Looking inside the tunneling process Nirit Dudovich Physics of Complex Systems, Weizmann Institute of Science

Co- authors Dror Shafir Oren Raz Hadas Soifer Oren Pedazur Michal Dagan Barry Bruner Collaborations: Olga Smirnova Misha Ivanov Yann Mairesse Serguei Patchkovskii Caterina Vozzi Salvatore Stagira2

Time resolved measurements in the attosecond regime The optical pulse pump/probe the process IR pulse Attosecond pulse Production Measurement The free electron probes the process Generating attosecond pulses has required a radically different approach from previous ultrafast optical methods. Attosecond pulses arise from highly nonlinear laser-atom interaction, while femtosecond pulses involve low order processes. The technology of attosecond measurement, however, is built on established methods of characterizing femtosecond pulses: the pulse is measured after it has left the region where it was produced. We offer a completely different approach: in-situ measurement. That is, we integrate attosecond pulse production and measurement in a manner that can be applied to many high-order non-linear interactions. The recollision process

Attosecond Science High harmonics generation E>100eV Acceleration by the electric field Re-collision Tunnel ionization Generating attosecond pulses has required a radically different approach from previous ultrafast optical methods. Attosecond pulses arise from highly nonlinear laser-atom interaction, while femtosecond pulses involve low order processes. The technology of attosecond measurement, however, is built on established methods of characterizing femtosecond pulses: the pulse is measured after it has left the region where it was produced. We offer a completely different approach: in-situ measurement. That is, we integrate attosecond pulse production and measurement in a manner that can be applied to many high-order non-linear interactions. High harmonics generation

Re-collision as a pump – probe scheme H. Niikura, et al., Nature 421, (2003). X. M. Tong et al., Phys. Rev. Lett. 91 (2003). M. Lein, Phys. Rev. Lett. 94, (2005). M. Lein, J. Phys. B, 40 (2007).   Re-collision S. Baker et al., Science 312, (2006). O. Smirnova, et al. Nature 460 (2009). O. Smirnova et al., PNAS 106, (2009). B. K. McFarland et al., Science 322, (2008). Tunnel ionization Optical cycle pump probe

Field induced tunnel ionization When does an electron leave the tunneling barrier? What is the instantaneous probability? Does the process evolve in an adiabatic manner? Can we resolve multi-channels ionization?   Tunneling through a static barrier   Field induced tunneling How can we look at this process? All we have is the emitted specrtum L. V. Keldysh Sov. Phys. JETP 20 1307 (1965) 6

Re-collision as a pump – probe scheme Electric field How does the time of ionization map into our experiment? Time [cycle] Distance P. B. Corkum,, Phys. Rev. Lett. 71, 1994 (1993).

Re-collision as a pump – probe scheme When does an electron leave the tunneling barrier? What is the instantaneous probability? Does the process evolve in an adiabatic manner? Can we resolve multi-channels ionization? The induced dipole moment is described by: Re(t0) Im(t0) The semi-classical action The main contribution to the integral comes from the stationary points: The solution is found in the complex plane of t0

Recollision as a measurement The output is the high harmonic spectrum - We need additional information X(t0)=0 V(t0)=0 X(t)=0 Can we keep it simple? c The recollision process provides an Angstrom-attosecond resolution Any deviations are mapped to the properties of the recolliding electron

“kicking” the recollision process We add a weak second harmonic field If the field is much weaker than the fundamental field it acts as an amplitude gate

“kicking” the recollision process

Gating the recollision process - Helium 70 60 Gate 50 Energy (harmonic number) 40 30 20 max (t0) -0.1 0.1 0.2 0.3 -0.4  [cycle]

Reconstructing the ionization times Harmonic order D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, Serguei Patchkovskii, M. Yu. Ivanov, O. Smirnova and N. Dudovich, Nature 485, 343 (2012).

Re-collision as a pump – probe scheme When does an electron leaves the tunneling barrier? What is the instantaneous probability? Does the process evolve in an adiabatic manner? Can we resolve multi-channels ionization? The induced dipole moment is described by: Re(t0) Im(t0) The semi-classical action

“kicking” the recollision process – parallel perturbation   Can we measure the imaginary time? We can add a parallel perturbation This perturbation adds a small phase shift and perturbs the ionization step. In the limit of a small Keldysh parameter we are left with a phase shift How do we perform the measurement? How can we separate the two mechanisms? J M Dahlstr¨om, A L’Huillier and J Mauritsson, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 095602x

Interferometry in High Harmonic Generation 17 19 21 23 25 27 29 exp(-i ) A(N) exp(-i ) A(N) A(N) exp(i ) A(N) exp(i) exp(i ) Odd harmonics Even harmonics

Interferometry in High Harmonic Generation Even harmonics π Odd harmonics Two color delay N. Dudovich, O. Smirnova, J. Levesque, M. Yu. Ivanov, D. M. Villeneuve and P. B. Corkum, Nature Physics 2, 781 (2006). A(N) exp(-i ) A(N) exp(-i ) A(N) exp(i ) A(N) exp(i) exp(i ) Odd harmonics Even harmonics

Interferometry in High Harmonic Generation Even harmonics π + Odd harmonics Two color delay A(N) exp(-i -) exp(-i ) A(N) exp(-i -) exp(-i ) A(N) exp(i +) exp(i ) A(N) exp(i) exp(i +) exp(i ) Odd harmonics Even harmonics

Interferometry in High Harmonic Generation odd- even Harmonic Order

Reconstruction of the imaginary times 30 40 50 60 70 0.05 0.1 0.15 0.2 Harmonic order Time [rad]

Mapping the tunneling process Moment of Ionization Probability 30 40 50 60 70 0.05 0.1 0.15 0.2 Harmonic order Time [rad]

The link between ionization and recollision Ionization time: 190 attoseconds 170 attoseconds 210 attoseconds 250 attoseconds 270 attoseconds 230 attoseconds

Multiple channel ionization Destructive interference O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum and M. Y. Ivanov, Nature 460, 972 (2009) D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, Serguei Patchkovskii, M. Yu. Ivanov, O. Smirnova and N. Dudovich, Nature 485, 343 (2012).

Gating multi channels ionization Ionization gate HOMO-2 HHG Energy (harmonic number) HOMO   [cycle] Ionization times [attosecond] Phase jump

Gating multi channels ionization Single channel - 90 degrees Two channels - 0 degrees Energy (harmonic number) HHG Energy (harmonic number) HHG  [cycle]  [cycle] We observe a clear signature to two channels ionization , probing a delay of 50 attoseconds in the ionization times. D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, Serguei Patchkovskii, M. Yu. Ivanov, O. Smirnova and N. Dudovich, Nature 485, 343 (2012).

Re-collision as a pump – probe scheme Recollision processes provide temporal information with attosecond resolution. We have measured the tunneling ionization time in simple systems, directly confirming the analysis based on the path integral formalism. We can measure a delay related to multiple orbitals tunneling In more complex molecular systems the tunneling process involves attosecond core rearrangements leading to a real time-delay associated with different tunneling channels.

Gating multi channels ionization

The link between ionization and recollision Classical solution Stationary solution M. Lewenstein et al., Phys Rev A 49, 2117 1994.

Reconstructing the ionization times

Tunneling - stationary solution We have linked the real part to the time at which the electron leaves the Coulomb barrier The imaginary part is linked to the instantaneous tunneling probability Can we measure it? The stationary solution is complex

Gating the recollision process Ionization Return D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, Serguei Patchkovskii, M. Yu. Ivanov, O. Smirnova and N. Dudovich, Nature 485, 343 (2012).

Gating the recollision process 2D Gate Displacement Gate: GLmax(N) Angular Gate: Gmax(N) GLmax(t0,t) Gmax(t0,t) t0 t

Gating the recollision process Displacement gate 70 60 50 HHG 40 30 20 -0.1 -0.2 -0.3 -0.4  [cycle] How do we reconstruct the dynamics? There are two unknown parameters – t0 and t

Recollision as a measurement The output is the high harmonic spectrum - We need additional information Can we keep it simple? The optimal gate Perturbative manipulation A window in the ionization time Can be shifted

Interferometry in High Harmonic Generation Delay [fs] 16 18 20 22 24 26 17 19 21 23 25 27 N. Dudovich, O. Smirnova, J. Levesque, M. Yu. Ivanov, D. M. Villeneuve and P. B. Corkum, Nature Physics 2, 781 (2006).

Reconstructing the ionization times Short trajectories Long trajectories

Reconstructing the ionization times

Field induced tunnel ionization Pioneering experiments How can we look at this process? All we have is the emitted specrtum P. Eckle et al., Science (2008) A. N. Pfeiffer et al., Nature Physics (2012). M. Uiberacker et al., Nature (2007). 38

Gating the recollision process Angular gate 60  50 HHG 40 HHG  30 20 -0.1 -0.2 -0.3 -0.4  [cycle]

Interferometry in High Harmonic Generation odd- even Harmonic Order

Interferometry in High Harmonic Generation

The link between ionization and recollision

The link between ionization and recollision Short trajectories Energy (harmonic number) Long trajectories M. Lewenstein et al., Phys Rev A 49, 2117 1994.

Reconstructing the ionization times

Reconstructing the ionization times

Scaling the gating mechanism – 1.4

“kicking” the recollision process – parallel perturbation The interference between two adjacent half cycle leads to the generation of odd harmonics. The second harmonic field breaks the symmetry and leads to the generation of even harmonics.

Re-collision as a pump – probe scheme

Re-collision as a pump – probe scheme We have an extremely accurate measurement – the electron is born at the origin, propagate on an attosecond time scale and returns to the origion Can we study the internal dynamics? Can we link each trajectory to its ionization time? Such a measurement will provide a direct insight into one of the most fundamental strong field phenomena – field induced tunnel ionization

Attosecond pulse generation process Re-collision Acceleration by the electric field E>100eV Tunnel ionization Ionization potential Kinetic energy Optical radiation with attoseconds duration

Attosecond pulse train The multi-cycle regime High harmonics generation H15 23.3eV H21 32.6eV H27 41.9eV H39 60.5eV

Kicking the recollision process - Helium He - normalized 70 60 50 Energy (harmonic number) 40 30 20 max (t0) -0.1 0.1 0.2 0.3 -0.4 -0.1 0.1 0.2 0.3 -0.4  [cycle]  [cycle]

Kicking the recollision process - Helium He - normalized 70 ∆Y()=0 ∆Y(t0)=0 Gate (“kick”) 60 50 Energy (harmonic number) 40 30 20 max (t0) -0.1 0.1 0.2 0.3 -0.4  [cycle]

Reconstructing the ionization times Energy (harmonic number) Harmonic order Why do we observe a significant deviation from the classical model?

Reconstructing the ionization times Energy (harmonic number) Harmonic order

Stationary Phase approximation       Weight   M. Lewenstein et al., Phys Rev A 49, 2117 1994.

Catastrophe Theory Mapping objects from one dimension to another dimensions can lead to singularities: Singularities are classified according to Catastrophe theory This classification tells us about the shape, intensity, width and diffraction pattern of the caustic. Think of how the density of the folded “ideal” paper is mapped to the plane!

The link between ionization and recollision The classical description links: t0 t E The quantum description: The quantum picture approaches the classical at the stationary points M. Lewenstein et al., Phys Rev A 49, 2117 1994.

Field induced tunnel ionization Pioneering experiments How can we look at this process? All we have is the emitted specrtum P. Eckle et al., “Attosecond Ionization and Tunneling Delay Time Measurements in Helium”, Science (2008) A. N. Pfeiffer et al., “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms”, Nature Physics (2012). 59

Return times M. Hentschel et al., Nature 414, (2001) Y. Mairesse, et al., Science 302, (2003). N. Dudovich et al., Nature Physics 2, (2006).

Ionization times ?

Interferometry in High Harmonic Generation odd- even Harmonic Order

Multiple channel ionization -13.8 eV -17.3 eV -18.1 eV O. Smirnova, et al., Nature 460, 972 (2009). B. K. McFarland et al., Science 322, (2008).

The link between ionization and recollision Energy (harmonic number) Real times 0.2 0.6 1 1.4 30 50 70 c 3 4 5 6 c Classical solution Stationary solution Time [rad] Time [rad] c 0.4 0.8 1.2 30 50 70 Imaginary times Time [rad] M. Lewenstein et al., Phys Rev A 49, 2117 1994.