Atomic Physics 2017

In our experiments, we generate arrays of up to 50 optical tweezers arranged in arbitrary two-dimensional geometries, each containing a single cold atom, and separated by distances of a few micrometers. This is achieved by active sorting of atoms in larger arrays that are initially loaded stochastically [1]. By exciting the atoms to Rydberg states (with principal quantum numbers in the range 50–100), we can induce strong, tunable dipolar interactions between the atoms [2]. This system is an ideal platform for the quantum simulation of spin Hamiltonians. By using van der Waals interactions we can implement the quantum Ising model in a transverse field and observe the dynamics of the magnetization and of correlation functions following a quantum quench [3]. Using resonant dipole-dipole interactions, we observed the propagation of a spin excitation in a minimalistic spin chain governed by the XY Hamiltonian [4,5]. References [1] D. Barredo et al., Science 354, 1021 (2016). [2] A. Browaeys, D. Barredo, and T. Lahaye, J. Phys. B 49, 152001 (2016). [3] H. Labuhn et al., Nature 534, 667 (2016). [4] D. Barredo et al., Phys. Rev. Lett. 114, 113002 (2015). [5] S. de Léséleuc et al., Phys. Rev. Lett. 119, 053202 (2017).

The recent observation of Rydberg excitons in Cu$_2$O allows us to study Rydberg physics in a semiconductor [1]. Similar to Rydberg atoms, these highly excited states show characteristic scaling laws in dependence on the principal quantum number $n$. In this work we present scaling laws of Rydberg excitons with and without external magnetic and electric fields. We find characteristic scaling laws with $n$ with some discrepancies between excitons and atoms, but surprisingly mostly similarities even though the underlying physics such as the complex valence band structure are quite different [2]. Furthermore, we study Rydberg excitons in the presence of an electron-hole plasma [3]. Already at ultralow plasma densities of less than one hundredth electron-hole pair within an exciton volume, the highest absorption lines start to disappear while the exciton energy does not change at these plasma densities and also their linewidths remain constant, indicating that the free carriers do not induce decoherence. The bandgap is reduced by injected free carriers, scaling with their density as $\rho_{eh}^{1/2}$. An exciton line disappears when the band edge crosses the exciton energy. This opens the possibility to control the maximally observable principal quantum number through the plasma-induced band gap modulation. To maximally reduce the bandgap shift and observe even higher $n$ we investigated the Rydberg series at ultralow laser powers and temperatures in the mK range. [1] T. Kazimierczuk et al., Nature 514, (2014), p. 343 . [2] J. Heckötter et al. Phys. Rev. B 96, 125142 (2017). [3] J. Heckötter et al. arXiv:1709.00891 [cond-mat.mtrl-sci].

When an impurity is immersed into an environment, it changes its properties due to its interactions with the surrounding medium. The impurity is dressed by many-body excitations and forms a quasiparticle, the polaron. Depending on the character of the environment and the form of interactions, different types of polarons are created. In this talk, I will review recent experimental and theoretical progress on studying the many-body physics of polarons in ultracold atomic systems [1]. In the second part of the talk I will then focus on impurities interacting with bosonic quantum gases. Specifically, I will discuss progress on the theoretical description of Rydberg excitations coupled to Bose-Einstein condensates. In such systems the interaction between the Rydberg atom and the Bose gas is mediated by the Rydberg electron. This gives rise to a new polaronic dressing mechanisms, where instead of collective excitations, molecules of gigantic size dress the Rydberg impurity. We develop a functional determinant approach [1,2] to describe the dynamics of such Rydberg systems which incorporates atomic and many-body theory. Using this approach we predict the appearance of a superpolaronic state which has recently been observed in experiments [3,4], and I will discuss its relation to Feshbach Bose polarons observed in ultracold atom experiments [5]. References [1] R. Schmidt, M. Knap, D. A. Ivanov, J.-S. You, M. Cetina, and E. Demler, arXiv:1702.08587 (2017); review article to appear in Rep. Prog. Phys. [2] R. Schmidt, H. Sadeghpour, and E. Demler, Phys. Rev. Lett. 116, 105302 (2016). [3] F. Camargo et al., arXiv:1706.03717 (2017). [4] R. Schmidt et al., arXiv:1709.01838 (2017). [5] N. Jørgensen et al., Phys. Rev. Lett. 117, 055302 (2016).

Off-resonant optical coupling of an atomic ground state to a Rydberg state, so-called "Rydberg-dressing" has been proposed as a versatile method to implement various long-range interacting spin models with ultracold atoms. Here, we present experimental results on the realization of Rydberg-dressed Ising interactions in an atomic Mott insulator of Rubidium-87 by coupling to a Rydberg p-state on a single-photon transition in the ultraviolet. While initial interferometric experiments in a two-dimensional sample demonstrated control over the dressed interactions, a collective dissipation process reduced the lifetime of the system. More recent measurements for a Rydberg-dressed 1d spin chain with long-range Ising interactions show significantly increased lifetimes. We substantiate the improved coherence by tracing purely interaction-driven collapse and revival dynamics of the magnetization in a 1d spin chain. Our single-atom-sensitive local detection with the quantum gas microscope allows for shedding light on the remaining decoherence processes as well as the microscopic mechanisms driving the dynamics.

Rydberg polaritons offer a unique way to create strong interactions for photons. We utilize these interactions to demonstrate a photon-photon quantum gate. To achieve this, a photonic control qubit is stored in a quantum memory consisting of a superposition of a ground state and a Rydberg state in an ultracold atomic gas. This qubit interacts with a photonic target qubit in the form of a propagating Rydberg polariton to generate a conditional pi phase shift, as in Ref. [1]. Finally, the control photon is retrieved. We measure two controlled-NOT truth tables and the two-photon state after an entangling-gate operation. This work is an important step toward applications in optical quantum information processing, such as deterministic photonic Bell-state detection which is crucial for quantum repeaters. [1] D. Tiarks et al., Science Advances 2, 1600036 (2016).

The goal of the project is the experimental realization of long-range coherent interactions between Rydberg atoms mediated by a superconducting coplanar microwave resonator at a finite temperature. Here, we report on the preparation of ultra-cold rubidium Rydberg atoms near a superconducting co-planar microwave cavity. We measure the lifetime of Rydberg states in the cryogenic environment, we characterize the Stark-shift of Rydberg states near the superconducting chip surface and describe our progress towards the coupling of Rydberg atoms to the cavity field.

In recent years, the combination of electromagnetically induced transparency and strongly interacting Rydberg-states has emerged as a promising avenue towards generating strong optical nonlinearities for exploring photonic many-body physics or applications to all-optical quantum information processing. In this talk, I will outline the theoretical description of emerging photonics interactions in interacting cold gases and semiconductor exciton systems. Recently developed schemes that alleviate obstacles of current Rydberg-EIT approaches will be described. New functionalities that follow from these ideas as well as related experiments will also be discussed.

Rydberg molecules, consisting of a neutral ground-state atom bound to a Rydberg electron via electron-neutral scattering, offer a unique possibility to prepare diatomic molecules with large permanent electric dipole moments. Of particular interest in this context are so called trilobite-molecules, which attain extreme dipolar character as a consequence of the scattering-induced admixture of high-L Rydberg orbits. Yet, these states are generally difficult to laser associate due to angular momentum conservation. Here, I will present experiments demonstrating that for suitable principal quantum numbers resonant coupling of the orbital motion of the Rydberg electron with the nuclear spin of the ground-state atom, mediated by electron-neutral scattering, hybridizes the trilobite molecular potential with the more conventional S-type molecular state. This provides a general path to associate trilobite molecules with large electric dipole moments. Spectroscopic data including the determination of the dipole moment is presented and compared to calculated potential energy curves.

Rydberg Atoms in highly excited electronic states with n=30-100 are recent additions to the versatile toolkit of ultracold atomic physics. When resonant dipole dipole interactions involving two atomic states are at play, these furnish interesting model system for e.g. energy transport (static Rydberg atom assemblies) or multi-Born-Oppenheimer surface motion (moving atoms). We will discuss the interplay of this kind of dynamics with the host cold gas, in which Rydberg excitations are typically embedded. We show how the cold gas can allow continuous observation of the atomic motion or excitation transport, in turn leading to controllable decoherence. Thus the system of Rydberg aggregates embedded in cold gases furnishes a versatile quantum simulation platform for open quantum systems. [1] S. Wüster and J.M. Rost arxiv:1707.04099 (2017). [2] D. Schönleber et al. PRL 114 123005 (2015). [3] H. Schempp et al. PRL 115, 093002 (2015). [4] S. Wüster, PRL 119 013001 (2017).

The large electric dipole transition moments associated with highly excited Rydberg states of atoms and molecules make them ideal model systems with which to study resonant energy transfer processes. These Förster resonances are widely exploited in experiments with gases of ultracold Rydberg atoms [1]; and in the past the discrete transfer of rotational energy to [2], changes in the fluorescence lifetimes of [3], and the ionisation of [4] Rydberg atoms as a result of resonant energy transfer in collisions with polar ground state molecules has been investigated in the absence of externally applied fields. In this talk I will describe new experiments in which the resonant transfer of energy from the inversion sublevels in the ground electronic state of ammonia, to triplet Rydberg states in helium with principal quantum numbers between 36 and 41, has been studied [5]. In zero electric field, the transition between the 40s and 40p Rydberg states is close to resonant with the inversion transitions in the ground state of ammonia. For Rydberg states with principal quantum numbers between 36 and 39 the ns-to-np transitions can be tuned through resonance with the inversion transitions using electric fields < 10 V/cm. In this work we have studied the electric-field dependence of the energy transfer process using Rydberg-state-selective detection schemes involving direct state-selective electric field ionisation, and microwave spectroscopy. The experimental data are in good agreement with a simple theoretical model of the energy transfer process based on the impact approximation. Through microwave spectroscopy of atoms that have undergone energy transfer we have also probed the environment in which the atom-molecule interactions take place, and characterised contributions from ions produced in the collisions. These results open possibilities for studies of atom-molecule collisions at low temperature in merged beams [6] where long-range dipole-dipole interactions may be exploited to regulate access to short-range chemical processes, e.g., Penning ionisation. They also represent a step toward the implementation of proposals to use resonant dipole interactions between Rydberg atoms and cold polar molecules for non-destructive detection [7], characterisation of rotational state populations [8], coherent control [9], and molecular cooling [10,11]. [1] P Pillet and T F Gallagher, J. Phys. B 49, 174003 (2016). [2] K. A. Smith, F. G. Kellert, R. D. Rundel, F. B. Dunning, and R. F. Stebbings, Phys. Rev. Lett. 40, 1362 (1978). [3] L. Petitjean, F. Gounand, and P. R. Fournier, Phys. Rev. A 31, 71 (1984); Phys. Rev. A 33, 143 (1986). [4] X. Ling, M. T. Frey, K. A. Smith, and F. B. Dunning, J. Chem. Phys. 98, 2486 (1993). [5] V. Zhelyazkova and S. D. Hogan, Phys. Rev. A 95, 042710 (2017). [6] P. Allmendinger, J. Deiglmayr, O. Schullian, K. Höveler, J. A. Agner, H. Schmutz, and F. Merkt, Phys. Chem. Chem. Phys. 17, 3596 (2016). [7] M. Zeppenfeld, EPL 118, 13002 (2017). [8] E. Kuznetsova, S. T. Rittenhouse, H. R. Sadeghpour, and S. F. Yelin, Phys. Rev. A 94, 032325 (2016). [9] E. Kuznetsova, S. T. Rittenhouse, H. R. Sadeghpour, and S. F. Yelin, Phys. Chem. Chem. Phys., 13, 17115 (2011). [10] S. D. Huber and H. P. Büchler, Phys. Rev. Lett. 108, 193006 (2012). [11] B. Zhao, A. W. Glaetzle, G. Pupillo, and P. Zoller, Phys. Rev. Lett. 108, 193007 (2012).

About a decade ago, the so-called {\it lochfra{\ss}} effect was predicted that creates a vibrational wavepacket in the non-ionized neutral molecule upon strong-field ionization. It was shortly thereafter experimentally observed in molecular deuterium. However, as was pointed out in those works, the vibrational wavepacket could, in principle, also be generated by bond softening (the dressed-state description of stimulated Raman scattering). Using the surprising stability of the formed wavepacket it was possible to distinguish the two processes and to confirm {\it lochfra{\ss} to be (predominantly) responsible for the experimental parameters. We have now revisited the processes in order to investigate the astonishing robustness of the two effects and why it was possible to distinguish the two processes by the absolute phase of the wavepacket, despite the fact that the experiment used laser pulses with no control over the carrier-envelope phase. The result reveals that a much more general control mechanism is responsible that is expected to be an extremely robust and thus useful alternative for the standard generation of coherent wavepackets using light fields.

We argue that the quenched ultracold plasma formed in a supersonic molecular beam presents an experimental platform for studying quantum many-body physics of disordered systems in the long-time and finite energy-density limits. An experiment that quenches a plasma of nitric oxide to an ultracold system of Rydberg molecules, forms a gas of ions and electrons that exhibits a state of arrested relaxation. The qualitative features of this state fail to conform with classical models. Here, we develop a microscopic quantum description for the arrested phase based on an effective many-body spin Hamiltonian that includes both dipole-dipole and van der Waals interactions. This effective model offers a way to envision the quantum disordered non-equilibrium physics of this system. J. Sous,1,2, M. Schulz-Weiling,1 H. Sadeghi,3 M. Aghigh,3 L. Melo,3 R. Haenel,1 J. S. Keller,3 and E. R. Grant1,3 1Department of Physics & Astronomy, University of British Columbia, Vancouver, BC V6T 1Z3, Canada 2Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada 3Department of Chemistry, University of British Columbia, Vancouver, BC V6T 1Z3, Canada

The Rydberg constant is of interest due to its relation to other fundamental constants and its central role in calculations of atomic energy levels. Its current relative uncertainty stands at 5.9x10$^{-12}$ [1]. However, a large discrepancy involving the proton radius and the Rydberg constant has emerged in recent experiments on muonic hydrogen and deuterium (“proton radius puzzle” [2]). One concern expressed by a leading author of [2] is that “physicists have misgauged the Rydberg constant” [3]. A validation of the Rydberg constant using an independent method is therefore of great urgency and high value. The work reported here aims at measuring the Rydberg constant and other atomic constants, such as polarizabilities, using long-lived circular Rydberg atoms, which are insensitive to critical systematics that limit the accuracy in spectroscopy of low-lying atomic states (nuclear penetration and QED shifts). The large Rydberg-atom size enables a new method of atom trapping and spectroscopy that exploits the “A-square term” of the atom-field interaction. The method requires a light field that is spatially modulated within the atomic volume, and that is amplitude-modulated in time, at a frequency near that of the probed Rydberg transition. Rydberg atoms in electro-optically modulated standing-wave light fields (amplitude-modulated optical lattices) are ideal for this. The experimental approach to measure the Rydberg constant, as well as possible implementations in a microgravity experiment, will be discussed. A comprehensive study of the systematics expected in this measurement will be presented. A new high-precision measurement of the rubidium g-level quantum defects is reported. Results are compared with another recent measurement [4]. [1] http://physics.nist.gov/cuu/Constants/ [2] For recent work, see http://science.sciencemag.org/content/353/6300/669 [3] https://www.quantamagazine.org/20160811 [4] J. Lee, J. Nunkaew, and T. Gallagher, Physical Review A 94, 022505 (2016)].

We propose and study theoretically a new technique to fully characterize the temporal structure of attosecond pulses by photoionization of a bound coherent low-energy Rydberg wavepacket [1]. The non-degenerate energy levels of the initial wavepacket make it possible to interfere different spectral components of pulses by photoelectron interferometry, thus, revealing the attosecond temporal structure directly by quantum beating. Associated inner-shell processes have also been estimated [2]. Finally, the bound wavepacket technique has been tested in an Attosecond Transient Absorption (ATAS) setting, where energy-resolved absorption of the attosecond pulse is measured (instead of photoelectrons) [3]. Surprisingly, we find that the ATAS setting does not allow for lag-free measurements. Simulations performed using the Time-Dependent Configurations-Interactions Singles (TDCIS) and Many-Body Perturbation Theory (MBPT) show that lag-free measurements is a possibility if photoelectrons are detected as a function of energy and free-propagation time of the wavepacket. References: [1] Stefan Pabst and J M Dahlström Eliminating the dipole phase in attosecond pulse characterization using Rydberg wave packets Physical Review A 94 013411 (2016) [2] Stefan Pabst and Jan Marcus Dahlström Characterizing attosecond pulses in the soft x-ray regime Journal of Physics B: Atomic, Molecular and Optical Physics 50 104002 (2017) [3] Jan Marcus Dahlström, Stefan Pabst and Eva Lindroth Attosecond transient absorption of a bound wave packet coupled to a smooth continuum arXiv:1706.10048 [physics.optics] (Accepted for Journal of Optics in 2017)

We demonstrate the control of electron-electron correlation in frustrated double ionization (FDI) of the two-electron triatomic molecule D$_{3}^{+}$ when driven by two orthogonally polarized two-color laser fields. We employ a three-dimensional semi-classical model that fully accounts for the electron and nuclear motion in strong fields. We analyze the FDI probability and the distribution of the momentum of the escaping electron along the polarization direction of the longer wavelength and more intense laser field. These observables when considered in conjunction bear clear signatures of the prevalence or absence of electron-electron correlation in FDI, depending on the time-delay between the two laser pulses. We find that D$_{3}^{+}$ is a better candidate compared to H$_{2}$ for demonstrating also experimentally that electron-electron correlation indeed underlies FDI. A. Chen, M. Kling and A. Emmanouilidou Phys. Rev. A 96, 033404 (2017). A. Chen, H. Price, A.Staudte and A. Emmanouilidou Phys. Rev. A 94, 043408 (2016).

The interaction of high intensity, short-wavelength, short-pulse radiation with matter is a fundamental problem of current research1. Its understanding is essential for virtually all experiments with new super intense X-ray sources, in particular for flash imaging of nm sized particles. Clusters as finite systems with the density of bulk solids are ideal samples to study fundamental light–matter interaction processes in all wavelength regimes2-5. Recently, initial experiments with short wave length pulses have shown that single nm-sized gas phase particles and clusters can be imaged by single shot scattering6-10. Especially with free electron lasers new avenues are opened to investigate transition states11 and ultrafast processes12, 13 with unprecedented spatial and temporal resolution. While short wavelength radiation from hard x-ray sources is essential for the high spatial resolution, soft x-rays can provide 3D-information since the light also efficiently scattered to rather large angles10. This offers new routes for structure determination in cluster and nanometer-scale science. References 1 A. A. Sorokin, S. V. Bobashev, T. Feigl, K. Tiedtke, H. Wabnitz, and M. Richter, Physical Review Letters 99 (2007). 2 T. Ditmire, T. Donnelly, A. M. Rubenchik, R. W. Falcone, and M. D. Perry, Phys. Rev. A 53, 3379 (1996). 3 C. Bostedt, et al., Physical Review Letters 100, 133401 (2008). 4 U. Saalmann, C. Siedschlag, and J. M. Rost, J. Phys. B 39, R39 (2006). 5 T. Fennel, K. H. Meiwes-Broer, J. Tiggesbaumker, P. G. Reinhard, P. M. Dinh, and E. Suraud, Reviews of Modern Physics 82, 1793 (2010). 6 C. Bostedt, M. Adolph, E. Eremina, M. Hoener, D. Rupp, S. Schorb, H. Thomas, A. R. B. de Castro, and T. Moller, Journal of Physics B-Atomic Molecular and Optical Physics 43, 194011 (2010). 7 C. Bostedt, et al., Physical Review Letters 108, 093401 (2012). 8 D. Rupp, et al., New Journal of Physics 14 (2012). 9 L. F. Gomez, et al., Science 345, 906 (2014). 10 I. Barke, et al., Nature communications 6, 4648 (2015). 11 D. Rupp, et al., Physical review letters 117 (2016). 12 T. Gorkhover, et al., Physical Review Letters 108 (2012). 13 T. Gorkhover, et al., Nature Photonics 10, 93 (2016).

Machine learning has begun to impact different sciences, ranging from engineering to biology and medicine. Recent breakthroughs repeatedly made headlines, yielding systems to play the ancient game of Go at superhuman performance, translating speech to text, or recognizing objects in photos. Physicists are now starting out to use techniques from machine learning in order to advance their own research. In this talk, I will provide a gentle introduction to concepts in machine learning and to essential vocabulary used by researchers of this discipline. Current topics (e.g., Deep Learning) will be included in the discussion and why they can become important for basic research.

Understanding the structural and dynamical properties of water at solid-liquid interfaces and in ionic solutions is essential for unravelling the atomistic details of key steps in electrochemistry, heterogeneous catalysis and corrosion. In recent years, in particular ab initio molecular dynamics simulations (MD) based on density-functional theory (DFT) have contributed significantly to the understanding of these processes. Still, due to their high computational costs, ab initio MD simulations are restricted to comparably small systems and short simulation times. This limitation can be overcome by employing machine-learning-based high-dimensional neural network potentials (NNPs), which are constructed from a set of electronic structure data and enable carrying out large-scale simulations with close to first-principles accuracy for a variety of systems. In this talk the methodology of high-dimensional NNPs is discussed, and results from NNP-MD simulations for liquid water, ions in water, and water interacting with metal and oxide surfaces are presented.

Many of the most relevant chemical properties of matter depend explicitly on atomistic and electronic details, rendering a first principles approach to chemistry mandatory. Alas, even when using high-performance computers, brute force high-throughput screening of compounds is beyond any capacity for all but the simplest systems and properties due to the combinatorial nature of chemical space, i.e. all compositional, constitutional, and conformational isomers. Consequently, efficient exploration algorithms need to exploit all implicit redundancies present in chemical space. I will discuss recently developed statistical learning approaches for interpolating quantum mechanical observables in compositional and constitutional space. Results for our models indicate remarkable performance in terms of accuracy, speed, universality, and size scalability.

I will discuss how quantum theory of molecular dynamics can benefit from machine learning. In particular, I will argue that combining machine learning with quantum dynamics calculations allows one to ask questions previously considered unfeasible and may help solve problems generally considered unfeasible. I will show results illustrating a few examples of such questions, including: What is the least number of ab initio points sufficient to describe quantum dynamics of polyatomic systems accurately? Given an approximate potential energy surface, where in the configuration space should a single ab initio point be added to improve quantum dynamics the most? Given a specific modification of the quantum dynamics observables, what is the corresponding change of the potential energy surface? I will show that accurate quantum dynamics results for a three-dimensional chemical reaction can be obtained with a potential energy surface produced with only 30 ab initio points by a machine-learning algorithm combining Bayesian optimization and Gaussian Process regression. I will also illustrate that machine learning methods can be developed to extrapolate quantum properties of quasi-particles, such as the dispersion of polarons, even in models with sharp transitions, which thus opens the prospect for machine learning algorithms to identify quantum phase transitions.

Accurate simulations of molecules and materials from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce overall costs significantly by rapidly and accurately interpolating between reference calculations. Effectively, the problem of solving a complex equation such as the electronic Schrödinger equation for many related inputs is mapped onto a nonlinear statistical regression problem. I will present a brief overview of this line of research and results for our latest contribution, the many-body tensor representation [Huo & Rupp, arXiv 1704.06439, 2017].

Atoms in strong laser fields are ionized when the electron tunnels trough the barrier formed by the superposition of the nucleus’ and the laser’s potentials. The dynamics of the ionized electron wave-packets are one of the most important aspects of attosecond science. A simple yet powerful technique to study this process with attosecond resolution utilizes intense elliptically polarized near-infrared pulses. Probing the deflection of the photoelectron wave-packet in the field yields information on the timing of the tunneling ionization and sheds light on questions regarding nonadiabaticity and time delays in tunnel ionization, which has been a subject of a long controversy. In order to study the tunnel ionization process on fundamental targets, we performed experiments on the single-electron system He+ by combining an ion beam target with elliptically polarized laser fields. The results are discussed by comparison with a full solution of the time-dependent Schrödinger equation (TDSE) and semiclassical models in order to identify the contributions of the various underlying effects. Further, the investigation is extended by examining the target- and charge-state-dependence as well as double ionization. P. Wustelt1, 2, H.Ni3, M. Möller1, 2, A. M. Sayler1, 2, J.M.Rost3 and G.G. Paulus1, 2 1: Institute of Optics and Quantum Electronics, FSU Jena 2: Helmholtz Institute Jena 3: Max Planck Institute for the Physics of Complex Systems, Dresden

New approach [1,2] to study the spontaneous emission of the atomic system in the presence of the high-intensity laser field is applied to study the process of harmonic generation. The analysis is based on the consideration of quantum system interaction with quantized field modes being in vacuum state, while the intense laser field is considered classically beyond the perturbation theory. The analysis of the emission from the single atom irradiated by the high-intensity femtosecond laser pulse of Ti-Sa laser and its second harmonic is presented. It is demonstrated that not only odd but also even harmonics can be emitted if the laser field is strong enough. The origin of even harmonics is studied. The obtained results are compared with those found in the frames of semiclassical approach widely used to study the harmonic generation. It is found that semiclassical approach is inapplicable in the strong-field limit. References [1] A.V. Bogatskaya, E.A. Volkova and A.M. Popov EPL 116, 14003 (2016). [2] A.V. Bogatskaya, E.A. Volkova and A.M. Popov Laser Phys. Lett. 14, 055301 (2017).