Echoes are common in many areas of physics, including NMR, plasma physics, nonlinear optics, cavity quantum electrodynamics, cold atoms physics, and dynamics of proton storage rings. Recently, we found (probably) the simplest classical system featuring the echo phenomenon — a collection of randomly oriented free rotors with dispersed rotational velocities. Following the excitation by a pair of time-delayed impulsive kicks, the ensemble's mean orientation or alignment exhibits multiple and fractional echoes. These echoes result from kick-induced filamentation of the rotational phase space, and I will discuss a simple toy model explaining this phenomenon at the high school level. Then, I will present the first experimental demonstration of the predicted alignment echoes (full and fractional) in a thermal gas of CO2 molecules excited by a pair of femtosecond laser pulses [1,2]. Later, we used the coincidence Coulomb explosion imaging technique for direct spatiotemporal analysis of various molecular alignment echoes (full, fractional, rotated, and imaginary) [3]. The described mechanism of echo formation is rather general and has implications in other fields of physics. The SLAC demonstration of the efficient generation of high harmonics (up to the 75th) from tailored electron beams in free-electron lasers [4] is based on a mechanism similar to fractional echoes of high order observed in our molecular experiments. Alignment echoes provided an efficient tool for studies on collisional relaxation in dense molecular gases [5]. Recently, we extended our studies to single quantum objects and considered echoes in a single vibrating molecule (observed in 2020 [6]) and echoes in a single quantum Kerr-nonlinear oscillator [7], which is a paradigmatic model in cavity and circuit quantum electrodynamics, and quantum optomechanics. Finally, we will discuss how the search for echoes in single quantum systems led us to suggest a new kind of spectroscopy of the Gravitational Quantum States (GQS) of ultra-cold neutrons, atoms, and anti-atoms bouncing in the Earth's gravitational field [8].
[1] G. Karras, E. Hertz, F. Billard, B. Lavorel, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y.Prior, and I.Sh. Averbukh, Phys. Rev. Lett., 114, 153601 (2015)
[2] G. Karras, E. Hertz, F. Billard, B. Lavorel, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I.Sh. Averbukh, Phys. Rev. A 94, 033404 (2016)
[3] Kang Lin, Peifen Lu, Junyang Ma, Xiaochun Gong, Qiying Song, Qinying Ji, Wenbin Zhang, Heping Zeng, Jian Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I.Sh. Averbukh, Phys. Rex. X 6, 041056 (2016)
[4] E. Hemsing, M. Dunning, B. Garcia, C. Hast, T. Raubenheimer, G. Stupakov and D. Xiang, Nat. Photonics 10, 512 (2016).
[5] H. Zhang, B. Lavorel, F. Billard, J.-M. Hartmann, E. Hertz, O. Faucher, Junyang Ma, Jian Wu, Erez Gershnabel, Yehiam Prior, and Ilya Sh. Averbukh, Phys.Rev.Lett. 122, 193401 (2019).
[6] Junjie Qiang, Ilia Tutunnikov, Peifen Lu, Kang Lin, Wenbin Zhang, Fenghao Sun, Yaron Silberberg, Yehiam Prior, Ilya Sh. Averbukh, and Jian Wu, Nature Physics, 16, 328–333 (2020);
[7] I. Tutunnikov, K. V. Rajitha, and I. Sh. Averbukh, Phys.Rev. A 103, 013717 (2021)
[8] I. Tutunnikov, K. V. Rajitha , A. Yu. Voronin, V. V. Nesvizhevsky, and I. Sh. Averbukh, Phys. Rev. Lett. 126, 170403 (2021)