Attosecond control of electrons emitted from a nanoscale metal tip

Attosecond science is based on steering of electrons with the electric field of well-controlled femtosecond laser pulses. It has led to, for example, the generation of XUV light pulses with a duration in the sub-100-attosecond regime, to the measurement of intra-molecular dynamics by diffraction of an electron taken from the molecule under scrutiny, and to novel ultrafast electron holography. All these effects have been observed with atoms or molecules in the gas phase. Although predicted to occur, a strong light-phase sensitivity of electrons liberated by few-cycle laser pulses from solids has hitherto been elusive. Here we show a carrier-envelope (C-E) phase-dependent current modulation of up to 100% recorded in spectra of electrons laser-emitted from a nanometric tungsten tip. Controlled by the C-E phase, electrons originate from either one or two sub-500as long instances within the 6-fs laser pulse, leading to the presence or absence of spectral interference. We also show that coherent elastic re-scattering of liberated electrons takes place at the metal surface. Due to field enhancement at the tip, a simple laser oscillator suffices to reach the required peak electric field strengths, allowing attosecond science experiments to be performed at the 100-Megahertz repetition rate level and rendering complex amplified laser systems dispensable. Practically, this work represents a simple, exquisitely sensitive C-E phase sensor device, which can be shrunk in volume down to ~ 1cm3. The results indicate that the above-mentioned novel attosecond science techniques developed with and for atoms and molecules can also be employed with solids. In particular, we foresee sub-femtosecond (sub-) nanometre probing of (collective) electron dynamics, such as plasmon polaritons, in solid-state systems ranging in size from mesoscopic solids via clusters to single protruding atoms.Comment: Final manuscript version submitted to Natur

A possible method for non-Hermitian and non-PTPT-symmetric Hamiltonian systems

A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator $\eta_+$ represents the $\eta_+$-pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-$PT$-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator $\eta_+$ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-$PT$-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.Comment: 15 pages, no figures; v2: clarifications added; v3: 16 pages, 1 figure, clarifications made clearer; v4: 19 pages, the main context is completely rewritten; v5: 25 pages, title slightly changed, clarifications added, the final version to appear in PLOS ON

Selective scattering between Floquet-Bloch and Volkov states in a topological insulator

The coherent optical manipulation of solids is emerging as a promising way to engineer novel quantum states of matter. The strong time periodic potential of intense laser light can be used to generate hybrid photon-electron states. Interaction of light with Bloch states leads to Floquet-Bloch states which are essential in realizing new photo-induced quantum phases. Similarly, dressing of free electron states near the surface of a solid generates Volkov states which are used to study non-linear optics in atoms and semiconductors. The interaction of these two dynamic states with each other remains an open experimental problem. Here we use Time and Angle Resolved Photoemission Spectroscopy (Tr-ARPES) to selectively study the transition between these two states on the surface of the topological insulator Bi2Se3. We find that the coupling between the two strongly depends on the electron momentum, providing a route to enhance or inhibit it. Moreover, by controlling the light polarization we can negate Volkov states in order to generate pure Floquet-Bloch states. This work establishes a systematic path for the coherent manipulation of solids via light-matter interaction.Comment: 21 pages, 6 figures, final version to appear in Nature Physic

Quasistationary Stabilization of the Decay of a Weakly-Bound Level and Its Breakdown in a Strong Laser Field

Although it was pointed out about 10 years ago that an atomic decay rate might decrease as the intensity of a high-frequency laser field increases, there still does not exist any complete understanding of either the physical origin of this interesting nonlinear phenomenon or its dependence on the atomic and field parameters. Essentially, the problem consists in that the phenomenon requires a major modification of the standard picture of photoeffect in a strong laser field. In Reference #1 the origin of this stabilization is related to a particular distortion of an atomic potential by an intense monochromatic high-frequency field. This phenomenon is called adiabatic or quasistationary stabilization (QS). For the case of Rydberg levels, another (interference) mechanism of QS was suggested. Both theories predict an unlimited decrease of the decay rate (or of the width Γ of an atomic level, i.e., of the imaginary part of the complex quasienergy, ε = Re ε – iΓ/2 ) as the laser field amplitude increases. In recent years the idea of “dynamic stabilization” (DS) has become popular. It originates from the pulse form of a laser field rather than from any intrinsic property of the atom in a strong monochromatic field. Within this model the numerous simulations point also to the possibility of a breakdown of stabilization for the case of superintense short laser pulses. However, a recent paper, using the quasistationary quasienergy states (QQES) as an adiabatic basis for the laser pulse has shown that DS has the same (quasistationary) origin as QS. Finally, a number of authors deny the existence of stabilization, in particular, of QS for ionization from a short-range potential and of DS in pulsed fields. Obviously, these controversies and ambiguities are caused by the complexity of the numerical solution of the Cauchy problem for the time-dependent Schrödinger equation in a strong field and by the absence of analyses for exactly solvable analytical models. We analyze the exactly solvable problem of an electron in a three-dimensional, short-range potential and consider the two questions: does a QS-like behavior of the decay rate exist for this model, and, if so, is there an upper intensity limit of the QS regime

STRONG-FIELD PHYSICS Ionization surprise

Faisal F. STRONG-FIELD PHYSICS Ionization surprise. NATURE PHYSICS. 2009;5(5):319-320.The common picture of how atoms and molecules are ionized in intense laser fields has had decades of success. However, the observation of an unexpected but apparently universal low-energy photoionization feature suggests this picture is incomplete