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Stammer P, Rivera-Dean J, Lamprou T, Pisanty E, Ciappina MF, Tzallas P, Lewenstein M. High Photon Number Entangled States and Coherent State Superposition from the Extreme Ultraviolet to the Far Infrared. PHYSICAL REVIEW LETTERS 2022; 128:123603. [PMID: 35394324 DOI: 10.1103/physrevlett.128.123603] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Revised: 02/07/2022] [Accepted: 03/01/2022] [Indexed: 06/14/2023]
Abstract
We present a theoretical demonstration on the generation of entangled coherent states and of coherent state superpositions, with photon numbers and frequencies orders of magnitude higher than those provided by the current technology. This is achieved by utilizing a quantum mechanical multimode description of the single- and two-color intense laser field driven process of high harmonic generation in atoms. It is found that all field modes involved in the high harmonic generation process are entangled, and upon performing a quantum operation, lead to the generation of high photon number optical cat states spanning from the far infrared to the extreme ultraviolet spectral region. This provides direct insights into the quantum mechanical properties of the optical field in the intense laser matter interaction. Finally, these states can be considered as a new resource for fundamental tests of quantum theory, quantum information processing, or sensing with nonclassical states of light.
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Affiliation(s)
- Philipp Stammer
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max Born Strasse 2a, D-12489 Berlin, Germany
| | - Javier Rivera-Dean
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Theocharis Lamprou
- Foundation for Research and Technology-Hellas, Institute of Electronic Structure & Laser, GR-70013 Heraklion (Crete), Greece
- Department of Physics, University of Crete, P.O. Box 2208, GR-70013 Heraklion (Crete), Greece
| | - Emilio Pisanty
- Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max Born Strasse 2a, D-12489 Berlin, Germany
- Department of Physics, King's College London, Strand, WC2R 2LS London, United Kingdom
| | - Marcelo F Ciappina
- Physics Program, Guangdong Technion-Israel Institute of Technology, Shantou, Guangdong 515063, China
- Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Paraskevas Tzallas
- Foundation for Research and Technology-Hellas, Institute of Electronic Structure & Laser, GR-70013 Heraklion (Crete), Greece
- ELI-ALPS, ELI-Hu Non-Profit Ltd., Dugonics tér 13, H-6720 Szeged, Hungary
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
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Abstract
The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades.
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