Floquet group theory and its application to selection rules in harmonic generation

Neufeld, Ofer; Podolsky, Daniel K.; Cohen, Oren

doi:10.1038/s41467-018-07935-y

Cited by 194 publications

(138 citation statements)

References 65 publications

Supporting

Mentioning

127

Contrasting

Order By: Relevance

“…We first briefly review dynamical symmetries (DSs) and selection rules in HHG [35] and explain how they can be utilized for chiral spectroscopy. We focus on the microscopic response of a molecule to an intense laser pulse, ⃗ EðtÞ.…”

Section: Dynamical Symmetry Breaking In Chiral Mediamentioning

confidence: 99%

“…More generally, selection rules are derived as constraints that are a consequence of the invariance of H Ω with respect to a unitary spatiotemporal transformation (see Ref. [35], which presents a general derivation through group theory for DSs). When the media is nonoriented, the laser pulse interacts with all possible rigid-body orientations of the molecule uniformly.…”

Section: Dynamical Symmetry Breaking In Chiral Mediamentioning

confidence: 99%

“…To achieve this separation, we suggest using pump fields that (i) generate bright high harmonics, (ii) exhibit a reflection-or inversionrelated DS that leads to forbidden harmonic selection rules in achiral media (easy to observe) that are broken in chiral media, and (iii) do not exhibit other DSs that also lead to the same selection rule but are not broken by chiral media (such as rotational DSs). To elucidate this last requirement, consider the following counterexample: Within the DA, a single monochromatic beam (linearly, elliptically, or circularly polarized) exhibits a dynamical inversion symmetry that forbids even harmonic generation [35]. Thus, one may expect to measure even harmonics from chiral media driven by such a field.…”

Section: Dynamical Symmetry Breaking In Chiral Mediamentioning

confidence: 99%

“…We follow the notation in Ref. [35], whereσ ij represents reflection about the ij plane,τ 2 represents temporal translation by half of the fundamental period (T), andι represents spatial inversion. Hence, Eq.…”

Section: Dynamical Symmetry Breaking In Chiral Mediamentioning

confidence: 99%

See 3 more Smart Citations

Ultrasensitive Chiral Spectroscopy by Dynamical Symmetry Breaking in High Harmonic Generation

et al. 2019

Self Cite

View full text Add to dashboard Cite

We propose and numerically demonstrate a new chiral spectroscopy method that is based on a universal system-independent mechanism of dynamical symmetry breaking in high harmonic generation (HHG). The proposed technique relies only on intense electric-dipole transitions and not on their interplay with magnetic dipole transitions. The symmetry breaking results in the emission of otherwise "forbidden" harmonics from chiral media (i.e., that are not emitted from achiral or racemic media), yielding a huge, nearly background-free, chiral-achiral signal that is correlated to the magnitude of the medium's enantiomeric excess. The handedness of the medium can be directly detected by measuring the polarization helicity of the emitted harmonics. Moreover, the strength of the "allowed" harmonics (that are not related to symmetry breaking) is chirality independent; hence, they can be used as a reference to probe chiral degrees of freedom within a single measurement. We numerically demonstrate up to 99% chiral-achiral signal level (normalized difference between the chiral and achiral HHG spectra) from microscopic gas-phase emission using state-of-the-art models for HHG in bromochlorofluoromethane and propylene oxide. We expect the new method to give rise to precise tabletop characterization of chiral media in the gas phase and for highly sensitive time-resolved probing of dynamical chiral processes with femtosecond-to-attosecond temporal resolution.

show abstract

Section: Dynamical Symmetry Breaking In Chiral Mediamentioning

confidence: 99%

Section: Dynamical Symmetry Breaking In Chiral Mediamentioning

confidence: 99%

Section: Dynamical Symmetry Breaking In Chiral Mediamentioning

confidence: 99%

Section: Dynamical Symmetry Breaking In Chiral Mediamentioning

confidence: 99%

See 2 more Smart Citations

Ultrasensitive Chiral Spectroscopy by Dynamical Symmetry Breaking in High Harmonic Generation

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…harmonic generation [14][15][16][17]. Similarly, symmetry-breaking is widely used in surface-sensitive sum-frequency generation [18], second-harmonic imaging of multiferroic domains in solids [19], and high-order harmonic generation from atoms [20][21][22], molecules [23,24] and solids [25][26][27][28].…”

mentioning

confidence: 99%

A dynamical symmetry triad in high-harmonic generation revealed by attosecond recollision control

et al. 2020

Self Cite

View full text Add to dashboard Cite

A key element of optical spectroscopy is the link between observable selection rules and the underlying symmetries of an investigated physical system. Typically, selection rules directly relate to the sample properties probed by light, yielding information on crystalline structure or chirality, for example. Considering light-matter coupling more broadly may extend the scope of detectable symmetries, to also include those directly arising from the interaction. In this letter, we experimentally demonstrate an emerging class of symmetries in the electromagnetic field emitted by a strongly driven atomic system. Specifically, generating high-harmonic radiation with attosecond-controlled two-color fields, we find different sets of allowed and forbidden harmonic orders. Generalizing symmetry considerations of circularly polarized high-harmonic generation, we interpret these selection rules as a complete triad of dynamical symmetries. We expect such emergent symmetries also for multi-atomic and condensed-matter systems, encoded in the spectral and spatial features of the radiation field. Notably, the observed phenomenon gives robust access to chiral processes with few-attosecond time precision.The concept of emergence describes the appearance of entirely new properties of a coupled system, which only arise from the interaction of its constituents. In light-matter interaction, emergent phenomena are particularly prominent in strongly driven states of matter, as evident in light-induced variants of superconductivity [1], the Hall effect [2], and topological insulators [3] in the condensed phase, as well as exceptional points in molecules [4,5], Kramers-Henneberger states in gases [6,7], and time-crystals in isolated many-body systems [8,9]. Such emergent states are often governed by novel symmetry properties and topologies, which may be probed by external or emitted radiation fields. However, while much attention is drawn to the light-induced creation of novel states of matter, a wider scope should also include possible emergent states of the radiation field.Here, we report on the experimental observation of an emergent class of symmetries in the electromagnetic field emitted by a strongly driven atomic system. Specifically, we analyze the sets of allowed and forbidden harmonic orders in high-harmonic generation from tailored bi-circular and bi-elliptical fields. Corroborated by theoretical modeling, the identified selection rules correspond to a complete triad of dynamical symmetries. We believe that the general principles underlying our observations will be equally relevant for other systems, including crystalline solids.Spectral and polarization selection rules serve as direct measures for the symmetries of the underlying Hamiltonian and interaction [10,11]. Canonical examples in linear and perturbative nonlinear probing are molecular analysis by Raman and infrared spectroscopy [12,13] or selection rules in wave mixing and

show abstract

Fano Resonances for Tilted Linear and Quadratic Band Touching Dispersions in a Harmonically Driven Potential Well

Gregefalk,

Black‐Schaffer,

Nag

2023

Annalen der Physik

View full text Add to dashboard Cite

Considering models with tilted linear and quadratic band touching dispersions, the effect of the transverse linear tilt on the transmission spectra is analyzed through a harmonically driven potential well oriented longitudinally. Employing the Floquet scattering matrix formalism, Fano resonances are found as an outcome of matching between the Floquet sidebands and quasi‐bound states, where the tilt renormalizes their energies and wave vectors. It is found that the Fano resonance energy decreases (increases) for linear (quadratic) band touchings as the magnitude of the transverse momentum increases, indicating a distinct signature of the underlying band dispersion in the transmission profile. The sign of the product of the transverse momentum and the tilt also determines the relative shift in the Fano resonance energy with respect to the untilted case for both band dispersions, suggesting a possible tunability of the Fano resonance for tilted systems. Importantly, the tilt strength can also be directly determined by measuring the Fano resonance energy as function of the transverse momenta direction. The shot noise spectra and their differential property are further studied where an inflection region and undulation, respectively, is found around the Fano resonance energy. Interestingly, differential shot noise and transmission spectra both qualitatively behave in a similar fashion and might thus serve as important observables for future experiments on driven solid‐state systems.

show abstract

Floquet group theory and its application to selection rules in harmonic generation

Cited by 194 publications

References 65 publications

Ultrasensitive Chiral Spectroscopy by Dynamical Symmetry Breaking in High Harmonic Generation

Ultrasensitive Chiral Spectroscopy by Dynamical Symmetry Breaking in High Harmonic Generation

A dynamical symmetry triad in high-harmonic generation revealed by attosecond recollision control

Fano Resonances for Tilted Linear and Quadratic Band Touching Dispersions in a Harmonically Driven Potential Well

Contact Info

Product

Resources

About