Mountain echoes are a well-known phenomenon, where an impulse excitation is mirrored by the rocks to generate a replica of the original stimulus, often with reverberating recurrences. For spin echoes in magnetic resonance and photon echoes in atomic and molecular systems the role of the mirror is played by a second, time delayed pulse which is able to reverse the flow of time and recreate the original event. Recently, laser-induced rotational alignment and orientation echoes were introduced for molecular gases, and discussed in terms of rotational-phase-space filamentation. Here we present, for the first time, a direct spatiotemporal analysis of various molecular alignment echoes by means of coincidence Coulomb explosion imaging. We observe hitherto unreported spatially rotated echoes, that depend on the polarization direction of the pump pulses, and find surprising imaginary echoes at negative times. PACS numbers:In 1950, Erwin Hahn reported [1] that if a spin system is irradiated by two properly timed and shaped pulses, a third pulse appears at twice the delay between the first two. The intuitive explanation was given in terms of time reversal, namely the second pulse reverses the direction of propagation of the original excitation, leading to reappearance of the original impulse [2]. In the absence of interaction with the environment, the full original excitation is recovered, but with environmental influences, various dephasing and energy loss processes may be probed. Following the original discovery in the realms of spins, echoes were observed in many other nonlinear physical situations such as photon echo [3], cyclotron echo [4], plasma wave echo [5], echoes in cold atoms [6,7], cavity QED [8], and even in particle accelerators [9,10]. Echoes form the basis for many modern methodologies ranging from Magnetic Resonance Imaging (MRI) [11] to short-wavelength radiation generation in free-electron * lasers [12][13][14][15]. Echoes are a classical phenomenon that is different from another well-known effect: quantum revivals [16][17][18] which are caused by the energy quantization of physical systems. Recently, a new type of echoes was introduced: molecular alignment echoes [19,20]. When a gas of molecules undergoes excitation by an ultrashort laser pulse, the molecules experience a torque causing transient alignment of the ensemble along the laser polarization axis (for a review of laser molecular alignment, see [21][22][23][24]). A pair of time-delayed laser pulses results in three alignment events: two of them immediately following each excitation, and a third one, an echo, that appears with a delay equal to that between the exciting pulses. This delay can be shorter than the rotational revival time, so that the echo provides access to rapidly dephasing molecular dynamics. The formation of these echoes is caused by the kick-induced filamentation of the rotational phase space [19], a phenomenon well known in the physics of particle accelerators [32]. Moreover, fractional echoes were predicted and observed in mo...

A molecule can be optically accelerated to rotate unidirectionally at a frequency of a few terahertzes which is many orders higher than the classical mechanical rotor. Such a photon-induced ultrafast molecular unidirectional rotation has been well explored as a controllable spin of the molecular nuclear wave packet. Although it has been observed for more than 10 years, a complete imaging of the unidirectional rotating nuclear wave packet is still missing, which is essentially the cornerstone of all the exploring applications. Here, for the first time, we experimentally visualize the time-dependent evolution of the double-pulse excited molecular unidirectional rotation by Coulomb explosion imaging the rotational nuclear wave packet. Our results reveal comprehensive details undiscovered in pioneering measurements, which exhibits as a joint of the quantum revival of the impulsively aligned rotational wave packet and its unidirectional rotation following the angular momentum conservation. The numerical simulations well reproduce the experimental observations and intuitively revivify the thoroughgoing evolution of the rotational wave packet.Comment: 15 pages, 5 figure

A phase-controlled orthogonal two-color (OTC) femtosecond laser pulse is employed to probe the time delay of photoelectron emission in the strong-field ionization of atoms. The OTC field spatiotemporally steers the emission dynamics of the photoelectrons and meanwhile allows us to unambiguously distinguish the main and sideband peaks of the above-threshold ionization spectrum. The relative phase shift between the main and sideband peaks, retrieved from the phase-of-phase of the photoelectron spectrum as a function of the laser phase, gradually decreases with increasing electron energy, and becomes zero for the fast electron which is mainly produced by the rescattering process. Furthermore, a Freeman resonance delay of 140±40 attoseconds between photoelectrons emitted via the 4f and 5p Rydberg states of argon is observed.

Orientation and alignment of molecules by ultrashort laser pulses is crucial for a variety of applications and has long been of interest in physics and chemistry, with the special emphasis on stereodynamics in chemical reactions and molecular orbitals imaging. As compared to the laser-induced molecular alignment, which has been extensively studied and demonstrated, achieving molecular orientation is a much more challenging task, especially in the case of asymmetric-top molecules. Here, we report the experimental demonstration of all-optical field-free three-dimensional orientation of asymmetric-top molecules by means of phase-locked cross-polarized two-color laser pulse. This approach is based on nonlinear optical mixing process caused by the off-diagonal elements of the molecular hyperpolarizability tensor. It is demonstrated on SO2 molecules and is applicable to a variety of complex nonlinear molecules.

We experimentally visualize the dissociative frustrated double ionization of hydrogen molecules by using few-cycle laser pulses in a pump-probe scheme, in which process the tunneling ionized electron is recaptured by one of the outgoing nuclei of the breaking molecule. Three internuclear distances are recognized to enhance the dissociative frustrated double ionization of molecules at different instants after the first ionization step. The recapture of the electron can be further steered to one of the outgoing nuclei as desired by using phase-controlled two-color laser pulses. Both the experimental measurements and numerical simulations suggest that the Rydberg atom is favored to emit to the direction of the maximum of the asymmetric optical field. Our results on the one hand intuitively visualize the dissociative frustrated double ionization of molecules, and on the other hand open the possibility to selectively excite the heavy fragment ejected from a molecule.