Relativistic and Ultrashort
Relativistic features of the under-the-barrier dynamics in laser-induced ionization
We have investigated the role of relativistic effects during the under-the-barrier dynamics in laser-induced ionization. An interesting finding was that even during this short time before the release of the electron from the bound state, relativistic effects arise imprinting their signature on the electron dynamics and characteristics.\A0 An intuitive picture for the relativistic tunneling regime is developed demonstrating that the tunneling picture applies also in the relativistic case by introducing position dependent energy levels. The quantum dynamics in the classically forbidden region features two time scales, the typical time that characterizes the probability density\92s decay of the ionizing electron under the barrier (Keldysh time) and the time interval which the electron wave packet spends inside the barrier (Eisenbud-Wigner-Smith tunneling time). In the relativistic regime, an electron momentum shift as well as a spatial shift of the ionized electron wave packet along the laser propagation direction arise during the under-the-barrier motion which are caused by the laser magnetic field induced Lorentz force. The momentum shift is proportional to the Keldysh time, while the wave-packet\92s spatial drift is proportional to the Eisenbud-Wigner-Smith time. The signature of the momentum shift is shown to be present in the ionization spectrum at the detector and, therefore, observable experimentally, see Fig. 1. In contrast, the signature of the Eisenbud-Wigner-Smith time delay disappears at far distances for pure tunneling dynamics [1,2].
 M. Klaiber, E. Yakaboylu, H. Bauke, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 110, 153004 (2013); arXiv:1205.2004v1 [physics.atom-ph]
 E. Yakaboylu, M. Klaiber, H. Bauke, K. Z. Hatsagortsyan and C. H. Keitel,\A0 arXiv:1309.0610 [quant-ph]
Spin dynamics in relativistic ionization
Spin effects arise during the relativistic tunneling ionization process . We have investigated the spin-resolved ionization dynamics employing the relativistic Coulomb corrected dressed strong field approximation [4,5], and taking into account the laser field driven electron spin dynamics in the bound state.\A0 Even if an electron is very tightly bound to an ionic core, it may still be crucially affected by a laser field of moderate intensity. Spin effects in the tunneling regime of ionization are built up in three steps: spin precession in the bound state, spin rotation during tunneling, and spin precession during the electron motion in the continuum, see Fig. 3. The magnitude and scaling of the spin-flip and spin asymmetry effects at ionization are reduced, when the electron spin dynamics in the bound state is taken into account.\A0 However, with super-strong laser fields a large spin-flip effect is measurable when employing highly charged ions, initially polarized along the laser propagation direction. The anticipated spin-flip effect is expected to be measurable with modern laser techniques combined with an ion storage facility.
Such measurements require an initially polarized target of ions and detection of the photoelectron polarization via Mott polarimetry. The electron spin flip can also be revealed via measurement of ion parameters, relating the angular momentum change of the ion during ionization to the electron spin change. The spin flip will be indicated by a non-vanishing signal for the difference in the ion angular distribution when appliying of left versus right circularly polarized laser fields.
In a different study the spin oscillations of a bunch of electrons have been investigated as a function of the interaction time with an intense laser field (see fig. 8 in the Theory Division webpage). For intensities of the order of 1018 W/cm2 the magnetic component is weak enough that quantum features (so-called collapses and revivals) become measurable in the dynamics .
 M. Klaiber, E. Yakaboylu, H. Bauke, C. M\FCller, G. G. Paulus and K. Z. Hatsagortsyan,\A0 arXiv:1305.5379 [physics.atom-ph]
 M. Klaiber, E. Yakaboylu, and K. Z. Hatsagortsyan, Phys. Rev. A 87, 023418 (2013);\A0\A0 arXiv:1301.5764 [physics.atom-ph]
 M. Klaiber, E. Yakaboylu, and K. Z. Hatsagortsyan, Phys. Rev. A 87, 023417 (2013);\A0 arXiv:1301.5761 [physics.atom-ph]
 O. D. Skoromnik, I. D. Feranchuk, C. H. Keitel, Phys. Rev A 87, 052107 (2013)
Relativistic high-order harmonic generation
Relativistic effects are very dramatic for ATI and HHG processes based on the three-step process (tunneling ionization-excursion in the laser field-recollsion with the atomic core). The laser magnetic field induces a drift of the ionized electron in the laser propagation direction which severely suppresses the probability of the electron to revisit the ionic core and, consequently, the yield of ATI electrons or harmonic photons . That is why the HHG frequencies cannot be increased by a straightforward increase of the laser intensity. To this purpose we have considered different setups for the suppression of the magnetically induced drift in the relativistic regimes of HHG. For example, we have employed various combinations of fields or particular atomic systems such as pre-accelerated highly charged ions, exotic atomic systems (positronium). What appears particularly promising for the suppression of the relativistic drift is the use of a HHG scheme with counter-propagating attosecond pulse trains where a special method for phase-matching has been developed.
The conventional method of HHG uses sinusoidal laser fields. Is it possible to modify the laser pulse in such a way that it would allow efficient rescattering in the strongly relativistic regime and thus allow HHG in the hard x-ray domain? We have shown that this is feasible by employing strong laser pulses tailored as an attosecond pulse train (APT) . The temporal tailoring of the laser pulse is intended to concentrate the ionizing and accelerating laser forces in short time intervals within the laser period, maintaining the average intensity of the pulse constant. This is due to the fact that in the tailored laser pulse, fragments are avoided in the electron trajectory, in contrast to the sinusoidal laser pulse where the electron acceleration is compensated by deceleration without a net energy gain by the electron, while the electron nevertheless continues to drift in the laser propagation direction. By the tailoring, the time span when the electron moves with relativistic velocity is decreased and a shorter drift in the laser propagation direction is obtained, leading to an increase of the recombination probability.
We have shown in  that strong counter-propagating\A0 APT employed as a driving field for HHG can be very useful to suppress the relativistic drift. This is achieved by reverting the relativistic drift of the ionized electron during the motion in APTs (see Fig. 4). The electron dynamics in APTs is the following. The electron is ionized by one APT, driven by this pulse up to the end of the pulse, then taken by the second counter-propagating pulse that realizes the rescattering with the atomic core.\A0 The second pulse induces a reverted drift toward the atomic core. The drift in the different pulses actually cancel each other out, due to which the initial momentum of the recolliding electron in the laser propagation direction can be small.\A0 As a result, the ionization probability and the HHG yield are enhanced. This concerns HHG from a single atom. Can coherent phase matched HHG emission is realized by this setup from a macroscopic gas target? Our investigation shows that this is the case.\A0 The propagation of the harmonics through the medium and the scaling of HHG into the multi-keV regime are investigated in . We show that the phase-mismatch caused by the free electron background can be compensated by an additional phase of the emitted harmonics specific to the considered setup which depends on the delay time between the pulse trains. This renders feasible the phase-matched emission of harmonics with photon energies of several tens of keV\A0 from an underdense plasma.
In the relativistic regime the XUV or x-ray assistance can be employed to overcome the relativistic drift motion [10,11]. Thereby, the XUV frequency has to exceed the ionization energy to liberate the electron with a single photon and to deliver a significant initial momentum to the freed electron, see Fig. 5. This way the electron can obtain sufficient momentum in the direction opposite to the laser propagation direction to compensate for subsequent drift motion and return to the atomic core, recombine, and emit harmonics after the excursion in the relativistically strong laser field. The medium is a gas of multiply charged ions with ionization energy large enough to withstand the strong optical laser field. We have shown the feasibility of phase-matched emission and the macroscopic yield of harmonics in the relativistic regime of the x-ray assisted HHG setup in a strong IR laser field . Generally, the efficiency of HHG is rather small even in the nonrelativistic regime due to the wave packet spreading. In the relativistic regime, the single-atom HHG emission rate continues to decrease even when the relativistic drift is compensated. Thus, a large phase-matching volume is crucial in order to achieve a significant HHG yield. Furthermore, the large ponderomotive potential is likely to result in rapid phase changes if ions emit under different conditions. For generating relativistic harmonics both challenges have to be met: circumventing the drift and having the setup stable against phase changes. This setup overcomes both issues and renders a measurable HHG yield in the relativistic regime possible, see Fig.6.
We have proposed a method for engineering the HHG phase which is achieved by shaping a laser pulse and employing XUV light or x rays for ionization . This renders the production of bandwidth-limited attosecond pulses possible while avoiding the use of filters for chirp compensation. By adding the first 8 Fourier components to a sinusoidal field of 1016\A0 W/cm2 , the bandwidth-limited emission of 8 as is shown to be possible from a Li2+\A0 gas. The scheme is extendable to the zs-scale. In a similar way one can engineer the continuum fraction of the electron wave packet in HHG such that a quasi-monochromatic recollision with the atomic core is rendered possible even for parts of the wave packet that were launched to the continuum at different laser phases . Because of this, the HHG spectrum is shown to be enhanced in a specified controllable spectral window.\A0
 M. C. Kohler, T. Pfeifer,\A0 K. Z. Hatsagortsyan, and C. H. Keitel, Frontiers of atomic high-harmonic generation (review)
Adv. Atom. Mol. Opti. Phys. 61, 159 (2012) arXiv:1201.5094v1 [physics.atom-ph]
 M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. A 75, 063413 (2007).
 K. Z. Hatsagortsyan, M. Klaiber, C. M\FCller, M. C. Kohler, and C. H. Keitel, Opt. Soc. Am. B 25, 92 ( 2008).
 M. C. Kohler, M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, EPL 94, 14002 (2011);\A0 arXiv:1008.0511v1 [physics.atom-ph]
 M. Klaiber, K. Z. Hatsagortsyan, C. M\FCller, and C. H. Keitel, Optics Letters\A0 33, 411 (2008);\A0 arXiv:0708.3360
 M. C. Kohler, K. Z. Hatsagortsyan, Phys. Rev. A 85, 023819 (2012); arXiv:1111.4113 [physics.atom-ph]
 M. C. Kohler, C. H. Keitel, and K. Z. Hatsagortsyan,
Optics Express, 19, 4411 (2011); arXiv:1101.5885v1 [physics.atom-ph]. Included in research highlights of Nature Photonics 5, 250 (2011)
 M. C. Kohler and K. Z. Hatsagortsyan, JOSA B 30, 57 (2013).
Coherent x-ray generation from below-threshold harmonics
The possibility of x-ray emission employing below-threshold-harmonic (BTH) generation in the nontunneling regime is considered in . The interaction of a tightly bound valence electron in a highly charged ion with intense XUV laser radiation is investigated in the weakly relativistic regime by numerical solution of the two dimensional relativistically corrected Schroedinger equation. Highly charged with a large ionization potential are applied because in the BTH regime the HHG emission frequency is limited by the ionization potential. A high density of ions is necessary for sizable HHG yield, which can be realized using underdense plasma.
However, in this case a large free-electron background will exist, hindering the realization of phase matching for the emitted x rays with the driving infrared laser field. To weaken the phase-matching problem, we employ a strong XUV field to drive the harmonic generation process, as at higher frequencies the plasma refractive index is closer to one. High frequencies are also necessary to avoid the fully relativistic regime because the laser magnetic-field-induced drift also has consequences for BTH, see Fig. 7. The harmonics below the ionization energy of the tightly bound system are found to be emitted with much higher probability than the standard plateau harmonics of loosely bound systems in the tunneling ionization regime for the same photon energy. This paves a path toward coherent hard x rays.
Attosecond pulses at keV photon energies from high-order harmonic generation with core electrons
High-order harmonic generation (HHG) in simultaneous intense near-infrared (NIR) laser light and brilliant x rays above an inner-shell absorption edge is examined in . A tightly bound inner-shell electron is transferred into the continuum. Then, NIR light takes over and drives the liberated electron through the continuum until it eventually returns to the cation leading in some cases to recombination and emission of a high-order harmonic photon that is upshifted by the x-ray photon energy, see Fig. 8. We have applied this scenario to 1s electrons of neon atoms. The boosted harmonic light is used to generate a single attosecond pulse in the keV regime. This opens prospects for x-ray HHG spectroscopy for time-resolving core electrons atosecond dynamics.
Coulomb focusing effects in strong-field processes
The recent experiments of DiMauro group on the photoionization of atoms and molecules in strong mid-infrared laser fields reveal a previously unexpected characteristic spike-like low-energy structure (LES) in the energy distribution of electrons emitted along the laser polarization direction, see Fig. 9. These observations manifest a striking contrast to the prediction of the SFA or the SFA with Coulomb corrections and point to a lack of complete understanding of strong field physics. Varying the laser polarization from linear to circular, LES is significantly reduced. The latter indicates that rescattering is playing an essential role in this process. However, many questions arise: How exactly does the LES arise? Why does it have a peaked structure? Why is the effect of rescattering more pronounced in mid-infrared laser fields? We have investigated and identified the mechanism of LES using the classical-trajectory Monte Carlo method with tunneling and the Coulomb field of the atomic core fully taken into account . With a qualitative theoretical estimation for the Coulomb field effects: initial Coulomb focusing (CF), multiple forward scattering, and asymptotic CF, we have quantified their relative role in the electron dynamics and conclude that (1) the behavior of the transverse (with respect to the laser polarization direction) momentum change of the electron due to Coulomb field effects with respect to the ionization phase is the key for understanding of the LES, see Fig. 10, and (2) at mid-infrared wavelengths, multiple scattering of the ionized electron plays a significant nonperturbative role .
Coulomb focusing in an elliptically polarized laser field
It appears that the Coulomb focusing has a significant role also in a laser field of elliptical polarization, although it is known that the rescattering effect is reduced in this regime. We have investigated the role of Coulomb focusing in above-threshold ionization in a mid-infrared laser field of elliptical polarization [18[. We have shown that multiple forward scattering of the ionized electron by the atomic core has the dominated contribution in Coulomb focusing up to moderate ellipticity values, see Fig. 11. The multiple forward scattering causes squeezing of the transverse momentum-space volume, which is the main factor influencing the normalized yield at moderate ellipticities. It is responsible for the peculiar energy scaling of the ionization normalized yield along the major polarization axis, and for the creation of a characteristic low-energy structure in the photoelectron spectrum. At large ellipticities, the main CF effect is due to the initial Coulomb disturbance at the exit of the ionization tunnel. The initial Coulomb disturbance, as our estimates show, enhances the ionization yield. This is because the electrons are tunneled out at larger laser fields or with smaller initial transverse momentum when the initial CF is taken into account for the electron drifting along the main polarization axis. The enhancement factor is shown to be sharply pronounced at intermediate ellipticities when both of the above-mentioned enhancement mechanisms contribute. In this region of ellipticity, the yield is enhanced by an order of magnitude due to the CF.
 Chengpu Liu and K. Z. Hatsagortsyan, Phys. Rev. Lett. 105, 113003 (2010);\A0 arXiv:1007.5173v1 [physics.atom-ph].
 C. Liu and K. Z. Hatsagortsyan, J. Phys. B 44, 095402 (2011);\A0\A0 arXiv:1011.1810v1 [physics.atom-ph]
 C. Liu and K. Z. Hatsagortsyan, Phys. Rev. A 85, 023413 (2012) ; arXiv:1109.5645v2 [physics.atom-ph]
Radiation reaction effects in strong laser fields
Radiation-reaction-force-induced nonlinear mixing of Raman sidebands of an ultraintense laser pulse in plasma
When an electron moves in an external field it may radiate losing in this way energy and momentum. This effect is known as radiation reaction . During the interaction of strong laser radiation with electrons, the radiation reaction can play an important role in the relativistic regime. In our recent work  we found a surprising counter-intuitive effect of the radiation reaction for Raman scattering of a strong radiation in plasma. Usually, one relates the radiation reaction effect to a resulting damping and could expect that this would cause decreasing\A0 the growth rate of the Raman scattering. In contrast to that our calculation shows a significant increase of the forward Raman scattering (FRS) growth rate, see Fig. 12. Our calculation is based on the solution of the Landau-Lifshitz classical equation of motion taking into account the radiation reaction force perturbatively. The reason for this unexpected effect of radiation reaction is that the radiation reaction force causes a phase shift in the nonlinear current densities that drive the two Raman sidebands (anti-Stokes and Stokes waves). Because of the latter\A0\A0 the nonlinear mixing of two sidebands of the FRS becomes possible mediated by the radiation reaction force. This mixing results in a strong enhancement in the growth of the forward Raman scattering instability. In the absence of the radiation reaction force, nonlinear currents that drive the Stokes and the anti-Stokes modes have opposite polarizations. Consequently, the phase shift induced by the radiation is opposite for these modes. This results in the interaction between the nonlinear current terms, culminating into phase shift accumulation. We term the nonlinear mixing of the two modes due to the radiation reaction force as the manifestation of this accumulation of phase shifts, and it leads to the enhanced growth rate of the FRS instability. One can also intuitively argue that this growth enhancement occurring due to the availability of an additional channel of radiation-reaction-force-induced laser energy decay and its efficient utilization by both the Stokes and the anti-Stokes modes. In other words, due to nonlinear mixing of the two Raman sidebands, they assist each other to extract the energy from the propagating laser wave.
The radiation reaction force strongly enhances the growth of the FRS only when both the Stokes and the anti-Stokes modes are the resonant modes of the plasma. The growths of the FRS with only the resonant Stokes wave excitation and the backwards Raman scattering (BRS) are also enhanced by the inclusion of the radiation reaction force, although the enhancement is\A0 minor\A0 due to the absence of the radiation-reaction-force-induced nonlinear mixing of the anti-Stokes and the Stokes modes. Thus, the radiation reaction force appears to strongly enhance the growth of the SRS involving four-wave decay interaction. These results are important for the ELI Project, as the ultraintense laser pulses are expected to create dense plasma by strongly ionizing the ambient air and also by producing the electron-positron pairs. The subsequent interaction of this plasma with the laser pulse can lead to the onset of parametric instabilities leading to significant change in the frequency spectra and shapes of these extremely intense short laser pulses due to the radiation reaction force. Moreover, contrary to nonlinear Compton scattering of a counter-propagating relativistic electron in a strong laser field aiming to discern the signatures of the radiation reaction force on the spectra of high-energy gamma-ray photons , enhanced FRS due to the radiation reaction force provides an alternative way to detect the radiation reaction effects in the spectra of low-energy optical photons.
Radiation dominated regime
Unlike in the nonrelativistic case, a situation can occur in the ultrarelativistic regime in which the radiation reaction force becomes comparable with the Lorentz force in the laboratory frame while being much smaller in the instantaneous rest frame of the electron. This is the so-called radiation dominated regime in which the electron dynamics and its radiation are supposed to be significantly modified due to the radiation reaction. In the classical regime of interaction we have found a strong signatures of radiation reaction below the Radiation-Dominated Regime . The influence of radiation reaction on multiphoton Thomson scattering by an electron colliding head-on with a strong laser beam is investigated in a new regime, in which the momentum transferred on average to the electron by the laser pulse approximately compensates the one initially prepared. This equilibrium is shown to be far more sensitive to the influence of radiation reaction than previously studied scenarios, see Fig. 13. As a consequence, the radiation reaction can be experimentally observed with currently available laser systems.
Quantum radiation reaction effects in multiphoton Compton scattering are investigated in  in the realm of quantum electrodynamics. We identify the quantum radiation reaction with the multiple photon recoils experienced by the laser-driven electron due to consecutive incoherent photon emissions. After determining a quantum radiation dominated regime, we demonstrate how in this regime quantum signatures of the radiation reaction strongly affect multiphoton Compton scattering spectra and that they could be measurable in principle with presently available laser technology, see Fig. 14.
Photoemission of a single-electron wave packet
in a strong laser field
We have studied the amount of light that an electron scatters out the side of a laser and showed that even when it spreads to the scale of the wavelength of the driving laser field, it cannot be treated as an extended classical charge distribution, but rather behaves as pointlike emitter carrying information on its initial quantum state [23,24].
 A. Di Piazza, C. M\FCller, K. Z. Hatsagortsyan, and C.H. Keitel, Rev. Mod. Phys. 84, 1177 (2012);\A0 arXiv:1111.3886v1 [hep-ph]
 N. Kumar, K. Z. Hatsagortsyan, C. H. Keitel,
Phys. Rev. Lett. 111, 105001 (2013);\A0\A0 arXiv:1307.3939 [physics.plasm-ph]
 A. Di Piazza, K. Z. Hatsagortsyan and C. H. Keitel,
Phys. Rev. Lett. 102, 254802 (2009);\A0 arXiv:0810.1703 [physics.class-ph]
 A. Di Piazza, K. Z. Hatsagortsyan, and C.H. Keitel,
Phys. Rev. Lett. 105, 220403 (2010); arXiv:1007.4914v1 [hep-ph]
 J. Peatross, C. M\FCller, K. Z. Hatsagortsyan and C. H. Keitel, Phys. Rev. Lett. 100, 153601 (2008); arXiv:0712.0259 [quant-ph]
 J. P. Corson, J. Peatross, C. M\FCller, and K. Z. Hatsagortsyan, Phys. Rev. A 84, 053831 (2011).
Nonlinear QED effects in strong laser fields
Bragg scattering of light in vacuum structured
by strong periodic fields
Super-strong laser fields offer unique possibilities for the investigation of the quantum vacuum. Different effects of vacuum QED nonlinearities induced by strong laser fields have been considered. Elastic photon-photon scattering is a process quite feasible for experimental observation. We have shown that using a setup of multiple crossed superstrong laser beams the photon-photon scattering rate can be significantly enhanced due to Bragg interference . The Bragg interference arising at a specific impinging direction of the probe wave concentrates the scattered light in specular directions, see Fig. 15. The interference maxima are enhanced with respect to the usual vacuum polarization effect proportional to the square of the number of modulation periods within the interaction region. The enhancement is maintained also in the total probability of the scattering, integrated by the scattering angle. The Bragg scattering can be employed to detect the vacuum polarization effect in a setup of multiple crossed superstrong laser beams with parameters envisaged in the future Extreme Light Infrastructure. Similar enhancement effects will exist in all types of inelastic light-by-light scattering and other processes based on spatially modulated vacuum polarization.
Pair production in laser fields oscillating
in space and time
In the extremely strong Schwinger field electron-positron pair can be created. Usually, the laser field in a node of a standing wave is approximated by an oscillating laser field. What is the role of the laser magnetic field for pair production process? When the pair production coherence length is on order of or larger than the laser wavelength, the laser magnetic field effect cannot be neglected. This effect we investigate in  where the production of electron-positron pairs from vacuum by counter-propagating laser beams of linear polarization has been studied numerically solving Dirac equation. In contrast with the usual approximate approach, the spatial dependence and magnetic component of the laser field are taken into account. We show that the latter strongly affects the creation process at high laser frequency: the production probability is reduced, the kinematics is fundamentally modified, the resonant Rabi-oscillation pattern is distorted, and the resonance positions are shifted, multiplied, and split, se Fig. 16. The narrow peak splitting of the resonant pair production probability could serve as a sensitive probe of the quasienergy band structure and, generally, of QED in superstrong spatially and temporally inhomogeneous fields.
Streaking at high energies with electrons
and positrons (SHEEP)
We proposed a detection scheme for characterizing high-energy γ-ray pulses down to the zeptosecond timescale, employing the pair production process in strong laser fields . In contrast to existing attosecond metrology techniques, our method is not limited by atomic shell physics and therefore capable of breaking the MeV photon energy and attosecond timescale barriers. It is inspired by attosecond streak imaging, but builds upon the high-energy process of electron\96positron pair production in vacuum through the collision of a test pulse with an intense laser pulse, see Fig. 17. The scheme is shown to be feasible in the upcoming Extreme Light Infrastructure laser facility where the required three beams can be available: strong infrared beam, x-ray beam and combined with the γ -ray test beam.\A0
Investigating positronium dynamics in intense laser fields, in addition to the coherent x-ray generation during electron-positron recombinations, we have predicted gamma-radiation of narrow bandwidth due to laser-enhanced annihilations of both particles . Without an external laser field, ortho-positronium annihilates spontaneously into three photons. In the laser field, the channel that involves two gamma-quanta and one laser-photon can be enhanced by means of stimulated emission of laser photons, see Fig. 20. Due to energy-momentum conservation, in this case the bandwidth of the gamma-radiation is connected with the bandwidth of the low-frequency radiation and, therefore, is narrow. We thus obtain gamma-radiation which is enhanced in intensity and narrow in bandwidth. \A0
Enhancing the lifetime of positronium atoms
via collective radiative effects
We have proposed to harness cooperative spontaneous emission of an ensemble of Ps atoms to provide a way for controlling the annihilation dynamics. We employ a dense ensemble of (para- and ortho-) Ps atoms in which the atoms interact with each other via the common radiation field, see Fig. 21.
Using a three-level model system (which incorporates annihilation) for a Ps atom driven by a resonant laser field, we investigate the role of collective spontaneous radiative processes on the population dynamics and its influence on the annihilation evolution of the ensemble. Two schemes are developed for the enhancement of the annihilation lifetime of the Ps ensemble. In the first scheme, the radiative decay on the 3D-2P transition is collective, other than on the 2P-1S transition, and is controlled by the density of the gas. In the second scheme, both transitions are collective, but the strength of the first is enhanced by a cavity, leading to population trapping in the 2P state and, consequently, to significant lifetime enhancement.\A0
 G. Yu. Kryuchkyan and K. Z. Hatsagortsyan, Phys. Rev. Lett. 107, 053604 (2011); arXiv:1102.4013 [quant-ph].
 M. Ruf, G. R. Mocken, C. M\FCller, K. Z. Hatsagortsyan and C. H. Keitel, Phys. Rev. Lett. 102, 080402 (2009); arXiv:0810.4047 [physics.atom-ph].
 A. Ipp, J. Evers, C. H. Keitel, and K. Z. Hatsagortsyan, Phys. Lett. B 702, 383 (2011) arXiv:1008.0355v2 [physics.ins-det]
 K. Z. Hatsagortsyan, C. M\FCller, and C. H. Keitel, Europhys. Lett. 76, 29 (2006); arXiv: 0602093 [physics]
 C. Liu, M. C. Kohler, K. Z. Hatsagortsyan, C. M\FCller and C. H. Keitel, New J. Phys. 11, 105045 (2009); included in IOP Select
 B. Henrich, K. Z. Hatsagortsyan and C. H. Keitel, Phys. Rev. Lett. 93, 013601 (2004)\A0 arXiv: hep-th/0303188
 C. M\FCller, K. Z. Hatsagortsyan and C. H. Keitel, Physics Letters B 659, 209 (2008); arXiv:0705.0917 [hep-ph]
 Ni Cui, M. Macovei, K. Z. Hatsagortsyan and C. H. Keitel, Phys. Rev. Lett. 108, 243401 (2012)\A0 arXiv:1112.1621v1 [quant-ph]