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Subcycle squeezing of light from a time flow perspective


Light as a carrier of information and energy plays a fundamental role in both general relativity and quantum physics, linking these areas that are still not fully compliant with each other. Usually the quantum nature of light is described in the frequency domain. Even for broadband quantum states with a well-defined carrier frequency, a quasi-continuous-wave picture is still applicable. However, recent access to subcycle quantum features of electromagnetic radiation promises a new class of time-dependent quantum states of light. Paralleled with the developments in attosecond science, these advances motivate an urgent need for a theoretical framework that treats arbitrary wavepackets of quantum light intrinsically in the time domain. Here, we formulate a consistent time-domain theory of the generation and sampling of few-cycle and subcycle pulsed squeezed states, leading to a relativistic interpretation in terms of induced changes in the local flow of time. Our theory enables the use of such states as a resource for novel ultrafast applications in quantum optics and quantum information.

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Fig. 1: Scheme of the generation and detection set-up and the corresponding evolution of the MIR quantum field \(\hat \varepsilon (z,t)\) inside the nonlinear crystal for a half-cycle MIR driving field with effective squeezing strength r = 5.
Fig. 2: Behaviour of the conformal time with respect to the laboratory time illustrated for the half-cycle pulse (see equation (7)) with r = 5 and Γ0/(2π) = 26 THz.
Fig. 3: RDV as a function of the strength of the half-cycle driving field and probe pulse duration.
Fig. 4: Pulsed squeezing for single-cycle driving.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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We thank P. Sulzer and R. Haussmann for discussions. Support by the DFG via SFB767, by Baden-Württemberg Stiftung via the Elite programme for Postdocs (project ‘Fundamental aspects of relativity and causality in time-resolved quantum optics’) and by the Young Scholar Fund of the University of Konstanz is acknowledged. M.K. is indebted to the LGFG PhD fellowship programme of the University of Konstanz.

Author information




A.S.M., D.V.S. and G.B. conceived the idea. A.S.M. managed the project and supervised the research. M.K. found the exact analytical solution in the time domain, performed numerical calculations and prepared the figures. T.L.d.M.G. obtained the perturbative analytic solution via the squeezing operator in the frequency domain. M.K., T.L.d.M.G. and A.S.M. wrote the first version of the paper. D.V.S. and A.L. provided several important physical insights and interpretations. All authors discussed the results and contributed to the writing of the final manuscript.

Corresponding authors

Correspondence to Andrey S. Moskalenko or Guido Burkard.

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The authors declare no competing interests.

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Peer review information: Nature Physics thanks Mikhail Fedorov, Avi Pe’er, Dmitry Strekalov and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary text, Supplementary Figs. 1–5 and Supplementary references.

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Kizmann, M., Guedes, T.L.d.M., Seletskiy, D.V. et al. Subcycle squeezing of light from a time flow perspective. Nat. Phys. 15, 960–966 (2019).

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