Employing recent developed magneto-optical trap recoil ion momentum spectroscopy (MOTRIMS) combining cold atom, strong laser pulse, and ultrafast technologies, we study momentum distributions of the multiply ionized cold rubidium (Rb) induced by the elliptically polarized laser pulses (35 fs, $1.3 \times 10^{15}$ W/cm$^2$). The complete vector momenta of Rbn+ ions up to charge state n = 4 are recorded with extremely high resolution (0.12 a.u. for Rb$^+$). Variations of characteristic multi-bands displayed in momentum distributions, as the ellipticity varies from the linear to circular polarization, are interpreted qualitatively with the classical over-barrier ionization model. Present momentum spectroscopy of cold heavy alkali atoms presents novel strong-field phenomena beyond the noble gases.
We join the tribute to Professor N.B. Delone in this memorial issue by presenting the results of new calculations on the effects of ellipticity on double ionization by short and strong near-optical laser pulses.
Based on the strong-field approximation, we obtain analytical expressions for the initial momentum at the tunnel exit and instantaneous ionization rate of tunneling ionization in elliptically polarized laser fields with arbitrary ellipticity. The tunneling electron reveals a nonzero offset of the initial momentum at the tunnel exit in the elliptically polarized laser field. We find that the transverse and longitudinal components of this momentum offset with respect to the instantaneous field direction are directly related to the time derivatives of the instantaneous laser electric field along …
We investigate the strong-field ionization of atomic hydrogen in a few-cycle elliptically polarized infrared pulse by solving the time-dependent Schrödinger equation. The dependence of the photoelectron momentum distribution on the pulse intensity, ellipticity, length, envelope, and carrier envelope phase is analyzed. In particular, we explain the variation of the electron offset angle with asymptotic electron energy through the combined action of the field and the Coulomb potential, and demonstrate that low-ellipticity pulses make it possible to access the electron release time.
We examine correlated electron and doubly charged ion momentum spectra from strong field double ionization of Neon employing intense elliptically polarized laser pulses. An ellipticity-dependent asymmetry of correlated electron and ion momentum distributions has been observed. Using a 3D semiclassical model, we demonstrate that our observations reflect the sub-cycle dynamics of the recollision process. Our work reveals a general physical picture for recollision-impact double ionization with elliptical polarization, and demonstrates the possibility of ultrafast control of the recollision dynami…
We present an experimental investigation of ultrafast-laser driven Rabi oscillations of atomic rubidium. Since the broadband spectrum of an ultrafast laser pulse simultaneously couples all the electronic hyperfine transitions between the excited and ground states, the complex excitation linkages involved with the D1 or D2 transition are energy degenerate. Here, by applying the Morris-Shore transformation, it is shown that this multi-state system is reduced to a set of independent two-state systems and dark states. In experiments performed by ultrafast laser interactions of atomic rubidium in t…
We explore the influence of elliptical polarization on the (non)sequential two-photon double ionization of atomic helium with ultrashort extreme ultraviolet (XUV) light fields using time-dependent full ab-initio simulations. The energy and angular distributions of photoelectrons are found to be strongly dependent on the ellipticity. The correlation minimum in the joint angular distribution becomes more prominently visible with increasing ellipticity. In a pump-probe sequence of two subsequent XUV pulses with varying ellipticities, polarization tagging allows to discriminate between sequential …
We report on the observation and numerical calculation of ionization spectra of highly Stark-shifted Rydberg states of rubidium beyond the classical ionization threshold. In the numerical calculations, a complex absorbing potential (CAP) allows us to predict the energy levels and ionization rates of Rydberg states in this regime. Our approach of adjusting the CAP to the external electric field reduces the number of free parameters from one per resonance to a single one. Furthermore, we have measured the ionization spectra of magneto-optically trapped rubidium atoms which are excited to princip…
We perform high-resolution measurements of momentum distribution on Rb$^{n+}$ recoil ions up to charge state $n=4$, where laser-cooled rubidium atoms are ionized by femtosecond elliptically polarized lasers with the pulse duration of 35 fs and the intensity of 3.3$\times$10$^{15}$ W/cm$^2$ in the over-barrier ionization (OBI) regime. The momentum distributions of the recoil ions are found to exhibit multi-band structures as the ellipticity varies from the linear to circular polarizations. The origin of these band structures can be explained quantitatively by the classical OBI model and dedicat…
It is well-known from numerical and experimental results that the fraction of Rydberg states (excited neutral atoms) created by tunnel ionization declines dramatically with increasing ellipticity of laser light. We present a method to analyze this dependence on ellipticity, deriving a probability distribution of Rydberg states that agrees closely with recent experimental [1] and numerical results. In particular, contradicting the existing proposed mechanism [1] and general expectations, our results indicate that the dependence of Rydberg yield on laser ellipticity is not caused by a rescatteri…
The role of Coulomb focusing in above-threshold ionization in an elliptically polarized mid-infrared strong laser field is investigated within a semiclassical model incorporating tunneling and Coulomb field effects. It is shown that Coulomb focusing up to moderate ellipticity values is dominated by multiple forward scattering of the ionized electron by the atomic core that creates a characteristic low-energy structure in the photoelectron spectrum and is responsible for the peculiar energy scaling of the ionization normalized yield along the major polarization axis. At higher ellipticities, th…
Relativistic tunnel ionization of atoms by intense, elliptically polarized light is considered. The relativistic version of the Landau-Dykhne formula is employed. The general analytical expression is obtained for the relativistic photoelectron spectra. The most probable angle of electron emission, the angular distribution near this angle, the position of the maximum and the width of the energy spectrum are calculated. In the weak field limit we obtain the familiar non-relativistic results. For the case of circular polarization our analytical results are in agreement with recent derivations of …
The sub-cycle dynamics of electrons driven by strong laser fields is central to the emerging field of attosecond science. We demonstrate how the dynamics can be probed through high-order harmonic generation, where different trajectories leading to the same harmonic order are initiated at different times, thereby probing different field strengths. We find large differences between the trajectories with respect to both their sensitivity to driving field ellipticity and resonant enhancement. To accurately describe the ellipticity dependence of the long trajectory harmonics we must include a sub-c…
The energy distribution of an ultracold rubidium ion beam, which is intended to be used as the source for a focused ion beam instrument, is measured with a retarding field analyzer. The ions are created from a laser-cooled and compressed atomic beam by two-step photoionization in which the ionization laser power is enhanced in a build-up cavity. Particle tracing simulations are performed to ensure the analyzer is able to resolve the distribution. The lowest achieved full width 50% energy spread is $\left(0.205\pm0.006\right)$ eV. The energy spread originates from the variation in the ionizatio…
A two-step photoionization strategy of an ultracold rubidium beam for application in a focused ion beam instrument is analyzed and implemented. In this strategy the atomic beam is partly selected with an aperture after which the transmitted atoms are ionized in the overlap of a tightly cylindrically focused excitation laser beam and an ionization laser beam whose power is enhanced in a build-up cavity. The advantage of this strategy, as compared to without the use of a build-up cavity, is that higher ionization degrees can be reached at higher currents. Optical Bloch equations including the ph…
Photoionization of the rubidium (Rb) atoms cooled in a magneto-optical trap, characterized by the coexistence of the ground 5$S_{1/2}$ and the excited 5$P_{3/2}$ states, is investigated experimentally and theoretically with the 400 nm femtosecond laser pulses at intensities of $I=3\times10^9$ W/cm$^2$ - $4.5\times10^{12}$ W/cm$^2$. Recoil-ion momentum distribution (RIMD) of Rb$^+$ exhibits rich ring-like structures and their energies correspond to one-photon ionization of the 5$P_{3/2}$ state, two-photon and three-photon ionizations of the 5$S_{1/2}$ state, respectively. With the increasing of…
Multielectron double ionization with elliptically polarized light is examined theoretically using a classical ensemble method going beyond the single-active-electron approximation. A knee structure in the ion signal is found. Our analysis provides an explanation for newly observed SDI phenomena.
We investigate direct above-threshold ionization in diatomic molecules, with particular emphasis on how quantum interference is altered by a driving field of non-vanishing ellipticity. This interference may be either temporal, i.e., related to ionization events occurring at different times, or spatial, i.e., related to the electron emission at different centers in the molecule. Employing the strong-field approximation and saddle-point methods, we find that, in general, for non-vanishing ellipticity, there will be a blurring of the temporal and spatial interference patterns. The former blurring…
We report on precise measurements of absolute nonlinear ionization probabilities obtained by exposing optically trapped ultracold rubidium atoms to the field of an ultrashort laser pulse in the intensity range of $1 \times 10^{11}$ to $4 \times 10^{13}$ W/cm$^2$. The experimental data are in perfect agreement with ab-initio theory, based on solving the time-dependent Schrödinger equation without any free parameters. Ultracold targets allow to retrieve absolute probabilities since ionized atoms become apparent as a local vacancy imprinted into the target density, which is recorded simultaneousl…
We demonstrate an atom detector based on field ionization and subsequent ion counting. We make use of field enhancement near tips of carbon nanotubes to reach extreme electrostatic field values of up to 9x10^9 V/m, which ionize ground state rubidium atoms. The detector is based on a carpet of multiwall carbon nanotubes grown on a substrate and used for field ionization, and a channel electron multiplier used for ion counting. We measure the field enhancement at the tips of carbon nanotubes by field emission of electrons. We demonstrate the operation of the field ionization detector by counting…
The electron signals from the field ionization of two closely-spaced Rydberg states of \mbox{rubidium-85} are separated using quantum control. In selective field ionization, the state distribution of a collection of Rydberg atoms is measured by ionizing the atoms with a ramped electric field. Generally, atoms in higher energy states ionize at lower fields, so ionized electrons which are detected earlier in time can be correlated with higher energy Rydberg states. However, the resolution of this technique is limited by the Stark effect. As the electric field is increased, the electron encounter…
Increasing ellipticity usually suppresses the recollision probability drastically. In contrast, we report on a recollision channel with large return energy and a substantial probability, regardless of the ellipticity. The laser envelope plays a dominant role in the energy gained by the electron, and in the conditions under which the electron comes back to the core. We show that this recollision channel eciently triggers multiple ionization with an elliptically polarized pulse.
Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for nS, nP and nD states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show…
Photoionization of a cold atomic sample offers intriguing possibilities to observe collective effects at extremely low temperatures. Irradiation of a rubidium condensate and of cold rubidium atoms within a magneto-optical trap with laser pulses ionizing through 1-photon and 2-photon absorption processes has been performed. Losses and modifications in the density profile of the remaining trapped cold cloud or the remaining condensate sample have been examined as function of the ionizing laser parameters. Ionization cross-sections were measured for atoms in a MOT, while in magnetic traps losses …
A recent paper reported elliptically polarized high-order harmonics from aligned N$_2$ using a linearly polarized driving field [X. Zhou \emph{et al.}, Phys. Rev. Lett. \textbf{102}, 073902 (2009)]. This observation cannot be explained in the standard treatment of the Lewenstein model and has been ascribed to many-electron effects or the influence of the Coulomb force on the continuum electron. We show that non-vanishing ellipticity naturally appears within the Lewenstein model when using a multi-center stationary phase method for treating the dynamics of the continuum electron. The reason for…
We provide theoretical investigations of the response of the Ar and H atoms to an intense elliptically polarized few-cycle laser pulse, as a function of light ellipticity. The time-dependent Schr{ö}dinger equation describing the least-bound electron is solved numerically, and differential quantities such as the momentum distribution, the electron density in the continuum, and the above-threshold ionization spectra are computed. These quantities provide insight into the ionization dynamics and the electron rescattering process as a function of light ellipticity, and reveal great similarities be…
Elliptical dichroism is known in atomic photoionization as the difference in the photoelectron angular distributions produced in nonlinear ionization of atoms by left- and right-handed elliptically polarized light. We theoretically demonstrate that the maximum dichroism |Δ_{ED}|=1 always appears in two-photon ionization of any atom if the photon energy is tuned in so that the electron emission is dominantly determined by two intermediate resonances. We propose the two-photon ionization of atomic helium in order to demonstrate this remarkable phenomenon. The maximum elliptical dichroism could b…
The efficient photoionization of a Bose-Einstein condensate requires the creation of ions with the smallest possible transfer of atoms from the condensate into the thermal phase. The spontaneous decay from excited states into atomic states with momentum different from the initial one should be reduced. We investigate theoretically the two-photon ionization of a rubidium condensate using near resonant excitation to the 6P state and second photon at 421 nm or 1002 nm into the continuum. Different ionization schemes with coherent control of the first excitation and reduction of the spontaneous de…
With a classical ensemble model that including electron correlations during the whole ionization process, we investigated strong-field sequential double ionization of Ar by elliptically polarized pulses at the quantitative level. The experimentally observed intensity-dependent three-band or four-band structures in the ion momentum distributions are well reproduced with this classical model. More importantly, the experimentally measured ionization time of the second electrons [A. N. Pfeiffer et al., Nature Phys. 7, 428 (2011)], which can not be predicted by the standard independent-electron mod…
Photoelectron angular distributions following the non-resonant two-photon K-shell ionization of neutral atoms are studied theoretically. Using the independent particle approximation and relativistic second-order perturbation theory, the contributions of screening and relativistic effects to the photoelectron angular distribution are evaluated. A simple nonrelativistic expression is presented for the angle-differential cross section in dipole approximation for two-photon ionization by elliptically polarized photons, and its limitations are analyzed numerically. Moreover, we show that screening …
The total ionization rate of biharmonic ($ω+ 3ω$) ionization is studied within the independent particle approximation and the third order perturbation theory. Particular attention is paid to how the polarization of the biharmonic light field affects the total rate. The ratios of the biharmonic ionization rates for linearly and circularly polarized beams as well as for corotating and counterrotating elliptically polarized beams are analyzed, and how they depend on the beam parameters, such as photon frequency or phase between $ω$ and $3ω$ light beams. We show that the interference of the biharm…
We study ionization of atoms in strong elliptically-polarized laser fields. We focus on the physical origin of the offset angle in the photoelectron momentum distribution and its possible relation to a specific time. By developing a model which is based on strong-field approximation and considers the classical Coulomb scattering, we are able to quantitatively explain recent attoclock experiments in a wide region of laser and atomic parameters. The offset angle can be understood as arising from the scattering of the electron by the ionic potential when the electron exits the laser-Coulomb-forme…
We measure the collision rate coefficient between laser cooled Rubidium (Rb) atoms in a magneto-optical trap (MOT) and optically dark Rb+ ions in an overlapping Paul trap. In such a mixture, the ions are created from the MOT atoms and allowed to accumulate in the ion trap, which results in a significant reduction in the number of steady state MOT atoms. A theoretical rate equation model is developed to describe the evolution of the MOT atom number, due to ionization and ion-atom collision, and derive an expression for the ion-atom collision rate coefficient. The loss of MOT atoms is studied sy…
We study ionization of aligned H$_2^+$ in strong elliptically-polarized laser fields numerically and analytically. The calculated offset angle in photoelectron momentum distribution is several degrees larger for the molecule than a model atom with similar ionization potential at diverse laser parameters. Using a strong-field model that considers the properties of multi-center and single-center Coulomb potentials, we are able to quantitatively reproduce this angle difference between the molecule and the atom. Further analyses based on this model show that the response time of electron to light …
Using a three-dimensional semiclassical model, we study double ionization for strongly-driven He fully accounting for magnetic field effects. For linearly and slightly elliptically polarized laser fields, we show that recollisions and the magnetic field combined act as a gate. This gate favors more transverse - with respect to the electric field - initial momenta of the tunneling electron that are opposite to the propagation direction of the laser field. In the absence of non-dipole effects, the transverse initial momentum is symmetric with respect to zero. We find that this asymmetry in the t…
We present experimental data on the non-adiabatic strong field ionization of atomic hydrogen using elliptically polarized femtosecond laser pulses at a central wavelength of 390 nm. Our measured results are in very good agreement with a numerical solution of the time-dependent Schrödinger equation (TDSE). Experiment and TDSE show four above-threshold ionization (ATI) peaks in the electron's energy spectrum. The most probable emission angle (also known as 'attoclock-offset angle' or 'streaking angle') is found to increase with energy, a trend that is opposite to standard predictions based on Co…
We report the first measurement of the diffusion coefficients of francium and rubidium ions implanted in a yttrium foil. We developed a methodology, based on laser spectroscopy, which can be applied to radioactive and stable species, and allows us to directly take record of the diffusion time. Francium isotopes are produced via fusion-evaporation nuclear reaction of a 100 MeV 18-O beam on a Au target at the Tandem XTU accelerator facility in Legnaro, Italy. Francium is ionized at the gold-vacuum interface and Fr+ ions are then transported with a 3 keV electrostatic beamline to a cell for neutr…
A theory describing above-threshold ionization of atoms and ions in a strong electromagnetic field is presented. It is based on the widely known strong field approximation and incorporates the Coulomb interaction between the photoelectron and the nucleus using the method of complex classical trajectories. A central result of the theory is the Coulomb-corrected ionization amplitude whose evaluation requires little extra numerical effort. By comparing our predictions with the results of ab initio numerical solutions for two examples we show that the new theory provides a significant improvement …
We identify [Rb IV] 1.5973 and [Cd IV] 1.7204 micron emission lines in high-resolution (R=40,000) near-infrared spectra of the planetary nebulae (PNe) NGC 7027 and IC 5117, obtained with the IGRINS spectrometer on the 2.7-m telescope at McDonald Observatory. We also identify [Ge VI] 2.1930 $μ$m in NGC 7027. Alternate identifications for these features are ruled out based on the absence of other multiplet members and/or transitions with the same upper levels. Ge, Rb, and Cd can be enriched in PNe by s-process nucleosynthesis during the asymptotic giant branch (AGB) stage of evolution. To determ…
Elliptically polarized laser pulses (EPLPs) are widely applied in many fields of ultrafast sciences, but the ellipticity~($\varepsilon$) has never been in situ measured in the interaction zone of the laser focus. In this work, we propose and realize a robust scheme to retrieve the $\varepsilon$ by temporally overlapping two identical counter-rotating EPLPs. The combined linearly electric field is coherently controlled to ionize Xe atoms by varying the phase delay between the two EPLPs. The electron spectra of the above-threshold ionization and the ion yield are sensitively modulated by the pha…
We consider an electron in an atom driven by an infrared (IR) elliptically polarized laser field after its ionization by an ultrashort extreme ultraviolet (XUV) pulse. We find that, regardless of the atom species and the laser ellipticity, there exists XUV parameters for which the electron returns to its parent ion after ionizing, i.e., undergoes a recollision. This shows that XUV pulses trigger efficiently recollisions in atoms regardless of the ellipticity of the IR field. The XUV parameters for which the electron undergoes a recollision are obtained by studying the location of recolliding p…
We coincidently measure the molecular frame photoelectron angular distribution and the ion sum-momentum distribution of single and double ionization of CO molecules by using circularly and elliptically polarized femtosecond laser pulses, respectively. The orientation dependent ionization rates for various kinetic energy releases allow us to individually identify the ionizations of multiple orbitals, ranging from the highest occupied to the next two lower-lying molecular orbitals for various channels observed in our experiments. Not only the emission of a single electron, but also the sequentia…
The electron nondipole dynamics in tunneling ionization in an elliptically polarized laser field is investigated theoretically using a relativistic Coulomb-corrected strong-field approximation (SFA) based on the eikonal approximation of the Klein-Gordon equation. We calculate attoclock angle-resolved light-front momentum distributions at different ellipticities of the laser field in quasistatic and nonadiabatic regimes and analyze them with an improved Simpleman model. The nondipole correlations between longitudinal and transverse momentum components are examined. Deviations of the photoelectr…
We present a very efficient technique for solving the three-dimensional time-dependent Schrodinger equation. Our method is applicable to a wide range of problems where a fullly three-dimensional solution is required, i.e., to cases where no symmetries exist that reduce the dimensionally of the problem. Examples include arbitrarily oriented molecules in external fields and atoms interacting with elliptically polarized light. We demonstrate that even in such cases, the three-dimensional problem can be decomposed exactly into two two-dimensional problems at the cost of introducing a trivial rotat…
In the semiclassical picture of photoionization process in intense laser fields, the ionization rate solely depends on the amplitude of the electric field and the final photoelectron momentum corresponds to the instant of ionization of the photoelectron, however, this picture has never been checked rigorously. Recently an attosecond angular streaking technique based on this semiclassical perspective has been widely applied to temporal measurement of the atomic and molecular dynamics in intense laser fields. We use a Wigner-distribution-like function to calculate the time-emission angle distrib…
The nondirect product discrete variable representation (npDVR) is developed for the time-dependent Schrödinger equation with nonseparable angular variables and is applied to a hydrogen atom in elliptically polarized strong laser fields. The 2D npDVR is constructed on spherical harmonics orthogonalized on the 2D angular grids of the Popov and Lebedev 2D cubatures for the unit sphere. With this approach we have investigated the dynamics of a hydrogen atom initially in its ground state in elliptically polarized laser fields with the intensity up to $I=10^{14}$ W/{cm}$^2$ and wavelength of $λ=800$…
Two-photon ionization of Rubidium atoms in a magneto-optical trap and a Bose-Einstein condensate (BEC) is experimentally investigated. Using 100 ns laser pulses, we detect single ions photoionized from the condenstate with a 35(10)% efficiency. The measurements are performed using a quartz cell with external electrodes, allowing large optical access for BECs and optical lattices.
Nonlinear relativistic ionization phenomena induced by a strong laser radiation with elliptically polarization are considered. The starting point is the classical relativistic action for a free electron moving in the electromagnetic field created by a strong laser beam. The application of the relativistic action to the classical barrier-suppression ionization is briefly discussed. Further the relativistic version of the Landau-Dykhne formula is employed to consider the semiclassical sub-barrier ionization. Simple analytical expressions have been found for: (i) the rates of the strong-field non…
The intermediate domain of strong-field ionization between the tunneling and the multiphoton regimes is investigated using the strong field approximation and the imaginary-time method. An intuitive model for the dynamics is developed which describes the ionization process within a nonadiabatic tunneling picture with a coordinate dependent electron energy during the under-the-barrier motion. The nonadiabatic effects in the elliptically polarized laser field induce a transversal momentum shift of the tunneled electron wave packet at the tunnel exit, a delayed appearance in the continuum as well …
Attosecond angular streaking measurements have revealed deep insights into the timing of tunnel ionization processes of atoms in intense laser fields. So far experiments of this type have been performed only with a cold-target recoil-ion momentum spectrometer (COLTRIMS). Here, we present a way to apply attosecond angular streaking experiments to a velocity map imaging spectrometer (VMIS) with few-cycle pulses at a repetition rate of 10 kHz and a high ionization yield per pulse. Three-dimensional photoelectron momentum distributions from strong-field ionization of helium with an elliptically po…
Strong-field ionization and rescattering beyond the long-wavelength limit of the dipole approximation is studied with elliptically polarized mid-IR pulses. We have measured the full three-dimensional photoelectron momentum distributions (3D PMDs) with velocity map imaging and tomographic reconstruction. The ellipticity-dependent 3D-PMD measurements revealed an unexpected sharp, thin line-shaped ridge structure in the polarization plane for low momentum photoelectrons. With classical trajectory Monte Carlo (CTMC) simulations and analytical methods we identified the associated ionization dynamic…
We present a very sensitive and scalable method to measure the population of highly excited Rydberg states in a thermal vapor cell of rubidium atoms. We detect the Rydberg ionization current in a 5 mm electrically contacted cell. The measured current is found to be in excellent agreement with a theory for the Rydberg population based on a master equation for the three level problem including an ionization channel and the full Doppler distributions at the corresponding temperatures. The signal-to-noise ratio of the current detection is substantially better than purely optical techniques.
A single-atom 'double-slit' experiment is realized by photo-ionizing Rubidium atoms using two independent low power lasers. The photoelectron wave of well-defined energy recedes to the continuum either from the 5P or 6P states in the same atom, resulting in two-path interference imaged in the far field using a photoelectron detector. Even though the lasers are independent and not phase locked, the transitions within the atom impart the phase relationship necessary for interference. The experiment is designed so that either 5P or 6P states are excited by one laser, before ionization by the seco…
