Twisted electrons may carry orbital angular momentum (OAM) as free particles, which manifest as a vortex of rotating phase. Recent advances have allowed the generation and, importantly, measurement of such particles. In this talk, I will explore the properties and applications of these twisted continuum states in attoscience. In particular, I will present our work showing general conservation laws for the OAM of photoelectrons after ionization by a strong circularly or linearly polarized laser field, as well as a new interpretation for the interference spirals formed by two time-delayed circularly polarized fields.
I will also present, our new results on entanglement and OAM in non-sequential double ionization (NSDI). Where we demonstrate that there is entanglement in the OAM between the two photoelectrons in NSDI. Due to the quantization of OAM, this entanglement may be simply understood through conservation laws. We also explore efficient methods to quantify and measure the entanglement, in particular by using an entanglement witness. Importantly, the methodology presented here could be applied to other systems to help understand and exploit entanglement in attosecond processes. Finally, I will discuss ongoing work on using OAM and helicity of photoelectrons removed via a strong laser field to detect enantiomers from chiral targets.  Y. Kang, E. Pisanty, M. Ciappina, M. Lewenstein, C. Figueira de Morisson Faria, and A. S. Maxwell, Conservation laws for electron vortices in strong-field ionisation, Eur. Phys. J. D 75, 199 (2021).  A. S. Maxwell, G. S. J. Armstrong, M. F. Ciappina, E. Pisanty, Y. Kang, A. C. Brown, M. Lewenstein, and C. Figueira de Morisson Faria, Manipulating twisted electrons in strong-field ionization, Faraday Discuss. 228, 394 (2021).  A. S. Maxwell, L. B. Madsen and M. Lewenstein, Entanglement of Orbital Angular Momentum in Non-Sequential Double Ionization, arXiv:2111.10148 (2021)  A. S. Maxwell and C. Figueira de Morisson Faria, Controlling Below-Threshold Nonsequential Double Ionization via Quantum Interference, Phys. Rev. Lett. 116, 143001 (2016).