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Publications

Peer Reviewed Publications

  1. Gavin McCauley, Benjamin Cruikshank, Denys I. Bondar, and Kurt Jacobs “Completely Positive, Accurate Master Equation for Weakly-Damped Quantum Systems Across All Regimes” Accepted to npj Quantum Information [arXiv:1906.08279]

  2. Gerard McCaul and Denys I. Bondar “Classical Influence Functionals: Rigorously Deducing Stochasticity From Deterministic Dynamics” Accepted to European Physical Journal Special Topics [arXiv:1904.04918]

  3. Christian Arenz, Denys I. Bondar, Daniel Burgarth, Cecilia Cormick, and Herschel Rabitz “Amplification of quadratic Hamiltonians” Quantum 4, 271 (2020) [arXiv:1806.00444]

    Abstract: Speeding up the dynamics of a quantum system is of paramount importance for quantum technologies. However, in finite dimensions and without full knowledge of the details of the system, it is easily shown to be impossible. In contrast we show that continuous variable systems described by a certain class of quadratic Hamiltonians can be sped up without such detailed knowledge. We call the resultant procedure Hamiltonian amplification (HA). The HA method relies on the application of local squeezing operations allowing for amplifying even unknown or noisy couplings and frequencies by acting on individual modes. Furthermore, we show how to combine HA with dynamical decoupling to achieve amplified Hamiltonians that are free from environmental noise. Finally, we illustrate a significant reduction in gate times of cavity resonator qubits as one potential use of HA.

  4. Yi-Siang Wang, Parmeet Nijjar, Xin Zhou, Denys I. Bondar, and Oleg V. Prezhdo “Combining Lindblad Master Equation and Surface Hopping to Evolve Distributions of Quantum Particles” Journal of Physical Chemistry B 124, 4326 (2020)

    Abstract: Motivated by the need to study nonequilibrium evolutions of many-electron systems at the atomistic ab initio level, as they occur in modern devices and applications, we developed a quantum dynamics approach bridging master equations and surface hopping (SH). The Lindblad master equation (LME) allows us to propagate efficiently ensembles of particles, while SH provides nonperturbative evaluation of transition rates that evolve in time and depend explicitly on nuclear geometry. We implemented the LME-SH technique within real-time time-dependent density functional theory using global flux SH, and we demonstrated its efficiency and utility by modeling metallic films, in which charge-phonon dynamics was studied experimentally and showed an unexpectedly strong dependence on adhesion layers. The LME-SH approach provides a general framework for modeling efficiently quantum dynamics in a broad range of complex many-electron condensed-matter and nanoscale systems.

  5. Gerard McCaul, Christopher Orthodoxou, Kurt Jacobs, George H. Booth, and Denys I. Bondar “Controlling Arbitrary Observables in Correlated Many-body Systems” Physical Review A 101, 053408 (2020) (Editors’ Suggestion) [arXiv:1912.06173]

    Featured in Making Materials Mimic Each Other

    Quantum control using laser light could turn insulators into conductors and vice-versa

    Research shows how to make lead act like gold, enabling optical computing

    The Midas touch

    Abstract: Here we present an expanded analysis of a model for the manipulation and control of observables in a strongly correlated, many-body system, which was first presented by McCaul et al. [G. McCaul et al., Phys. Rev. Lett. 124, 183201 (2020)]. A field-free, nonlinear equation of motion for controlling the expectation value of an essentially arbitrary observable is derived, together with rigorous constraints that determine the limits of controllability. We show that these constraints arise from the physically reasonable assumptions that the system will undergo unitary time evolution, and has enough degrees of freedom for the electrons to be mobile. Furthermore, we give examples of multiple solutions to generating target observable trajectories when the constraints are violated. Ehrenfest theorems are used to further refine the model and provide a check on the validity of numerical simulations. Finally, the experimental feasibility of implementing the control fields generated by this model is discussed.

  6. Gerard McCaul, Christopher Orthodoxou, Kurt Jacobs, George H. Booth, and Denys I. Bondar “Driven Imposters: Controlling Expectations in Many-Body Systems” Physical Review Letters 124, 183201 (2020) (Editors’ Suggestion) [arXiv:1911.05006]

    Featured in Making Materials Mimic Each Other

    Quantum control using laser light could turn insulators into conductors and vice-versa

    Research shows how to make lead act like gold, enabling optical computing

    Masters of disguise

    The Midas touch

    Abstract: We present a framework for controlling the observables of a general correlated electron system driven by an incident laser field. The approach provides a prescription for the driving required to generate an arbitrary predetermined evolution for the expectation value of a chosen observable, together with a constraint on the maximum size of this expectation. To demonstrate this, we determine the laser fields required to exactly control the current in a Fermi-Hubbard system under a range of model parameters, fully controlling the nonlinear high-harmonic generation and optically observed electron dynamics in the system. This is achieved for both the uncorrelated metalliclike state and deep in the strongly correlated Mott insulating regime, flipping the optical responses of the two systems so as to mimic the other, creating “driven imposters.” We also present a general framework for the control of other dynamical variables, opening a new route for the design of driven materials with customized properties.

  7. Denys I. Bondar and Alexander N. Pechen “Uncomputability and complexity of quantum control” Scientific Reports 10, 1195 (2020) [arXiv:1907.10082]

    Abstract: In laboratory and numerical experiments, physical quantities are known with a finite precision and described by rational numbers. Based on this, we deduce that quantum control problems both for open and closed systems are in general not algorithmically solvable, i.e., there is no algorithm that can decide whether dynamics of an arbitrary quantum system can be manipulated by accessible external interactions (coherent or dissipative) such that a chosen target reaches a desired value. This conclusion holds even for the relaxed requirement of the target only approximately attaining the desired value. These findings do not preclude an algorithmic solvability for a particular class of quantum control problems. Moreover, any quantum control problem can be made algorithmically solvable if the set of accessible interactions (i.e., controls) is rich enough. To arrive at these results, we develop a technique based on establishing the equivalence between quantum control problems and Diophantine equations, which are polynomial equations with integer coefficients and integer unknowns. In addition to proving uncomputability, this technique allows to construct quantum control problems belonging to different complexity classes. In particular, an example of the control problem involving a two-mode coherent field is shown to be NP-hard, contradicting a widely held believe that two-body problems are easy.

  8. Denys I. Bondar, Francois Gay-Balmaz, and Cesare Tronci “Koopman wavefunctions and classical-quantum correlation dynamics” Proceedings of the Royal Society A 475, 2229 (2019) [arXiv:1802.04787]

    Abstract: Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman–von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical–quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect—the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. For example, the density matrix of the quantum subsystem is always positive definite. While the Liouville density of the classical subsystem is generally allowed to be unsigned, its sign is shown to be preserved in time for a specific infinite family of hybrid classical–quantum systems. The proposed description is illustrated and compared with previous theories using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.

  9. Gerard McCaul, Alexander Pechen, and Denys I. Bondar “Entropy nonconservation and boundary conditions for Hamiltonian dynamical systems” Physical Review E 99, 062121 (2019) [arXiv:1904.03473]

    Abstract: Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new dynamical phase associated with such a construction is identified. By choosing distributions not belonging to this class, we produce explicit examples of both free particles and harmonic systems evolving in a bounded phase-space in such a way that entropy is nonconserved. While these nonconserving states are classically forbidden, they may be interpreted as states of a quantum system tunneling through a potential barrier boundary. In this case, the allowed boundary conditions are the only distinction between classical and quantum systems. We show that the boundary conditions for a tunneling quantum system become the criteria for entropy preservation in the classical limit. These findings highlight how boundary effects drastically change the nature of a system.

  10. Renan Cabrera, Andre Campos, Herschel A. Rabitz, and Denys I. Bondar “Operational dynamical modeling of spin 1/2 relativistic particles: The Dirac equation and its classical limit” European Physical Journal Special Topics, doi:10.1140/epjst/e2018-800075-7 (2019) [arXiv:1805.08243]; invited article for collection: Non-equilibrium Dynamics: Quantum Systems and Foundations of Quantum Mechanics.

    Abstract: The formalism of Operational Dynamical Modeling [Bondar et al., Phys. Rev. Lett. 109, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic Ehrenfest theorems by assuming that the coordinates and momenta do not commute. Forbidding creation of antiparticles and requiring the commutativity of the coordinates and momenta lead to classical Spohn’s equation [Spohn, Ann. Phys. 282, 420 (2000)]. Moreover, Spohn’s equation turns out to be the classical Koopman-von Neumann theory underlying the Dirac equation.

  11. Dmitry V. Zhdanov, Denys I. Bondar, and Tamar Seideman “Friction as a consistent quantum-mechanical concept” Physical Review A 98, 042133 (2018) [arXiv:1810.00614]

    Abstract: A quantum analog of friction (understood as a completely positive, Markovian, translation-invariant, phenomenological model of dissipation) is known to be at odds with detailed balance in the thermodynamic limit. We show that this is not the case for quantum systems with internal (e.g., spin) states nonadiabatically coupled to translational dynamics. For such systems, a quantum master equation is derived which phenomenologically accounts for the frictional effect of a uniform zero-temperature environment. A simple analytical example is provided. Conjectures regarding the finite-temperature case are also formulated. The results are important for efficient simulations of complex molecular dynamics and quantum reservoir engineering applications.

  12. Shanon L. Vuglar, Dmitry V. Zhdanov, Renan Cabrera, Tamar Seideman, Christopher Jarzynski, and Denys I. Bondar “Nonconservative forces via quantum reservoir engineering” Physical Review Letters 120, 230404 (2018) [arXiv:1611.02736]

    Abstract: A systematic approach is given for engineering dissipative environments that steer quantum wave packets along desired trajectories. The methodology is demonstrated with several illustrative examples: environment-assisted tunneling, trapping, effective mass assignment, and pseudorelativistic behavior. Nonconservative stochastic forces do not inevitably lead to decoherence—we show that purity can be well preserved. These findings highlight the flexibility offered by nonequilibrium open quantum dynamics.

  13. Andre G. Campos, Renan Cabrera, Herschel A. Rabitz, Denys I. Bondar “Analytic solutions to coherent control of the Dirac equation” Physical Review Letters 119, 173203 (2017) [arXiv:1705.02001] *ERRATUM*

    Abstract: A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell’s equations, which yield a desired evolution. In particular, we show how to achieve dispersionless rotation and translation of wave packets. Additionally, this formalism can handle control interactions beyond electromagnetic. This work reveals unexpected flexibility of the Dirac equation for control applications, which may open new prospects for quantum technologies.

  14. Dmitry V. Zhdanov, Denys I. Bondar, Tamar Seideman “No thermalization without correlations” Physical Review Letters 119, 170402 (2017) [arXiv:1706.00341]

    Abstract: The proof of the long-standing conjecture is presented that Markovian quantum master equations are at odds with quantum thermodynamics under conventional assumptions of fluctuation-dissipation theorems (implying a translation invariant dissipation). Specifically, except for identified systems, persistent system-bath correlations of at least one kind, spatial or temporal, are obligatory for thermalization. A systematic procedure is proposed to construct translation invariant bath models producing steady states that well approximate thermal states. A quantum optical scheme for the laboratory assessment of the developed procedure is outlined.

  15. Andre G. Campos, Denys I. Bondar, Renan Cabrera, Herschel Rabitz “How to make distinct dynamical systems appear spectrally identical” Physical Review Letters 118, 083201 (2017) (Editors’ Suggestion) [arXiv:1611.02699]

    Featured in Focus story: Atomic Impersonator

    The Royal Society of Chemistry: Ultrafast lasers promise to make lead ‘look like’ gold


    How atoms can impersonate each other

    Masters of disguise

    Received a public coverage in science section of Die Zeit, a major German newspaper; ; Department of Chemistry web page; and other outlets.

    Abstract: We show that a laser pulse can always be found that induces a desired optical response from an arbitrary dynamical system. As illustrations, driving fields are computed to induce the same optical response from a variety of distinct systems (open and closed, quantum and classical). As a result, the observed induced dipolar spectra without detailed information on the driving field are not sufficient to characterize atomic and molecular systems. The formulation may also be applied to design materials with specified optical characteristics. These findings reveal unexplored flexibilities of nonlinear optics.

  16. Renan Cabrera, Andre G. Campos, Denys I. Bondar, and Herschel A. Rabitz “Dirac open quantum system dynamics: formulations and simulations” Physical Review A 94, 052111 (2016) [arXiv:1409.1247]

    Abstract: We present an open-system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic dynamics within the von Neumann density matrix and Wigner phase-space descriptions. Employing these instruments, we gain important insights into the effect of quantum dephasing for relativistic systems in many branches of physics. In particular, the conditions for robustness of Majorana spinors against dephasing are established. Using the Klein paradox and tunneling as examples, we show that quantum dephasing does not suppress negative energy particle generation. Hence, the Klein dynamics is also robust to dephasing.

  17. Denys I. Bondar, Andre G. Campos, Renan Cabrera, Herschel A. Rabitz “Efficient computations of quantum canonical Gibbs state in phase space” Physical Review E 93, 063304 (2016) [arXiv:1602.07288]

    Abstract: The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation.

  18. Alexei Goun, Denys I. Bondar, Ali O. Er, Zachary Quine, and Herschel A. Rabitz “Photonic reagents for concentration measurement of fluorescent proteins with overlapping spectra” Scientific Reports 6, 25827 (2016)

    Abstract: By exploiting photonic reagents (i.e., coherent control by shaped laser pulses), we employ Optimal Dynamic Discrimination (ODD) as a novel means for quantitatively characterizing mixtures of fluorescent proteins with a large spectral overlap. To illustrate ODD, we simultaneously measured concentrations of in vitro mixtures of Enhanced Blue Fluorescent Protein (EBFP) and Enhanced Cyan Fluorescent Protein (ECFP). Building on this foundational study, the ultimate goal is to exploit the capabilities of ODD for parallel monitoring of genetic and protein circuits by suppressing the spectral cross-talk among multiple fluorescent reporters.

  19. Denys I. Bondar, Renan Cabrera, Andre Campos, Shaul Mukamel, and Herschel A. Rabitz “Wigner–Lindblad equations for quantum friction” The Journal of Physical Chemistry Letters 7, 1632 (2016) [arXiv:1412.1892] *CORRECTION*

    Public coverage Theorists smooth the way to solving one of quantum mechanics oldest problems.

    Abstract: Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.

  20. Renan Cabrera, Denys I. Bondar, Kurt Jacobs, and Herschel A. Rabitz “Efficient method to generate time evolution of the Wigner function for open quantum systems” Physical Review A 92, 042122 (2015) [arXiv:1212.3406]

    Abstract: The Wigner function is a useful tool for exploring the transition between quantum and classical dynamics, as well as the behavior of quantum chaotic systems. Evolving the Wigner function for open systems has proved challenging, however; a variety of methods have been devised but suffer from being cumbersome and resource intensive. Here we present an efficient fast-Fourier method for evolving the Wigner function that has a complexity of O(NlogN) where N is the size of the array storing the Wigner function. The efficiency, stability, and simplicity of this method allows us to simulate open-system dynamics previously thought to be prohibitively expensive. As a demonstration we simulate the dynamics of both one-particle and two-particle systems under various environmental interactions. For a single particle we also compare the resulting evolution with that of the classical Fokker–Planck and Koopman–von Neumann equations and show that the environmental interactions induce the quantum-to-classical transition as expected. In the case of two interacting particles we show that an environment interacting with one of the particles leads to the loss of coherence of the other.

  21. Andre G. Campos, Renan Cabrera, Denys I. Bondar, and Herschel A. Rabitz “Violation of Hudson’s theorem in relativistic quantum mechanics” Physical Review A 90, 034102 (2014) [arXiv:1402.1768]

    Abstract: In nonrelativistic quantum mechanics, Hudson’s theorem states that a Gaussian wave function is the only pure state corresponding to a positive Wigner function (WF). We explicitly construct non-Gaussian Dirac spinors with positive relativistic WFs. These pure relativistic states are coherent superpositions of particles and antiparticles, while the existence of positive WFs exclusive composed of particles is conjectured. These observations may open new directions in relativistic quantum information theory.

  22. Denys I. Bondar, Renan Cabrera, Dmitry V. Zhdanov, and Herschel A. Rabitz “Wigner phase space distribution as a wave function” Physical Review A 88, 052108 (2013) [arXiv:1202.3628]

    Abstract: We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman–von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function’s negativity.

  23. I. I. Bondar, V. V. Suran, and D. I. Bondar “Multiphoton-double-ionization probability linearly depends on laser intensity: Experimental studies of barium” Physical Review A 88, 023407 (2013) [arXiv:1306.1550]

    Abstract: Despite inherently complex multiphoton dynamics, our observations show that Ba double ionization with an infrared laser (8800-8920 cm-1) resembles a single-photon process; namely, its probability is proportional to the laser intensity. In this regime, single-electron ionization is due to a four-photon resonant transition through the highly perturbed state 6p2 1D2, whereas double ionization is realized by the two-electron mechanism. Furthermore, we argue that these conclusions are valid for other alkaline-earth-metal atoms and other parameters of laser radiation.

  24. Denys I. Bondar, Renan Cabrera, and Herschel A. Rabitz “Conceptual Inconsistencies in Finite-dimensional Quantum and Classical Dynamics”
    Physical Review A 88, 012116 (2013) [arXiv:1112.3679]

    Abstract: Utilizing operational dynamic modeling [D. I. Bondar et al., Phys. Rev. Lett. 109, 190403 (2012)], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities are also revealed, including the nonexistence of the free particle and ambiguity in defining potential forces. Non-Hermitian mechanics is shown to have the same problems. This work compromises a popular belief that finite-dimensional mechanics is a straightforward discretization of the corresponding infinite-dimensional formulation.

  25. Roberto Rey-de-Castro, Renan Cabrera, Denys I. Bondar, and Herschel Rabitz “Time-resolved quantum process tomography using Hamiltonian-encoding and observable-decoding” New Journal of Physics 15, 025032 (2013); invited article for Focus on Quantum Tomography.

    Abstract: The Hamiltonian encoding observable decoding (HE-OD) technique is experimentally demonstrated for process tomography of laser-induced dynamics in atomic Rb vapor. With the assistance of a laser pulse truncation method, a time dependent reconstruction of the quantum evolution is achieved. HE-OD can perform full as well as partial process tomography with appropriate measurements to characterize the system. The latter feature makes HE-OD tomography suitable for analyzing quantum processes in complex systems.

  26. Denys I. Bondar, Renan Cabrera, Robert R. Lompay, Misha Yu. Ivanov, and Herschel A. Rabitz “Operational Dynamic Modeling Transcending Quantum and Classical Mechanics” Physical Review Letters 109, 190403 (2012) [arXiv:1105.4014]

    This work was popularized by , and after the story featured on the Princeton University’s main web page it was reprinted by numerous science news web services including .

    Abstract: We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

  27. Denys I. Bondar and Wing-Ki Liu “Shapes of leading tunnelling trajectories for single-electron molecular ionization” Journal of Physics A 44, 275301 (2011) [arXiv:1010.2668]

    Abstract: Based on the geometrical approach to tunnelling by Hislop and Sigal (1989 Mem. AMS 78 No 399), we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single-active-electron models of molecular tunnelling ionization (i.e. theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short-range interactions and ‘almost’ linear in the case of long-range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the obtained results are discussed.

  28. Denys I. Bondar, Robert R. Lompay, and Wing-Ki Liu “Quantum mechanics of a free particle from properties of the Dirac delta function” American Journal of Physics 79, 392 (2011) [arXiv:1007.4243]

    Abstract: Based on the assumption that the probability density of finding a free particle is independent of position, we infer the form of the eigenfunction for the free particle, $<x|p > = \exp(ipx/\hbar)/\sqrt{2\pi\hbar}$. The canonical commutation relation between the momentum and position operators and the Ehrenfest theorem in the free particle case are derived solely from differentiation of the delta function and the form of $<x|p >$.

  29. D. I. Bondar, G. L. Yudin, W.-K. Liu, M. Yu. Ivanov, and A. D. Bandrauk “Nonsequential double ionization below laser-intensity threshold: Anticorrelation of electrons without excitation of parent ion” Physical Review A 83, 013420 (2011) [arXiv:1009.2072]

    Abstract: Two-electron correlated spectra of nonsequential double ionization below laser-intensity threshold are known to exhibit back-to-back scattering of the electrons, i.e., the anticorrelation of the electrons. Currently, the widely accepted interpretation of the anticorrelation is recollision-induced excitation of the ion plus subsequent field ionization of the second electron. We argue that another mechanism, namely, simultaneous electron emission, when the time of return of the rescattered electron is equal to the time of liberation of the bounded electron (i.e., the ion has no time for excitation), can also explain the anticorrelation of the electrons in the deep, below laser-intensity threshold regime. Our conclusion is based on the results of the numerical solution of the time-dependent Schrödinger equation for a model system of two one-dimensional electrons, as well as on an adiabatic analytic model that allows for a closed-form solution.

  30. Denys I. Bondar, Wing-Ki Liu, and Misha Yu. Ivanov “Enhancement and suppression of tunneling by controlling symmetries of a potential barrier” Physical Review A 82, 052112 (2010) [arXiv:1006.0905]

    Abstract: We present a class of two-dimensional (2D) systems which shows a counterintuitive property that contradicts a semiclassical intuition: A 2D quantum particle “prefers” tunneling through a barrier rather than traveling above it. Viewing the one-particle 2D system as a system of two 1D particles, it is demonstrated that this effect occurs due to a specific symmetry of the barrier that forces excitations of the interparticle degree of freedom that, in turn, lead to the appearance of an effective potential barrier even though there is no “real” barrier. This phenomenon cannot exist in 1D.

  31. G. L. Yudin, D. I. Bondar, S. Patchkovskii, P. B. Corkum, and A. D. Bandrauk “Unified ab initio treatment of attosecond photoionization and Compton scattering” Journal of Physics B 42, 205601 (2009) [arXiv:0810.2322]

    Abstract: We present a new theoretical approach to attosecond laser-assisted photo- and Compton ionization. Attosecond x-ray absorption and scattering are described by -matrices, which are coherent superpositions of ‘monochromatic’ -matrices in a laser-modified Furry representation. Besides refining the existing theory of the soft x-ray photoelectron attosecond streak camera and spectral phase interferometry (ASC and ASPI), we formulate a theory of hard x-ray photoelectron and Compton ASC and ASPI. The resulting scheme has a simple structure and leads to closed-form expressions for ionization amplitudes. We investigate Compton electron interference in the separable Coulomb–Volkov continuum with both Coulomb and laser fields treated non-perturbatively. We find that at laser-field intensities below 1013 Wcm−2 normalized Compton lines almost coincide with the lines obtained in the laser-free regime. At higher intensities, attosecond interferences survive integration over electron momenta, and feature prominently in the Compton lines themselves. We define a regime where the electron ground-state density can be measured with controllable accuracy in an attosecond time interval. The new theory provides a firm basis for extracting photo- and Compton electron phases and atomic and molecular wavefunctions from experimental data.

  32. Denys I. Bondar, Wing-Ki Liu, and Gennady L. Yudin “Adaptation of the modified adiabatic approximation to strong-field ionization” Physical Review A 79, 065401 (2009)[arXiv:0906.1284]

    Abstract: Savichev’s modified adiabatic approximation [Sov. Phys. JETP 73, 803 (1991)] is used to obtain a general form of a quantum-mechanical amplitude of ionization by a low-frequency laser field. The method possesses only one requirement that the frequency of the laser field must be low. Connections of the obtained result with the quasiclassical approximation and other previous investigations are discussed.

  33. Denys I. Bondar, Michael Spanner, Wing-Ki Liu, and Gennady L. Yudin “Photoelectron spectra in strong-field ionization by a high-frequency field” Physical Review A 79, 063404 (2009) [arXiv:0809.2819]

    Abstract: We analyze atomic photoelectron momentum distributions induced by bichromatic and monochromatic laser fields within the strong-field approximation (SFA), separable Coulomb-Volkov approximation (SCVA), and ab initio treatment. We focus on the high frequency regime—the smallest frequency used is larger than the ionization potential of the atom. We observe a remarkable agreement between the ab initio and velocity gauge SFA results while the velocity gauge SCVA fails to agree. Reasons of such a failure are discussed.

  34. Denys I. Bondar, Wing-Ki Liu, and Misha Yu. Ivanov “Two-electron ionization in strong laser fields below intensity threshold: signatures of attosecond timing in correlated spectra” Physical Review A 79, 023417 (2009) [arXiv:0809.2630]

    Abstract: We develop an analytical model of correlated two-electron ionization in strong infrared laser fields. The model includes all relevant interactions between the electrons, the laser field, and the ionic core nonperturbatively. We focus on the deeply quantum regime, where the energy of the active electron driven by the laser field is insufficient to collisionally ionize the parent ion, and the assistance of the laser field is required to create a doubly charged ion. In this regime, the electron-electron and the electron-ion interactions leave distinct footprints in the correlated two-electron spectra, recording the mutual dynamics of the escaping electrons.

  35. Denys I. Bondar “Instantaneous multiphoton ionization rate and initial distribution of electron momentum” Physical Review A 78, 015405 (2008) [arXiv:0805.1890]

    Abstract: The Yudin-Ivanov formula [Phys. Rev. A 64, 013409 (2001)] is generalized such that the most general analytical expression for single-electron spectra, which includes the dependence on the instantaneous laser phase, is obtained within the strong field approximation. No assumptions on the momentum of the electron are made. Previously known formulas for single-electron spectra can be obtained as approximations to the general formula.

  36. D. I. Bondar, M. Hnatich, and V. Yu. Lazur “Symbolic computations for the two-Coulomb-centers problem in the space of arbitrary dimension” Physics of Particles and Nuclei Letters 5, 255 (2008)

  37. V. V. Bondarchuk, I. M. Shvab, D. I. Bondar, and A. V. Katernoga “Simple model of scalar-vector interaction for the relativistic two-center problem” Physical Review A 76, 062507 (2007)

  38. D. I. Bondar, M. Hnatich, and V. Yu. Lazur “The two Coulomb centres problem at small intercentre separations in the space of arbitrary dimension” Journal of Physics A 40, 1791 (2007)

  39. D. I. Bondar, V. Yu. Lazur, and M. Hnatic “The two dimensional two coulomb centres problem at small intercenter separation” Journal of Physical Studies 10, 1 (2006) [in Ukrainian]

  40. D. I. Bondar, M. Hnatich, and V. Yu. Lazur “Two-dimensional problem of two Coulomb centers at small intercenter distances” Theoretical and Mathematical Physics 148, 1100 (2006)

  41. I. I. Bondar, V. V. Suran, and D. I. Bondar “Dependence of the efficiency of formation of Ba2+ ions by the two-electron mechanism in two laser fields on the laser radiation intensity” Optics and Spectroscopy 100, 340 (2006)

  42. D. I. Bondar, V. Yu. Lazur, I. M. Schwab, and S. Chalupka “The two-centre Coulomb problem in the quantum mechanics. Influence of the dimensions” Journal of Physical Studies 9, 304 (2005)

  43. I. I. Bondar, V. V. Suran, and D. I. Bondar “Dependence of doubly charged Ion formation by the two-electron mechanism on the intensity of laser radiation” Optics and Spectroscopy 96, 16 (2004)

  44. I. I. Bondar, V. V. Suran, and D. I. Bondar “Determination of the Spatial Distribution of Focused Laser Radiation from the Shape of the Stark Resonance Profile” Optics and Spectroscopy 96, 595 (2004)

  45. I. I. Bondar, V. V. Suran, and D. I. Bondar“Effect of the spatial distribution of laser radiation on the ion yield for the two-electron mechanism of doubly charged ion formation” Laser Physics 14, 64 (2004)