydberg atoms held in optical tweezer arrays offers a flexible mechanism for creating and controlling atom-atom interactions. We find that the state-dependent coupling between Rydberg atoms and local oscillator modes gives rise to two- and three-body interactions which are controllable through the strength of the local confinement. This approach even permits the cancellation of two-body terms such that three-body interactions become dominant. We analyze the structure of these interactions on two-dimensional bipartite lattice geometries and explore the impact of three-body interactions on system ground state on a square lattice. Focusing specifically on a system of $ ^{87} $Rb atoms, we show that the effects of the multi-body interactions can be maximized via a tailored dressed potential within a trapping frequency range of the order of a few hundred kHz and for temperatures corresponding to a $ >90% $ occupation of the atomic vibrational ground state. These parameters, as well as the multi-body induced time scales, are compatible with state-of-the-art arrays of optical tweezers. Our work shows a highly versatile handle for engineering multi-body interactions of quantum many-body systems in most recent manifestations on Rydberg lattice quantum simulators.
Floquet engineering or coherent time periodic driving of quantum systems has been successfully used to synthesize Hamiltonians with novel properties. In ultracold atomic systems, this has led to experimental realizations of artificial gauge fields, topological band structures, and observation of dynamical localization, to name just a few. Here we present a Floquet-based framework to stroboscopically engineer Hamiltonians with spatial features and periodicity below the diffraction limit of light used to create them by time-averaging over various configurations of a 1D optical Kronig-Penney (KP) lattice. The KP potential is a lattice of narrow subwavelength barriers spaced by half the optical wavelength ($lambda/2$) and arises from the non-linear optical response of the atomic dark state. Stroboscopic control over the strength and position of this lattice requires time-dependent adiabatic manipulation of the dark state spin composition. We investigate adiabaticity requirements and shape our time-dependent light fields to respect the requirements. We apply this framework to show that a $lambda/4$-spaced lattice can be synthesized using realistic experimental parameters as an example, discuss mechanisms that limit lifetimes in these lattices, explore candidate systems and their limitations, and treat adiabatic loading into the ground band of these lattices.
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