Experimental Evidence for Quantum Tunneling Time

Abstract

The first hundred attoseconds of the electron dynamics during strong field tunneling ionization are investigated. We quantify theoretically how the electron's classical trajectories in the continuum emerge from the tunneling process and test the results with those achieved in parallel from attoclock measurements. An especially high sensitivity on the tunneling barrier is accomplished here by comparing the momentum distributions of two atomic species of slightly deviating atomic potentials (argon and krypton) being ionized under absolutely identical conditions with near-infrared laser pulses (1300 nm). The agreement between experiment and theory provides clear evidence for a nonzero tunneling time delay and a nonvanishing longitudinal momentum of the electron at the "tunnel exit."

Superluminal tunneling of a relativistic half-integer spin particle through a potential barrier

“…Several theoretical and experimental studies in the past decades have examined phenomena involving superluminal waves and objects because of their implication in quantum and cosmological physics [1][2][3][4][5][6][7][8][9]. Among them, the study of the tunneling time problem is one of the topics that has most attracted the interest of quantum physicists [10][11][12][13][14][15].…”

Under-the-Tunneling-Barrier Recollisions in Strong-Field Ionization

“…Although all alternative definitions of the tunneling delay time are equally valid theoretical concepts, the Wigner concept [20] is physically relevant to the measurement of the photoelectron momentum distribution in the attoclock setup in the quasistatic regime, as proved in a recent experiment [10]. However the Wigner definition of the time delay via the derivative of the wave function phase, and its generalization for the strong field tunneling problem [18,[21][22][23][24] is applicable only in the quasistatic limit, i.e., when the laser induced barrier is (quasi-)static.…”

“…However the Wigner definition of the time delay via the derivative of the wave function phase, and its generalization for the strong field tunneling problem [18,[21][22][23][24] is applicable only in the quasistatic limit, i.e., when the laser induced barrier is (quasi-)static. Therefore, there is need for a generalization of the Wigner concept to the nonadiabatic regimes [25][26][27] of the strong field ionization, which may explain the discrepancy between the theory and the attoclock experiment at large Keldysh parameters [10].…”

“…However the Wigner definition of the time delay via the derivative of the wave function phase, and its generalization for the strong field tunneling problem [18,[21][22][23][24] is applicable only in the quasistatic limit, i.e., when the laser induced barrier is (quasi-)static. Therefore, there is need for a generalization of the Wigner concept to the nonadiabatic regimes [25][26][27] of the strong field ionization, which may explain the discrepancy between the theory and the attoclock experiment at large Keldysh parameters [10].The main workhorse for the theoretical treatment of the strong field ionization, the strong field approximation (SFA) [28][29][30], in its common form does not provide a signature of the tunneling time in the asymptotic momentum distribution. The same is true for the Coulomb corrected SFA (CCSFA) [31,32], and the Analytic R-matrix (ARM) theory [33][34][35], which include the Coulomb field of the atomic core for the continuum electron in the eikonal approximation [that is, in the Wentzel-Kramers-Brillouin (WKB) approximation combined with the perturbative accounting of the Coulomb field in the phase of the wave function].…”

“…Recently the attoclock technique has been developed [5,6] based on the strong field ionization of an atom in an elliptically polarized laser field, which attempts to map the photoelectron momentum at the detector into the time of the electron appearance in the continuum during strong field ionization. In this way the attoclock technique is assumed to extract information on the time-resolved dynamics of the electron released from the atomic bound state during strong field ionization, and in particular, on the time-delay of the tunneling electron wave packet from the atom in a strong laser field [5][6][7][8][9][10]. Furthermore, the interference structures in the high-resolution photoelectron momentum distribution (PMD), created by the direct and recolliding trajectories, allow an interpretation as time-resolved holographic imaging of atoms and molecules, which admits attosecond time-and Ångström spatial-resolution [11][12][13][14].…”