Superluminal matter waves

Palastro, J. P.; Ramsey, D.; Formanek, M.; Vieira, J.; Di Piazza, A.

doi:10.1103/physrevresearch.6.043075

Title: Superluminal matter waves

Journal Article · 29 October 2024 · Physical Review Research

DOI: https://doi.org/10.1103/physrevresearch.6.043075 · OSTI ID:2475974

^[1];

^[2];

^[3];

^[1]

University of Rochester, NY (United States)
The Extreme Light Infrastructure ERIC, Dolní Břežany (Czech Republic)
Universidade de Lisboa (Portugal)

The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the velocity is less than the vacuum speed of light. Here, we show that the Dirac equation admits free-particle solutions where the peak amplitude of the wave function can travel at any velocity, including those exceeding the vacuum speed of light, despite having a subluminal velocity expectation value. The solutions are constructed by superposing basis functions with correlations in momentum space. These arbitrary velocity wave functions feature a near-constant profile and may impact quantum mechanical processes that are sensitive to the local value of the probability density as opposed to expectation values.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: University of Rochester, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES); Marie Skłodowska-Curie; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0004144; NA0004144

OSTI ID:: 2475974

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 4 Vol. 6; ISSN 2643-1564

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (46)

The Dirac Equation Thaller, Bernd Theoretical and Mathematical Physics https://doi.org/10.1007/978-3-662-02753-0	book	August 1992
Sculpturing the electron wave function using nanoscale phase masks Shiloh, Roy; Lereah, Yossi; Lilach, Yigal Ultramicroscopy, Vol. 144 https://doi.org/10.1016/j.ultramic.2014.04.007	journal	September 2014
The reflection of electrons from standing light waves Kapitza, P. L.; Dirac, P. A. M. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 29, Issue 2 https://doi.org/10.1017/S0305004100011105	journal	May 1933
Discussion of the infinite distribution of electrons in the theory of the positron Dirac, P. A. M. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 30, Issue 2 https://doi.org/10.1017/S030500410001656X	journal	April 1934
Theory of Shaping Electron Wavepackets with Light Reinhardt, Ori; Kaminer, Ido ACS Photonics, Vol. 7, Issue 10 https://doi.org/10.1021/acsphotonics.0c01133	journal	August 2020
Production and application of electron vortex beams Verbeeck, J.; Tian, H.; Schattschneider, P. Nature, Vol. 467, Issue 7313 https://doi.org/10.1038/nature09366	journal	September 2010
Generation of electron Airy beams Voloch-Bloch, Noa; Lereah, Yossi; Lilach, Yigal Nature, Vol. 494, Issue 7437 https://doi.org/10.1038/nature11840	journal	February 2013
Self-accelerating Dirac particles and prolonging the lifetime of relativistic fermions Kaminer, Ido; Nemirovsky, Jonathan; Rechtsman, Mikael Nature Physics, Vol. 11, Issue 3 https://doi.org/10.1038/nphys3196	journal	January 2015
Free-electron crystals for enhanced X-ray radiation Wong, Lee Wei Wesley; Shi, Xihang; Karnieli, Aviv Light: Science & Applications, Vol. 13, Issue 1 https://doi.org/10.1038/s41377-023-01363-4	journal	January 2024
Attosecond coherent control of free-electron wave functions using semi-infinite light fields Vanacore, G. M.; Madan, I.; Berruto, G. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-05021-x	journal	July 2018
Space-time wave packets localized in all dimensions Yessenov, Murat; Free, Justin; Chen, Zhaozhong Nature Communications, Vol. 13, Issue 1 https://doi.org/10.1038/s41467-022-32240-0	journal	August 2022
Diffraction-free space–time light sheets Kondakci, H. Esat; Abouraddy, Ayman F. Nature Photonics, Vol. 11, Issue 11 https://doi.org/10.1038/s41566-017-0028-9	journal	October 2017
Spatiotemporal control of laser intensity Froula, Dustin H.; Turnbull, David; Davies, Andrew S. Nature Photonics, Vol. 12, Issue 5 https://doi.org/10.1038/s41566-018-0121-8	journal	March 2018
Observation of optical de Broglie–Mackinnon wave packets Hall, Layton A.; Abouraddy, Ayman F. Nature Physics, Vol. 19, Issue 3 https://doi.org/10.1038/s41567-022-01876-6	journal	January 2023
The Kapitza-Dirac effect Batelaan, H. Contemporary Physics, Vol. 41, Issue 6 https://doi.org/10.1080/00107510010001220	journal	November 2000
Smith–Purcell radiation of a vortex electron Pupasov-Maksimov, A.; Karlovets, D. New Journal of Physics, Vol. 23, Issue 4 https://doi.org/10.1088/1367-2630/abef97	journal	April 2021
The Quantum Theory of the Electron Dirac, P. A. M. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 117, Issue 778 https://doi.org/10.1098/rspa.1928.0023	journal	February 1928
An Undulatory Theory of the Mechanics of Atoms and Molecules Schrödinger, E. Physical Review, Vol. 28, Issue 6 https://doi.org/10.1103/PhysRev.28.1049	journal	December 1926
Spin-dependent two-photon Bragg scattering in the Kapitza-Dirac effect Ahrens, Sven; Liang, Zhenfeng; Čadež, Tilen Physical Review A, Vol. 102, Issue 3 https://doi.org/10.1103/PhysRevA.102.033106	journal	September 2020
Unveiling the transverse formation length of nonlinear Compton scattering Di Piazza, A. Physical Review A, Vol. 103, Issue 1 https://doi.org/10.1103/PhysRevA.103.012215	journal	January 2021
Exact solutions for the electromagnetic fields of a flying focus Ramsey, D.; Di Piazza, A.; Formanek, M. Physical Review A, Vol. 107, Issue 1 https://doi.org/10.1103/PhysRevA.107.013513	journal	January 2023
Subluminality of relativistic quantum tunneling Gavassino, L.; Disconzi, M. M. Physical Review A, Vol. 107, Issue 3 https://doi.org/10.1103/PhysRevA.107.032209	journal	March 2023
Two-dimensional simulation of the spin flip in the Kapitza-Dirac effect Ge, Ping; Ahrens, Sven; Shen, Baifei Physical Review A, Vol. 109, Issue 2 https://doi.org/10.1103/PhysRevA.109.022240	journal	February 2024
Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes Allen, L.; Beijersbergen, M. W.; Spreeuw, R. J. C. Physical Review A, Vol. 45, Issue 11 https://doi.org/10.1103/PhysRevA.45.8185	journal	June 1992
Effects of relativity on the time-resolved tunneling of electron wave packets Krekora, P.; Su, Q.; Grobe, R. Physical Review A, Vol. 63, Issue 3 https://doi.org/10.1103/PhysRevA.63.032107	journal	February 2001
Relativistic analysis of a wave packet interacting with a quantum-mechanical barrier Petrillo, Vittoria; Janner, Davide Physical Review A, Vol. 67, Issue 1 https://doi.org/10.1103/PhysRevA.67.012110	journal	January 2003
Kapitza-Dirac effect in the relativistic regime Ahrens, Sven; Bauke, Heiko; Keitel, Christoph H. Physical Review A, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevA.88.012115	journal	July 2013
Ionization waves of arbitrary velocity driven by a flying focus Palastro, J. P.; Turnbull, D.; Bahk, S. -W. Physical Review A, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevA.97.033835	journal	March 2018
Charged particle beam transport in a flying focus pulse with orbital angular momentum Formanek, Martin; Palastro, John P.; Vranic, Marija Physical Review E, Vol. 107, Issue 5 https://doi.org/10.1103/PhysRevE.107.055213	journal	May 2023
Spatial-temporal Gauss-Laguerre waves in dispersive media Longhi, Stefano Physical Review E, Vol. 68, Issue 6 https://doi.org/10.1103/PhysRevE.68.066612	journal	December 2003
Nondiffracting Accelerating Wave Packets of Maxwell’s Equations Kaminer, Ido; Bekenstein, Rivka; Nemirovsky, Jonathan Physical Review Letters, Vol. 108, Issue 16 https://doi.org/10.1103/PhysRevLett.108.163901	journal	April 2012
Optical Modulation of Electron Beams in Free Space García de Abajo, F. Javier; Konečná, Andrea Physical Review Letters, Vol. 126, Issue 12 https://doi.org/10.1103/PhysRevLett.126.123901	journal	March 2021
Space-Time Structured Plasma Waves Palastro, J. P.; Miller, K. G.; Follett, R. K. Physical Review Letters, Vol. 132, Issue 9 https://doi.org/10.1103/PhysRevLett.132.095101	journal	February 2024
Bragg Scattering of Free Electrons Using the Kapitza-Dirac Effect Freimund, Daniel L.; Batelaan, Herman Physical Review Letters, Vol. 89, Issue 28 https://doi.org/10.1103/PhysRevLett.89.283602	journal	December 2002
Semiclassical Dynamics of Electron Wave Packet States with Phase Vortices Bliokh, Konstantin Yu.; Bliokh, Yury P.; Savel’ev, Sergey Physical Review Letters, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevLett.99.190404	journal	November 2007
High-purity free-electron momentum states prepared by three-dimensional optical phase modulation Feist, Armin; Yalunin, Sergey V.; Schäfer, Sascha Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043227	journal	November 2020
Nonspreading relativistic electron wavepacket in a strong laser field Campos, Andre G.; Hatsagortsyan, Karen Z.; Keitel, Christoph H. Physical Review Research, Vol. 6, Issue 2 https://doi.org/10.1103/PhysRevResearch.6.023040	journal	April 2024
Transverse Electron-Beam Shaping with Light Chirita Mihaila, Marius Constantin; Weber, Philipp; Schneller, Matthias Physical Review X, Vol. 12, Issue 3 https://doi.org/10.1103/PhysRevX.12.031043	journal	September 2022
Generation of Nondiffracting Electron Bessel Beams Grillo, Vincenzo; Karimi, Ebrahim; Gazzadi, Gian Carlo Physical Review X, Vol. 4, Issue 1 https://doi.org/10.1103/PhysRevX.4.011013	journal	January 2014
Electron vortices: Beams with orbital angular momentum Lloyd, S. M.; Babiker, M.; Thirunavukkarasu, G. Reviews of Modern Physics, Vol. 89, Issue 3 https://doi.org/10.1103/RevModPhys.89.035004	journal	August 2017
Paraxial beams of spinning light Berry, Michael V. International Conference on Singular Optics, SPIE Proceedings https://doi.org/10.1117/12.317704	conference	August 1998
Nonspreading wave packets Berry, M. V.; Balazs, N. L. American Journal of Physics, Vol. 47, Issue 3 https://doi.org/10.1119/1.11855	journal	March 1979
Ultrafast Kapitza-Dirac effect Lin, Kang; Eckart, Sebastian; Liang, Hao Science, Vol. 383, Issue 6690 https://doi.org/10.1126/science.adn1555	journal	March 2024
Dirac equation studies in the tunneling energy zone De Leo, S.; Rotelli, P. P. The European Physical Journal C, Vol. 51, Issue 1 https://doi.org/10.1140/epjc/s10052-007-0297-4	journal	June 2007
An Introduction To Quantum Field Theory Peskin, Michael E. https://doi.org/10.1201/9780429503559	book	January 2018
Controlling the velocity of ultrashort light pulses in vacuum through spatio-temporal couplings Sainte-Marie, A.; Gobert, O.; Quéré, F. Optica, Vol. 4, Issue 10 https://doi.org/10.1364/OPTICA.4.001298	journal	January 2017

Similar Records

Volkov solutions for relativistic quantum plasmas

Journal Article · 2011 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) · OSTI ID:21560035

Mendonca, J T; Serbeto, A

Continuous control of light group velocity from subluminal to superluminal propagation with a standing-wave coupling field in a Rb vapor cell

Journal Article · 2011 · Physical Review. A · OSTI ID:21546855

Bae, In-Ho; Moon, Han Seb

Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line

Journal Article · 2003 · Physical Review. A · OSTI ID:20639961

Kim, Kyoungdae; Moon, Han Seb; Lee, Chunghee; +2 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Dirac equation

Title: Superluminal matter waves

Citation Formats

References (46)

Similar Records

Related Subjects