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Generation of optical Schrödinger cat states in intense laser–matter interactions

Abstract

The physics of intense laser–matter interactions1,2 is described by treating the light pulses classically, anticipating no need to access optical measurements beyond the classical limit. However, the quantum nature of the electromagnetic fields is always present3. Here we demonstrate that intense laser–atom interactions may lead to the generation of highly non-classical light states. This was achieved by using the process of high-harmonic generation in atoms4,5, in which the photons of a driving laser pulse of infrared frequency are upconverted into photons of higher frequencies in the extreme ultraviolet spectral range. The quantum state of the fundamental mode after the interaction, when conditioned on the high-harmonic generation, is a so-called Schrödinger cat state, which corresponds to a superposition of two distinct coherent states: the initial state of the laser and the coherent state reduced in amplitude that results from the interaction with atoms. The results open the path for investigations towards the control of the non-classical states, exploiting conditioning approaches on physical processes relevant to high-harmonic generation.

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Fig. 1: Schematic representation of the generation of optical ‘cat’ states.
Fig. 2: Calculated Wigner functions of a Schrödinger ‘kitten’ and a ‘cat’ state.
Fig. 3: Experimental approach and Wigner function of the coherent state of the laser.
Fig. 4: Measurement of the Wigner function of the genuine Schrödinger ‘cat’ state.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper are available from the corresponding authors on reasonable request.

Code availability

The codes used in this study are available from the corresponding authors upon request.

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Acknowledgements

We dedicate this work to the memory of Roy J. Glauber, the inventor of coherent states, also a wonderful mentor. We thank J. Biegert, I. Kaminer and P. Salières for enlightening discussions. We also thank I. Liontos, E. Skantzakis and S. Karsch from Max Plank Institute for Quantum Optics for their assistance on maintaining the performance of the Ti:Sa laser system and N. Pappadakis for his contribution on the development of the data acquisition and data analysis system. M.L. group acknowledges the European Research Council (ERC AdG) NOQIA, Spanish Ministry MINECO and State Research Agency AEI (FIDEUA PID2019-106901GB-I00/10.13039/501100011033, SEVERO OCHOA No. SEV-2015-0522 and CEX2019-000910-S, FPI), European Social Fund, Fundació Cellex, Fundació Mir-Puig, Generalitat de Catalunya (AGAUR grant no. 2017 SGR 1341, CERCA programme, QuantumCAT_U16-011424, co-funded by ERDF Operational Program of Catalonia 2014-2020), MINECO-EU QUANTERA MAQS (funded by State Research Agency (AEI) PCI2019-111828-2/10.13039/501100011033), EU Horizon 2020 FET-OPEN OPTOLogic (grant no. 899794), and the National Science Centre, Poland-Symfonia grant no. 2016/20/W/ST4/00314. M.F.C. acknowledges the Grantová agentura Ceské Republiky (GACR grant 20-24805J). J.R.-D. has received funding from the Secretaria d’Universitats i Recerca del Departament d’Empresa i Coneixement de la Generalitat de Catalunya, as well as the European Social Fund (L’FSE inverteix en el teu futur)–FEDER. P.T. group acknowledges LASERLABEUROPE (H2020-EU.1.4.1.2 grant ID 654148), FORTH Synergy Grant AgiIDA (grant no. 00133), the European Union’s Horizon 2020 framework programme for research and innovation under the NFFA-Europe-Pilot project (grant no. 101007417), the HELLAS-CH (MIS grant no. 5002735) (which is implemented under the Action for Strengthening Research and Innovation Infrastructures, funded by the Operational Program Competitiveness, Entrepreneurship and Innovation (NSRF 2014-2020) and co-financed by Greece and the European Union (European Regional Development Fund)), and the European Union’s Horizon 2020 research. ELI-ALPS is supported by the European Union and co-financed by the European Regional Development Fund (GINOP grant no. 2.3.6-15-2015-00001).

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Contributions

M.L. supervised the theoretical part of the work; M.F.C., J.R.-D. and E.P. equally contributed to the manuscript preparation and the development of the theoretical approach; P.S. contributed to the theoretical calculations; Th.L. contributed in the experimental runs and data analysis; P.T. supervised the experimental part of the work.

Corresponding authors

Correspondence to M. Lewenstein or P. Tzallas.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Discussion and Figs. 1–3.

Source data

Source Data Fig. 2

Calculated Wigner function of the optical kitten (Fig. 2a,b) and cat (Fig. 2c,d) states.

Source Data Fig. 3

Measured Wigner function of the laser coherent state (Fig. 3b).

Source Data Fig. 4

Measured Wigner function of the cat state.

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Lewenstein, M., Ciappina, M.F., Pisanty, E. et al. Generation of optical Schrödinger cat states in intense laser–matter interactions. Nat. Phys. 17, 1104–1108 (2021). https://doi.org/10.1038/s41567-021-01317-w

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