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Register a new userFloquet engineering of the Luttinger Hamiltonian
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Within the Floquet theory of periodically driven quantum systems, we developed the theory of light-induced modification of electronic states in semiconductor materials described by the Luttinger Hamiltonian (the electronic term $Gamma_8$). Particularly, exact solutions of the Floquet problem are found for the band edge in the cases of linearly and circularly polarized irradiation. It is shown that the irradiation changes electron effective masses near the band edge, induces anisotropy of the electron dispersion and splits the bands. It is demonstrated that the light-induced band splitting strongly depends on the light polarization. Namely, the circularly polarized light acts similarly to a stationary magnetic field and lifts the spin degeneracy of electron branches, whereas a linearly polarized light does not affect the spin degeneracy and only splits the bands in the center of the Brillouin zone. The present theory can be applied to describe electronic properties of various semiconductor structures irradiated by an electromagnetic field in the broad frequency range.
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We study the semi-classical motion of holes by exact numerical solution of the Luttinger model. The trajectories obtained for the heavy and light holes agree well with the higher order corrections to the abelian and the non-abelian adiabatic theories in Ref. [1] [S. Murakami et al., Science 301, 1378(2003)], respectively. It is found that the hole trajectories contain rapid oscillations reminiscent of the Zitterbewegung of relativistic electrons. We also comment on the non-conservation of helicity of the light holes.
Here we present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages. We first draw an analogy between the electronic band theory and superconductivity which enlightens the time-periodic dynamics of the Andreev bound states. We then show that the equivalent of the Wannier-Stark ladders observed in semiconducting superlattices via photocurrent measurements, appears as specific peaks in the finite frequency current fluctuations of superconducting multiterminal quantum dots. In order to probe the Floquet-Wannier-Stark ladder spectra, we have developed an analytical model relying on the sharpness of the resonances. The charge-charge correlation function is obtained as a factorized form of the Floquet wave-function on the dot and the superconducting reservoir populations. We confirm these findings by Keldysh Greens function calculations, in particular regarding the voltage and frequency dependence of the resonance peaks in the current-current correlations. Our results open up a road-map to quantum correlations and coherence in the Floquet dynamics of superconducting devices.
Controlling interactions is the key element for quantum engineering of many-body systems. Using time-periodic driving, a naturally given many-body Hamiltonian of a closed quantum system can be transformed into an effective target Hamiltonian exhibiting vastly different dynamics. We demonstrate such Floquet engineering with a system of spins represented by Rydberg states in an ultracold atomic gas. Applying a sequence of spin manipulations, we change the symmetry properties of the effective Heisenberg XYZ Hamiltonian. As a consequence, the relaxation behavior of the total spin is drastically modified. The observed dynamics can be qualitatively captured by a semi-classical simulation. Synthesising a wide range of Hamiltonians opens vast opportunities for implementing quantum simulation of non-equilibrium dynamics in a single experimental setting.
Dynamic manipulation of magnetism in topological materials is demonstrated here via a Floquet engineering approach using circularly polarized light. Increasing the strength of the laser field, besides the expected topological phase transition, the magnetically doped topological insulator thin film also undergoes a magnetic phase transition from ferromagnetism to paramagnetism, whose critical behavior strongly depends on the quantum quenching. In sharp contrast to the equilibrium case, the non-equilibrium Curie temperatures vary for different time scale and experimental setup, not all relying on change of topology. Our discoveries deepen the understanding of the relationship between topology and magnetism in the non-equilibrium regime and extend optoelectronic device applications to topological materials.
We review recent work on low-frequency Floquet engineering and its application to quantum materials driven by light, emphasizing van der Waals systems hosting Moire superlattices. These non-equilibrium systems combine the twist-angle sensitivity of the band structures with the flexibility of light drives. The frequency, amplitude, and polarization of light can be easily tuned in experimental setups, leading to platforms with on-demand properties. First, we review recent theoretical developments to derive effective Floquet Hamiltonians in different frequency regimes. We apply some of these theories to study twisted graphene and twisted transition metal dichalcogenide systems irradiated by light in free space and inside a waveguide. We study the changes induced in the quasienergies and steady-states, which can lead to topological transitions. Next, we consider van der Waals magnetic materials driven by low-frequency light pulses in resonance with the phonons. We discuss the phonon dynamics induced by the light and resulting magnetic transitions from a Floquet perspective. We finish by outlining new directions for Moire-Floquet engineering in the low-frequency regime and their relevance for technological applications.
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