Echoes in Single Quantum Systems


  Ilia Tutunnikov[1]   ,  J. Qiang[2]  ,  K. Lin[2]  ,  P. Lu[2]  ,  W. Zhang[2]  ,  F. Sun[2]  ,  K. V. Rajitha[1]  ,  Y. Silberberg[3]  ,  Y. Prior[1]  ,  J. Wu[2,4]  ,  I. Sh. Averbukh[1]  
[1] Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel
[2] State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China
[3] Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel
[4] Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi, China

Echoes in physics can be defined as spontaneous delayed responses following a series of pulsed excitations. Perhaps the most famous example is the spin echo [1]. Echoes are typically observed in inhomogeneously broadened ensembles of many particles evolving at different frequencies. Here, we describe a different class of echoes induced in the single isolated non-linear quantum systems, quantum-optical [2] and molecular ones [3]. The latter echoes have been observed by us in the vibrational motion of a single isolated  ion. In our experiments, a short laser pulse is used to impulsively excite a vibrational wave packet in the anharmonic ionic potential. The wave packet then oscillates and eventually disperses with time. A second delayed pulsed excitation is applied, giving rise to an echo – a partial recovery of the initial coherent oscillations. The vibrational dynamics of single molecules is visualized by a time-delayed probe pulse dissociating them one at a time. Quantum echoes may lead to the development of new tools for probing ultrafast processes in molecules and systems related to quantum information processing.

[1] E. L. Hahn, “Spin Echoes,” Phys. Rev. 80, 580 (1950).

[2] I. Tutunnikov, K. V. Rajitha, and I. Sh. Averbukh, “Echoes in a single quantum Kerr-
      nonlinear oscillator,” Phys. Rev. A 103, 013717 (2021).

[3] J. Qiang, I. Tutunnikov, P. Lu, et al. “Echo in a single vibrationally excited molecule,”
      Nat. Phys. 16, 328–333 (2020).