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Light emission from strongly driven many-body systems

Nature Physics volume 19, pages 551–561 (2023)Cite this article

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Abstract

Strongly driven systems of emitters offer an attractive source of light over broad spectral ranges up to the X-ray region. A key limitation of these systems is that the light they emit is mostly classical. We overcome this constraint by building a quantum-optical theory of strongly driven many-body systems, showing that the presence of correlations among the emitters creates emission of non-classical many-photon states of light. We consider the example of high-harmonic generation, by which a strongly driven system emits photons at integer multiples of the drive frequency. In the conventional case of uncorrelated emitters, the harmonics are in an almost perfectly multi-mode coherent state lacking any correlation between harmonics. By contrast, a correlation of the emitters before the strong drive is converted into non-classical features of the output light, including doubly peaked photon statistics, ring-shaped Wigner functions and correlations between harmonics. We propose schemes for implementing these concepts, creating the correlations between emitters via an interaction between them or their joint interaction with the background electromagnetic field. Our work paves the way towards the engineering of novel states of light over a broadband spectrum and suggests high-harmonic generation as a tool for characterizing correlations in many-body systems with attosecond temporal resolution.

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Fig. 1: Quantum theory of light emission by strongly driven many-body atomic systems.
Fig. 2: Many-body HHG.
Fig. 3: Quantum light from strongly driven super-radiant atoms.
Fig. 4: Quantum light from strongly driven interacting atoms.
Fig. 5: Correlated states of light.

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Data availability

All 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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The code is available from the authors upon reasonable request.

References

  1. Mukamel, S. et al. Roadmap on quantum light spectroscopy. J. Phys. B 53, 72002 (2020).

    Google Scholar 

  2. Aasi, J. et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photonics 7, 613–619 (2013).

    ADS  Google Scholar 

  3. Aasi, J. et al. Advanced LIGO. Class. Quantum Gravity 32, 74001 (2015).

    Google Scholar 

  4. Arrazola, J. M. et al. Quantum circuits with many photons on a programmable nanophotonic chip. Nature 591, 54–60 (2021).

    ADS  Google Scholar 

  5. Wu, L.-A., Kimble, H. J., Hall, J. L. & Wu, H. Generation of squeezed states by parametric down conversion. Phys. Rev. Lett. 57, 2520 (1986).

    ADS  Google Scholar 

  6. Pereira, S. F., Xiao, M., Kimble, H. J. & Hall, J. L. Generation of squeezed light by intracavity frequency doubling. Phys. Rev. A 38, 4931 (1988).

    ADS  Google Scholar 

  7. Breitenbach, G., Schiller, S. & Mlynek, J. Measurement of the quantum states of squeezed light. Nature 387, 471–475 (1997).

    ADS  Google Scholar 

  8. Agafonov, I. N., Chekhova, M. V. & Leuchs, G. Two-color bright squeezed vacuum. Phys. Rev. A 82, 11801 (2010).

    ADS  Google Scholar 

  9. Iskhakov, T. S., Pérez, A. M., Spasibko, K. Y., Chekhova, M. V. & Leuchs, G. Superbunched bright squeezed vacuum state. Opt. Lett. 37, 1919 (2012).

    ADS  Google Scholar 

  10. Spasibko, K. Y. et al. Multiphoton effects enhanced due to ultrafast photon-number fluctuations. Phys. Rev. Lett. 119, 223603 (2017).

    ADS  Google Scholar 

  11. Manceau, M., Spasibko, K. Y., Leuchs, G., Filip, R. & Chekhova, M. V. Indefinite-mean Pareto photon distribution from amplified quantum noise. Phys. Rev. Lett. 123, 123606 (2019).

    ADS  Google Scholar 

  12. Zavatta, A., Viciani, S. & Bellini, M. Quantum-to-classical transition with single-photon-added coherent states of light. Science 306, 660 (2004).

  13. Ourjoumtsev, A., Tualle-Brouri, R., Laurat, J. & Grangier, P. Generating optical Schrodinger kittens for quantum information processing. Science 312, 83 (2006).

  14. Lewenstein, M. et al. Generation of optical Schrödinger cat states in intense laser–matter interactions. Nat. Phys. 17, 1104–1108 (2021).

    Google Scholar 

  15. Ourjoumtsev, A., Jeong, H., Tualle-Brouri, R. & Grangier, P. Generation of optical ‘Schrödinger cats’ from photon number states. Nature 448, 784–786 (2007).

    ADS  Google Scholar 

  16. Sychev, D. V. et al. Enlargement of optical Schrödinger’s cat states. Nat. Photonics 11, 379–382 (2017).

    ADS  Google Scholar 

  17. Wakui, K., Takahashi, H., Furusawa, A. & Sasaki, M. Photon subtracted squeezed states generated with periodically poled KTiOPO4. Opt. Express 15, 3568 (2007).

  18. Deleglise, S. et al. Reconstruction of non-classical cavity field states with snapshots of their decoherence. Nature 455, 510–514 (2008).

    ADS  Google Scholar 

  19. Paul, P.-M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689 (2001).

  20. Agostini, P. & DiMauro, L. F. The physics of attosecond light pulses. Rep. Prog. Phys. 67, 813 (2004).

    ADS  Google Scholar 

  21. Corkum, P. B. Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994 (1993).

    ADS  Google Scholar 

  22. Lewenstein, M., Balcou, P., Ivanov, M. Y., L’Huillier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117 (1994).

    ADS  Google Scholar 

  23. Schafer, K. J., Yang, B., DiMauro, L. F. & Kulander, K. C. Above threshold ionization beyond the high harmonic cutoff. Phys. Rev. Lett. 70, 1599 (1993).

    ADS  Google Scholar 

  24. Tsatrafyllis, N., Kominis, I. K., Gonoskov, I. A. & Tzallas, P. High-order harmonics measured by the photon statistics of the infrared driving-field exiting the atomic medium. Nat. Commun. 8, 15170 (2017).

    ADS  Google Scholar 

  25. Tsatrafyllis, N. et al. Quantum optical signatures in a strong laser pulse after interaction with semiconductors. Phys. Rev. Lett. 122, 193602 (2019).

    ADS  Google Scholar 

  26. Gorlach, A., Neufeld, O., Rivera, N., Cohen, O. & Kaminer, I. The quantum-optical nature of high harmonic generation. Nat. Commun. 11, 4598 (2020).

    ADS  Google Scholar 

  27. Mandel, L. & Wolf, E. Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

  28. Scully, M. O. & Zubairy, M. S. Quantum Optics (Cambridge Univ. Press, 1997).

  29. Gerry, C., Knight, P., & Knight, P. L. Introductory Quantum Optics (Cambridge Univ. Press, 2005).

  30. Garrison, J. & Chiao, R. Quantum Optics (Oxford Univ. Press, 2008).

  31. Dicke, R. H. Coherence in spontaneous radiation processes. Phys. Rev. 93, 99 (1954).

    ADS  MATH  Google Scholar 

  32. Gross, M. & Haroche, S. Superradiance: an essay on the theory of collective spontaneous emission. Phys. Rep. 93, 301 (1982).

  33. Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138 (1993).

    ADS  Google Scholar 

  34. Kardar, M. Statistical Physics of Fields (Cambridge Univ. Press, 2007).

  35. Kardar, M. Statistical Physics of Particles (Cambridge Univ. Press, 2007).

  36. Brabec, T. & Kapteyn, H. Strong Field Laser Physics, Vol. 1 (Springer, 2008).

  37. Boyd, R. W. Nonlinear Optics (Academic, 2020).

  38. Vrakking, M. & Schultz, T. Attosecond and XUV Physics: Ultrafast Dynamics and Spectroscopy (Wiley Online Library, 2014).

  39. Dowling, J. P., Agarwal, G. S. & Schleich, W. P. Wigner distribution of a general angular-momentum state: applications to a collection of two-level atoms. Phys. Rev. A 49, 4101 (1994).

    ADS  Google Scholar 

  40. Joachain, C. J., Kylstra, N. J., & Potvliege, R. M. Atoms in Intense Laser Fields (Cambridge Univ. Press, 2012).

  41. Nurhuda, M. & Faisal, F. H. M. Numerical solution of time-dependent Schrödinger equation for multiphoton processes: a matrix iterative method. Phys. Rev. A 60, 3125 (1999).

    ADS  Google Scholar 

  42. Gardiner, C., Zoller, P., and Zoller, P. Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Science & Business Media, 2004).

  43. Porras, D. & Cirac, J. I. Collective generation of quantum states of light by entangled atoms. Phys. Rev. A 78, 53816 (2008).

    ADS  Google Scholar 

  44. McCaul, G., Orthodoxou, C., Jacobs, K., Booth, G. H. & Bondar, D. I. Driven imposters: controlling expectations in many-body systems. Phys. Rev. Lett. 124, 183201 (2020).

    ADS  Google Scholar 

  45. Paulisch, V., Perarnau-Llobet, M., González-Tudela, A. & Cirac, J. I. Quantum metrology with one-dimensional superradiant photonic states. Phys. Rev. A 99, 43807 (2019).

    ADS  Google Scholar 

  46. Witek, H., Cardoso, V., Ishibashi, A. & Sperhake, U. Superradiant instabilities in astrophysical systems. Phys. Rev. D. 87, 43513 (2013).

    ADS  Google Scholar 

  47. Bonifacio, R., Schwendimann, P. & Haake, F. Quantum statistical theory of superradiance. I. Phys. Rev. A 4, 302 (1971).

    ADS  Google Scholar 

  48. Bonifacio, R., Schwendimann, P. & Haake, F. Quantum statistical theory of superradiance II. Phys. Rev. A 4, 854 (1971).

    ADS  Google Scholar 

  49. Muniz, J. A. et al. Exploring dynamical phase transitions with cold atoms in an optical cavity. Nature 580, 602–607 (2020).

    ADS  Google Scholar 

  50. Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).

    ADS  Google Scholar 

  51. Lvovsky, A. I. & Raymer, M. G. Continuous-variable optical quantum-state tomography. Rev. Mod. Phys. 81, 299 (2009).

    ADS  Google Scholar 

  52. Smithey, D. T., Beck, M., Raymer, M. G. & Faridani, A. Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum. Phys. Rev. Lett. 70, 1244 (1993).

    ADS  Google Scholar 

  53. Leonhardt, U. Measuring the Quantum State of Light, Vol. 22 (Cambridge Univ. Press, 1997).

  54. Descamps, D. et al. Extreme ultraviolet interferometry measurements with high-order harmonics. Opt. Lett. 25, 135–137 (2000).

  55. Dudovich, N. et al. Measuring and controlling the birth of attosecond XUV pulses. Nat. Phys. 2, 781–786 (2006).

    Google Scholar 

  56. Smirnova, O. et al. High harmonic interferometry of multi-electron dynamics in molecules. Nature 460, 972–977 (2009).

    ADS  Google Scholar 

  57. Comby, A. et al. Absolute gas density profiling in high-order harmonic generation. Opt. Express 26, 6001 (2018).

  58. Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011).

    Google Scholar 

  59. Tancogne-Dejean, N., Mücke, O. D., Kärtner, F. X. & Rubio, A. Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics. Nat. Commun. 8, 745 (2017).

    ADS  Google Scholar 

  60. Ghimire, S. & Reis, D. A. High-harmonic generation from solids. Nat. Phys. 15, 10–16 (2019).

    Google Scholar 

  61. Sørensen, A. S. & Mølmer, K. Entangling atoms in bad cavities. Phys. Rev. A 66, 22314 (2002).

    ADS  MathSciNet  Google Scholar 

  62. Zibrov, A. S., Ye, C. Y., Rostovtsev, Y. V., Matsko, A. B. & Scully, M. O. Observation of a three-photon electromagnetically induced transparency in hot atomic vapor. Phys. Rev. A 65, 43817 (2002).

    ADS  Google Scholar 

  63. Ritsch, H., Domokos, P., Brennecke, F. & Esslinger, T. Cold atoms in cavity-generated dynamical optical potentials. Rev. Mod. Phys. 85, 553 (2013).

    ADS  Google Scholar 

  64. Perlin, M. A., Qu, C. & Rey, A. M. Spin squeezing with short-range spin-exchange interactions. Phys. Rev. Lett. 125, 223401 (2020).

    ADS  Google Scholar 

  65. Ma, J., Wang, X., Sun, C.-P. & Nori, F. Quantum spin squeezing. Phys. Rep. 509, 89 (2011).

  66. Gallagher, T. F., Rydberg Atoms, Vol. 3 (Cambridge Univ. Press, 2005).

  67. Omran, A. et al. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 365, 570 (2019).

  68. Browaeys, A. & Lahaye, T. Many-body physics with individually controlled Rydberg atoms. Nat. Phys. 16, 132–142 (2020).

    Google Scholar 

  69. Lloyd, S. Enhanced sensitivity of photodetection via quantum illumination. Science 321, 1463 (2008).

  70. Sayre, D., Kirz, J., Feder, R., Kim, D. M. & Spiller, E. Potential operating region for ultrasoft X-ray microscopy of biological materials. Science 196, 1339 (1977).

  71. Harada, K. et al. Real-time observation of vortex lattices in a superconductor by electron microscopy. Nature 360, 51–53 (1992).

    ADS  Google Scholar 

  72. Abo-Shaeer, J. R., Raman, C., Vogels, J. M. & Ketterle, W. Observation of vortex lattices in Bose–Einstein condensates. Science 292, 476 (2001).

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Acknowledgements

We thank R. Bekenstein, O. Cohen, E. G. Dalla Torre, M. Even Tzur, M. Faran, R. Ruimy, E. Shahmoon and J. Sloan for insightful discussion on related topics and especially D. Malz and M. Kruger for discussions and for comments on the manuscript, and M. E. Tsur for illustrating state-of-the-art methods for simulating HHG with one-dimensional atomic models. A.P. acknowledges support from the Royal Society and from the AFOSR MURI programme (grant no. FA9550-21-1-0069), and hospitality at the Technical University of Munich (TUM).

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  1. These authors contributed equally: Andrea Pizzi and Alexey Gorlach.

Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, MA, USA

    Andrea Pizzi & Nicholas Rivera

  2. Cavendish Laboratory, University of Cambridge, Cambridge, UK

    Andrea Pizzi

  3. Solid State Institute and Faculty of Electrical and Computer Engineering, Technion–Israel Institute of Technology, Haifa, Israel

    Alexey Gorlach & Ido Kaminer

  4. Massachusetts Institute of Technology, Cambridge, MA, USA

    Nicholas Rivera

  5. Faculty of Physics, University of Vienna, Vienna, Austria

    Andreas Nunnenkamp

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Pizzi, A., Gorlach, A., Rivera, N. et al. Light emission from strongly driven many-body systems. Nat. Phys. 19, 551–561 (2023). https://doi.org/10.1038/s41567-022-01910-7

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