Adiabatic Floquet Picture for Hydrogen Atom in an Intense Laser Field

Floquet engineering of optical lattices with spatial features and periodicity below the diffraction limit

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)…

Adiabatic stabilization of a circular state: theory compared to experiment

The probability that an atom of hydrogen, initially in the 5g(m=4) state, survives a 90-fs pulse of 620 nm wavelength is calculated both by direct integration of the time-dependent Schroedinger equation and by a Floquet calculation. The two methods give virtually identical results. The survival probability calculated for a one-electron model of neon, for the same initial state, pulse duration and wavelength, is in fair quantitative agreement with the experimental data of van Druten et al [Phys. Rev. A 55, 622 (1997)].

Floquet analysis of real-time wavefunctions without solving the Floquet equation

We propose a method to obtain Floquet states---also known as light-induced states---and their quasi-energies from real-time wavefunctions without solving the Floquet equation. This is useful for the analysis of various phenomena in time-dependent quantum dynamics if the Hamiltonian is not strictly periodic, as in short laser pulses, for instance. There, the population of the Floquet states depends on the pulse form and is automatically contained in the real-time wavefunction but not in the standard Floquet approach. Several examples in the area of intense laser-atom interaction are exemplarily…

Non-adiabatic coupling and adiabatic population transfer in quantum molecular systems

We show that a counter-intuitive pulse sequence leads to adiabatic passage between the vibrational levels of three harmonic potentials through parallel dark states in adiabatic approximation. However, the adiabatic assumptions break down for very intense pulses and non-adiabatic couplings result in the population transfer by light-induced potential shaping.

Observation of Floquet states in a strongly driven artificial atom

We present experiments on the driven dynamics of a two-level superconducting artificial atom. The driving strength reaches 4.78 GHz, significantly exceeding the transition frequency of 2.288 GHz. The observed dynamics is described in terms of quasienergies and quasienergy states, in agreement with Floquet theory. In addition, we observe the role of pulse shaping in the dynamics, as determined by non-adiabatic transitions between Floquet states, and we implement subnanosecond single-qubit operations. These results pave the way to quantum control using strong driving with applications in quantum…

Periodicity of the time-dependent Kohn-Sham equation and the Floquet theorem

The Floquet theorem allows to reformulate periodic time-dependent problems such as the interaction of a many-body system with a laser field in terms of time-independent, field-dressed states, also known as Floquet states. If this was possible for density functional theory as well, one could reduce in such cases time-dependent density functional theory to a time-independent Floquet density functional theory. We analyze under which conditions the Floquet theorem is applicable in a density-functional framework. By employing numerical {\em ab initio} solutions of the interacting time-dependent Sch…

Laser control of complete vibrational transfer in Na$_2$ using resonance coalescence

With a specific choice of laser parameters resulting into a so-called exceptional point in the wavelength-intensity plane, it is possible to produce the coalescence of two Floquet resonances describing the photodissociation of the molecule Na$_2$, which is one of the candidates for molecular cooling. Appropriately tuning laser parameters, following a contour around the exceptional point, the resonances exchange their labels. This represents a laser control of the vibrational transfer from one field-free state to another, through an adiabatic transport involving these resonances. The proportion…

强光-物质相互作用有效哈密顿量的协调

Reconciliation of effective Hamiltonians for intense light-matter interaction

通过准简并瑞利-薛定谔微扰理论（QD-RSPT）协调绝热消除、马尔可夫近似和极点近似，提出在强光下仍保持精度的有效哈密顿量构建方法，并展示其在低频和高频区域的准确性。

Floquet engineering of optical solenoids and quantized charge pumping along tailored paths in two-dimensional Chern insulators

The insertion of a local magnetic flux, as the one created by a thin solenoid, plays an important role in gedanken experiments of quantum Hall physics. By combining Floquet engineering of artificial magnetic fields with the ability of single-site addressing in quantum-gas microscopes, we propose a scheme for the realization of such local solenoid-type magnetic fields in optical lattices. We show that it can be employed to manipulate and probe elementary excitations of a topological Chern insulator. This includes quantized adiabatic charge pumping along tailored paths inside the bulk, as well a…

Perturbation theory for quasienergy (Floquet) solutions in the low-frequency regime of the oscillating electric field

For a simple illustrative model Hamiltonian for Xenon in low frequency linearly polarized laser field we obtain a remarkable agreement between the zero-order energy as well as amplitude and phase of the zero-order Floquet states and the exact eigenvalues and eigenfunctions of the Floquet operator. Here we use as a zero-order Hamiltonian the adiabatic Hamiltonian where time is used as an instantaneous parameter. Moreover, for a variety of low laser frequencies, $ω$, the deviation of the zero-order solutions from the exact quasi-energy (QE) Floquet solutions approaches zero at the time the oscil…

Understanding molecular harmonic emission at relatively long intense laser pulses: Beyond the Born-Oppenheimer approximation

The underlying physics behind the molecular harmonic emission in relatively long sin$^2$-like laser pulses is investigated. We numerically solved the full-dimensional electronic time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation for simple molecular ion H$_2^+$. The occurrence and the effect of electron localization, non-adiabatic redshift and spatially asymmetric emission are evaluated to understand better complex patterns appearing in the high-order harmonic generation (HHG) spectrum. Results show that the complex patterns in the HHG spectrum originate mainly from …