We consider driving multiorbital Mott insulators using laser radiation. We derive general expressions for periodically driven spin-orbital models using time-dependent perturbation theory in the strong interaction limit. We show that the effective exchange interactions of the Floquet spin-orbital Hamiltonian are highly tunable via variations of the frequency, amplitude, and polarization of the laser. We also take the effect of a finite bandwidth of excitations into account and study possible heating effects. We further apply our formalism to orthorhombic titanates YTiO_{3} and LaTiO_{3} based on first-principles calculations, and we find that the spin exchange interactions in these compounds can be engineered to a large extent by tuning the frequency and electric-field amplitude of the laser.
We consider driving multiorbital Mott insulators using laser radiation. We derive general expressions for periodically driven spin-orbital models using time-dependent perturbation theory in the strong interaction limit. We show that the effective exchange interactions of the Floquet spin-orbital Hamiltonian are highly tunable via variations of the frequency, amplitude, and polarization of the laser. We also take the effect of a finite bandwidth of excitations into account and study possible heating effects. We further apply our formalism to orthorhombic titanates YTiO_{3} and LaTiO_{3} based on first-principles calculations, and we find that the spin exchange interactions in these compounds can be engineered to a large extent by tuning the frequency and electric-field amplitude of the laser.
Intense light can alter the electronic properties of materials through its oscillating electric field. The effects on magnetic excitations in insulators, however, are indirect, since these are neutral and do not see the electric field directly. This study reports on how exchange interactions in single- and multiorbital Mott insulators are modified by electromagnetic radiation, whose frequency is assumed to be on the order of the Mott-Hubbard gap. The latter condition results in a nonvanishing creation rate of doubly occupied sites (doublons), which necessitates taking into account the finite bandwidth of the doublon excitations, a feature which goes beyond the na\"{\i}ve leading order strong correlation expansion. This ultimately leads to a complex-valued exchange parameter, where the real part represents the ``Floquet'' spin-exchange interaction, while the imaginary part reflects the creation rate of doublons.
We present a scheme to control the spin-exchange interactions by manipulating the orbital degrees of freedom using a periodic drive. We discuss two different protocols for orbital Floquet engineering. In one case, a periodic drive modifies the properties of the ligand orbitals which mediate magnetic interactions between transition-metal ions. In the other case, we consider drive-induced mixing of d orbitals on each magnetic ion. We first find that an AC Stark shift of orbitals induces a change comparable to that induced from photoinduced hopping schemes, but expands the applicable frequency ranges. Next, we find that radiatively induced coherent vibrations provide a realistic path for Floquet orbital engineering with short pulses of electric fields weaker than 0.5 V/\AA{} producing 5 changes in the magnetic coupling of Mott insulators such as the rare-earth titanates.
Magnetic exchange couplings can be tuned by coupling to periodic light, where the frequency and amplitude are typically varied: a process known as Floquet engineering. The polarization of the light is also important, and in this paper, we show how different polarizations, including several types of unpolarized light, can tune the exchange couplings in distinct ways. Using unpolarized light, for example, it is possible to tune the material without breaking either time-reversal or any lattice symmetries. To illustrate these effects generically, we consider single-band Hubbard models at half-filling on the honeycomb, square and triangular lattices. We derive the effective Heisenberg spin models to fourth order in perturbation theory for arbitrary fixed polarizations, and several types of unpolarized light that preserve time-reversal and lattice symmetries. Coupling these models to periodic light tunes first, second, and third neighbor exchange couplings, as well as ring exchange terms on the square and triangular lattices. Circularly polarized light induces chiral fields for the honeycomb and triangular lattices, which favors noncoplanar magnetism and potential chiral spin liquids. We discuss how to maximize the enhancement of the couplings without inducing heating.
Abstract In recent years, there has been an intense search for materials realizing the Kitaev quantum spin liquid model. A number of edge-shared compounds with strong spin-orbit coupling, such as RuCl3 and iridates, have been proposed to realize this model. Nevertheless, an effective spin Hamiltonian derived from the microscopic model relevant to these compounds generally contains terms that are antagonistic toward the quantum spin liquid. This is consistent with the fact that the zero magnetic field ground state of these materials is generally magnetically ordered. It is a pressing issue to identify protocols to drive the system to the limit of the Kitaev quantum spin model. In this work, we propose Floquet engineering of these Kitaev quantum magnets by coupling materials to a circularly polarized laser. We demonstrate that all the magnetic interactions can be tuned in situ by the amplitude and frequency of the laser, hence providing a route to stabilize the Kitaev quantum spin liquid phase.
The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.
Scalar spin chirality, a three-body spin correlation that breaks time-reversal symmetry, is revealed to couple directly to circularly polarized laser. This is shown by the Floquet formalism for the periodically driven repulsive Hubbard model with a strong-coupling expansion. A systematic derivation of the effective low-energy Hamiltonian for a spin degree of freedom reveals that the coupling constant for scalar spin chirality can become significant for a situation in which the driving frequency and the on-site interaction are comparable. This implies that the scalar chirality can be induced by circularly polarized lights, or that it can be used conversely for probing the chirality in Mott insulators as a circular dichroism.