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19. (Part 1) The Use of Intense Femtosecond Lasers in Atomic Physics Dr. Jason B. Greenwood School of Maths and Physics, Queen’s University Belfast Email: [email protected] 1. The Basics of Ultrafast Optics 1.1 Introduction Femtosecond lasers are used in atomic and molecular physics mainly for two reasons. Firstly, they provide ultrafast “shutter speeds” for imaging dynamics at the atomic and molecular level as the movement of atoms in molecules due to vibration, rotation or in chemical processes occurs on femtosecond timescales. This application led to Ahmed Zewail being awarded the Nobel Prize for Chemistry (nobelprize.org/nobel_prizes/chemistry/laureates/1999). Secondly, by squeezing energy into such a short timescale, high intensities and therefore high electromagnetic fields can be produced. By focussing these laser pulses, electric fields which are comparable to the binding energy of an electron in a H atom can be routinely produced. For instance, if a 1 mJ pulse of duration 25 fs is focussed down to a diameter of 20 μm = 2 10-3 cm, the intensity I is 0.001 I = 1.2 1016 W cm-2 2 3 15 25 10 4 2 10 To put this in perspective, the intensity of sunlight when it reaches Earth is about 0.1 Wcm-2. You would need a magnifying glass of roughly diameter of the Earth to focus sunlight to a similar intensity. The electric field E can be found from I 12 0 cE 2 E = 3.0 1011 V m-1 The atomic unit of electric field (the electric field experienced by an electron in an H atom in its ground state) is 5.1 1011 V m-1. It should also be noted that the use of femtosecond lasers to produce stable optical frequency combs, currently provides the most accurate measurements of fundamental constants. The Nobel prize was awarded for this work in 2005 (nobelprize.org/nobel_prizes/physics/laureates/2005). 1.2 Bandwidth of Femtosecond Laser Pulses In order to produce ultrashort pulses, this necessarily means that the bandwidth of the laser must be larger than the minimum determined by the uncertainty principle E t t 1 The time profile and spectrum of the pulse are related by a Fourier transform Spectrum Irradiance vs. time Long pulse FT time frequency FT-1 Short pulse time frequency Figure 1: The time-frequency relationship between pulse length and spectral bandwidth For a pulse with a temporal Gaussian intensity profile, with t measured as the full width half maximum (FWHM), the relationship is t 2.76 . For a pulse with central wavelength of 800 nm and 25 fs FWHM this corresponds to a bandwidth of 37 nm. 1.3 Kerr Lens Mode Locking A single pulse bouncing in a laser cavity results in the emission of an infinite train of pulses with temporal separation given by the round trip time in the cavity. A Fourier transform of this gives a comb of laser modes which are modulated by an envelope which depends on the pulse width (Figure 2). E(t) Laser Cavity Period T t F() FT Laser modes separated by 2 /T Figure 2: Spectral modes of a short pulse in a laser cavity However, if the laser modes have random phases, there is continuous wave emission. To produce an ultrashort pulse, the modes must be in phase (mode-locked). This gives a high intensity at the centre of the pulse which drops off sharply with time as the different frequencies get out of phase. There are a number of methods for achieving mode-locking. One of the most common is the use of Kerr lensing. Kerr lensing is a non-linear effect in a material in which the refractive index increases with intensity. The centre of an intense pulse experiences a larger phase delay due to the increased refractive index and the medium acts like a lens causing self-focussing. When the modes are locked, the intensity is high, and this is used to remove out of phase modes which lead to a continuous emission. In Figure 3 an aperture is introduced to the cavity so that only the pulsed, high-intensity modes are focussed through. Figure 3: Kerr Lens Mode-Locking 1.4 The Titanium:Sapphire Laser This is the femtosecond lasing medium of choice in research laboratories. The reason it is favoured is due to its large gain bandwidth and good thermal stability properties. The peak gain is around 800 nm but the medium will lase from 700 – 1000 nm (Figure 4). It is typically pumped by the second harmonic of a Nd:YAG laser (532nm). The Kerr lens mode-locked laser cavity is the basis of most Ti:Sapphire lasers and in principal can produce pulses which are as short as 5 fs (2 optical cycles at 800 nm). In order to achieve this, the dispersion in the crystal which tends to lengthen the pulse must be accounted for. Typical pulse energies from the oscillator are in the nJ range. Gain 700 800 Figure 4: Gain curve of a Titanium: Sapphire crystal 900 Wavelength 1000 (nm) 1.5 Dispersion When the pulse passes through a non-absorbing medium, e.g. glass, it lengthens due to positive dispersion caused by the wavelength dependent refractive index. This introduces a positive “chirp” to the pulse, whereby longer wavelengths are at the front of the pulse and shorter wavelengths at the rear. Glass Figure 5: The effect of dispersion on a femtosecond pulse For instance, an unchirped pulse of duration 30 fs will be stretched to about 45 fs after passing through 1 cm of fused silica. For an ultrashort 5 fs pulse, dispersion in air even needs to be taken into account. A positive or negative chirp can also be achieved using the dispersive properties of gratings and prisms. 1.6 Chirped Pulse Amplification (CPA) Until the mid-1980s, the highest intensities needed for strong field physics could only be produced at large laser facilities. When a short pulse is amplified, the increase in intensity introduces non-linear self-focussing which damages the gain medium. The only way around this was to expand the laser beam to very large diameters (meters as oppose to cm) to reduce the intensity. The development of CPA enabled university labs to access intense laser pulses using “table-top” devices. In the CPA scheme (Figure 6), to reduce the intensity in the gain medium, the pulses produced from the oscillator are expanded in time rather than space. In the stretcher, gratings (or prisms) are used to create a shorter path length for longer wavelengths (red) than for short wavelengths (blue) to generate a positive chirp. The reverse is achieved in the pulse compressor. Pulses are amplified either with a regenerative amplifier (a cavity with low gain and many passes through the amplifying crystal) or a multi-pass amplifier. The high gain, multi-pass amplifier shown in Figure 7 is favoured for producing short pulses as fewer passes through the crystal introduces less dispersion. However, as the gain is not constant for all wavelengths (Figure 4), the bandwidth of the amplified pulse is reduced, limiting the pulse length to more than 20 fs. Typical pulse output energies will be in the region of 1 mJ at a repetition rate of 1 kHz. Higher pulse energies can be achieved with further amplification stages at lower repetition rates. 1.7 Ultrashort pulses ( < 20 fs) To produce even shorter pulses, it is necessary to broaden the frequency spectrum of the pulse. This can be achieved by passing the pulse through a hollow capillary filled with a noble gas at several atmospheres. The pulse polarizes the gas which generates a non-linear response. As the refractive index becomes dependent on intensity, a frequency dependent phase is produced which generates a frequency shift. The leading edge of the pulse becomes “redder” while the trailing edge becomes “bluer”. The spectrally broadened output of the capillary will be chirped but can be compressed down to 5 fs using chirped mirrors. A chirped mirror possesses multiple dielectric mirrors which reflect different wavelengths at different depths. These variations in optical path lengths for different wavelengths are introduced for re-compression. Figure 6: A Chirped Pulse Amplification schematic. Pulses from the oscillator are stretched by a factor of more than 1000, amplified and then recompressed to produce a high-energy ultrashort pulse. Figure 7: Multi-pass Amplifier: To limit the heat load on the crystal, most of the incident pulses are rejected using a pulser picker - Pockel’s cell (PC). In this arrangement, the beam “walks” across the mirrors while passing through the crystal about 10 times before being ejected. 1.8 Pulse Measurement Knowledge of the laser pulse length is not only important for determining the intensity of the radiation but the interaction timescale determines how the field couples to the system. For instance in molecular dynamics, the fastest nuclear motion (10s of femtoseconds) occurs for vibrations of covalently bonded hydrogen atoms. Therefore, when molecules are irradiated by ultrashort ( < 10fs) pulses, the atoms can be considered frozen and molecular dissociation during the pulse is suppressed. It may also be important to measure the pulse envelope as variations in intensity can dynamically influence the outcome of the interaction. For ns lasers, this can be performed using fast photo-diodes, but at femtosecond timescales detectors are too slow to directly measure the pulse. The pulse itself is the only diagnostic with which a fast enough measurement can be performed. 1.8.1 Autocorrelation In autocorrelation, the pulse is split into two, passed through the arms of an interferometer which introduces a delay , overlapped and detected (Figure 8). If the electric fields of the pulses are E(t) and E(t-), when they are overlapped the intensity is I E t E t E t E t 2 E t E t 2 2 2 The set-up shown in Figure 8 is an example of an intensity autocorrelator where the pulses are overlapped at a slight angle in a non-linear crystal to generate second harmonic radiation ( I 2). Only the second harmonics emitted along the axis due to the temporal overlap of the pulses (the final term in the above expression) are detected. Therefore, the signal is given by 2 S E t E t dt I t I t dt By varying the delay , the width of the initial pulse can be determined from this autocorrelation function which is just a convolution of the pulse intensity with itself. For instance, the autocorrelation of a Gaussian pulse is a Gaussian with a FWHM 2 wider than the incident pulse. Input Pulse Beamsplitter Aperture Delayed Pulse Detector Delay Lens Non-linear crystal Figure 8: An intensity autocorrelator 1.8.2 FROG The limitation of an intensity autocorrelation is that any structure in the pulse envelope is effectively washed out in the convolution. In the most common implementation of a Frequency Resolved Optical Grating (FROG), autocorrelation signals are obtained as a function of the second harmonic frequency. Therefore, the detector in Figure 8 is replaced by a spectrometer. This signal can be plotted in two dimensions as a spectrograph. In effect the replica is used to sample the time dependent frequency of the pulse. An iterative algorithm is used to extract the time dependent frequency and phase, and hence the intensity envelope of the pulse (see www.physics.gatech.edu/gcuo/subIndex.html for more detail on pulse characterization using FROGs). Another, more complicated technique which can reproduce the electric field of the pulse using a non-iterative algorithm for single pulses is Spectral Interferometry for Direct Electric Field Reconstruction (SPIDER). This was developed by Ian Walmsley’s group in Oxford and information on it can be found on their website ultrafast.physics.ox.ac.uk/spider/index.html. 1.9 Pulse Shaping A FROG is useful in characterizing pulses which have complicated characteristics. Such pulses are being used in the study of coherent control of quantum systems. Variations in the pulse envelope can used to optimize the probability of the system emerging in a particular final state. For instance, a molecule ABC might have dissociation channels AB + C or A + BC. A strong laser pulse can be tailored to modify the potential energy surface dynamically so that one or other of the channels is favoured [1]. Femtosecond pulses are usually shaped by introducing different phase delays for the frequency components. A dispersive device such as a grating creates a spatial map of the frequency components which can then be delayed independently. This delay can be introduced through variations in refractive index as a function of position using an acoustooptical modulator or an array of liquid crystal modulators as shown in Figure 9. Electric fields can be applied to individual pixels to vary both the phase and amplitude of each frequency component. When recombined with another grating, the resulting pulse will have a Amore phase mask selectively delays colors. complicated temporal shape. Figure 9: Frequency dependent phase delay introduced by a liquid crystal modulator array. An amplitude mask shapes the spectrum. 1.10 A Focussed Gaussian Laser Pulse To generate the high intensities necessary for experiments, the pulse is focused into the atomic or molecular target. A drawback of this approach is that the interaction volume is not irradiated with a uniform intensity. Indeed every atom or molecule will experience a variation in intensity with time due to the pulse envelope. In an experiment this makes it very difficult to observe processes which are strong functions of intensity, such as changes in ionization rates enhanced by intensity dependent resonances. For a beam with a Gaussian spatial profile, its diameter D is defined as the width at which the intensity has dropped to e-2 of the central maximum. When focused by a lens or mirror of focal length f, at a distance z from the focal point and r from the axis, the intensity is given by I r , z , t I t 1 z / z 0 2 2r 2 exp 2 2 w0 1 z / z 0 where I(t) is the intensity envelope at the focus (r = 0, z = 0), w0 is beam waist diameter, and z0 is the Rayleigh length defined as the distance at which the intensity drops by a factor of 2 along the beam axis w02 2f w0 , z0 D The variation in intensity at the laser focus is shown in Figure 10. When focused into a gas jet, there is only a very small volume of gas being irradiated at the highest intensities. If ionization is being measured, although the rate depends strongly on intensity, the greatest contribution to the signal may be coming from the lower intensity “shells” which have a larger interaction volume. Figure 10: Isointensity Contours for an 800nm laser of 1mJ pulse energy, 50fs pulse length focused by a 250mm focal length lens with a beam size at the lens of 10mm. 2. Atoms in Intense Femtosecond Laser Fields 2.1 Ionization Excitation or ionization of an atom can be induced if the coupling between the ground state and an excited or continuum state is sufficiently strong. In a weak field excitation only occurs if the frequency of the radiation is resonant with the frequency difference of the states and selection rules are obeyed. In a strong field it is possible to ionize an atom even though the energy of one photon in insufficient, but may proceed by the absorption of many photons through Multi-Photon Ionization (MPI). But how can a photon be absorbed if it is not resonant with an intermediate level? It is possible for an atom to absorb a photon of energy to form a virtual state, for a time interval t governed by the uncertainty principle .t t 1 For an 800 nm photon (T = 2.5 fs, =1.55 eV, 0.057 a.u.), t 0.5 fs. By squeezing a large number of photons in time and space, the probability of this virtual state absorbing another photon is high. If the numbers of photons N absorbed is greater than the ionization potential, an electron is liberated with a kinetic energy Ee N I P Since the probability of absorbing the “next” photon is proportional to the intensity of the laser, the ionization rate is proportional to IN (can be derived from perturbation theory). Electron Yield 0 Electron energy Ee Figure 11: Electron energy spectrum obtained from multi-photon ionization An electron energy spectrum produced from this MPI process is shown in Figure 11. You will notice that there are a series of peaks in the spectrum which indicates that it is possible to absorb more photons than needed for ionization in a process known as Above Threshold Ionization (ATI). By conservation rules, a free electron cannot absorb energy from an applied field, but in this case an electron ionized to the continuum is not strictly free as it is still under the influence of the Coulomb field of the ion it has left behind. Although MPI proceeds when the field is “strong”, the electric field of the laser is still relatively weak compared to that binding the electron to the atom. Eventually, perturbation theory breaks down and energy levels are modified by AC stark shifting. The ionization limit of the atom is effectively raised as the total energy of the electron in the continuum must include the classical quiver energy of an electron in an oscillating field (the ponderomotive energy UP). UP can derived from the classical equations of motion. If initially the electron is at rest mx eE cos t eE sin t m eE x cos t x0 m 2 The ponderomotive energy UP is the cycle averaged kinetic energy 2 / e2 E 2 U P 12 mx 2 4m 2 0 In terms of intensity I 12 0 cE 2 x UP e2 I e 2 I2 9.3 10 6 I2 eV 2 0cm 2 8 0c3m 2 For an intensity of 1013 Wcm-2 at 800nm, UP 0.6 eV. As UP increases, it is possible to suppress some of the ATI peaks in a process known as channel closing. At an intensity of 1015 Wcm-2, UP 60 eV and the amplitude of a free electron is much larger than the size of the atom 1/ 2 xmax eE e2 2 I m 2 4 2 mc2 0c Weak field MPI 1.36 10 6 2 I 1 / 2 2.7 10 9 m 50 Bohr radii Strong field TI Figure 12: The atomic potentials for different ionization regimes Figure 12 shows the effect of the classical field of the laser on the atom in this regime at a particular instant of the laser cycle. Ionization can now proceed via tunnelling of the electron and is most likely to occur at the peak of the field. To quantify the boundary between MPI and tunnel ionization (TI), we can use the Keldysh parameter which is the ratio of the orbital rate of the electron to the tunnelling rate. It is given by 1/ 2 I P 2U P As a general rule MPI ( > 1), TI ( < 1). For << 1, the barrier may be completely suppressed so that the electron can move over the barrier (OB). For an H atom in a 800 nm field Intensity (W cm-2) 1012 10.6 Ionization Mechanism MPI 1013 3.4 MPI 1014 1.1 MPI/TI 1015 0.34 TI 1016 0.11 OB 2.2 Electron Spectroscopy Using Time of Flight As the interaction with a short pulse laser gives a well defined temporal and spatial interaction region, electron energy spectroscopy is often performed using time of flight techniques. The technique has been used in mass spectrometry for many years, but its use in electron spectroscopy requires much faster detectors and associated electronics to resolve the arrival times of light, fast electrons. The principal of a field free time of flight is very simple. A clock is started when the laser is fired, and the time t taken by the ionized electron to travel along a flight tube of length L is measured. 1/ 2 m t L 2E where L is the length of the tube and E is the kinetic energy of the ejected electron. The resolution is given by L m t 3 2 2E E 1 8 E E L m 1/ 2 E 1/ 2 t For modern detectors and electronics, time resolutions of t < 1ns are routinely achievable. If t = 0.5ns, E = 50 eV, L = 0.4m then E 0.5 eV. Electron spectra can be more efficiently obtained using a magnetic bottle mass spectrometer [2] shown in Figure 13. This device uses a strong magnetic field for 2 collection (up to 4 if an electric field is used) of the ejected electrons. The magnitude of the magnetic field is adiabatically reduced as the electrons move towards the detector so that the electron experiences a small change in field strength for each cyclotron orbit it undergoes. For this condition, if the electron is initially emitted at an angle i to the time of flight axis, to conserve its angular momentum the angle just before it is detected f is given by sin f 1/ 2 Bf sin i Bi where Bi and Bf are the initial and final field strengths. If Bi/Bf is large, all the electrons have f close to zero and have similar path lengths in the spectrometer. The magnetic field is typically generated using a permanent magnet close to the interaction region, while the time of flight tube is surrounded by a coil which produces a weak uniform field along the axis and by -metal shield which excludes any external fields. Figure 13: Magnetic Bottle Mass Spectrometer used at the Free Electron Laser at DESY (see Chapter 9, part 2 for details of this experiment) 2.3 Electron Re-collision When an electron is ionized, it is still under the influence of the Coulomb potential of the residual ion. As the electric field of the laser is periodic, the force on the electron will change direction which accelerates the electron back towards the ion. A purely classical analysis of the trajectory shows that depending on the phase of the field at which the electron is “born”, it will either quiver away from the core or return with an energy dependent on the phase[3]. The maximum return energy (3.17UP) is produced when the electron is liberated just after the field has gone through a maximum. In this re-collision process the electron can be elastically scattered, cause ionization leaving a multiply charged ion, or recombine generating an energetic photon. Signatures of these processes can be found in experiments which study the electrons, ions and photons produced from the laser interaction. For instance, if the ion charge state yield is measured as a function of the laser peak intensity, the behaviour shown in Figure 14 is typical. At low intensity, single ionization increases very steeply due to multi-photon ionization. As the intensity is increased, tunnel ionization takes over, until saturation is reached where there is a 100% probability of ionizing an atom in the laser focus. Above this intensity the ion yield still increases in proportion to I1.5 due to the expansion of the iso-intensity surfaces of the laser focus (Figure 10). The doubly charge ion can be produced if the intensity reaches a sufficiently high value during the remainder of the laser pulse (sequential ionization). However, a direct double ionization process can proceed via the re-collision mechanism which contributes to the enhanced signal at lower intensities than expected for sequential ionization (the “shoulder” in the data). Ion Yield 106 Saturation OB X X+ I 1.5 TI 105 Re-collision X X2+ 104 Sequential ionization X X+X2+ 103 102 MPI IN 101 100 1012 1013 1014 1015 Intensity I (Wcm-2) Figure 14: Single and double ionization of an atom as a function of intensity This process has been extensively studied experimentally using the technique of COLd Target Recoil Ion Momentum Spectroscopy (COLTRIMS) [4,5]. In Figure 15 a cold atomic or molecular beam is crossed with the focussed laser pulse. Perpendicular to both, an electric field is applied to extract the positive ions produced towards a 2D imaging detector while electrons move in the opposite direction towards a second detector. To ensure complete collection of the electrons an additional weak magnetic field is applied parallel to the electric field. From the hit position and time of flight of the electrons and ions, the momentum of the ejected electrons and recoiling ions can be determined giving a kinematically complete picture of the interaction. Figure 15: COLTRIMS experiment for studying the ionization and dissociation of atoms and molecules by intense laser fields see reference [5] 2.4 High Harmonic Generation A re-colliding electron can alternatively recombine to form an atom again with the emission of a photon at a harmonic frequency (High Harmonic Generation HHG). As the atom is initially centro-symmetric, by parity conservation the emitted harmonic must be odd. Using the classical picture, the maximum energy of an emitted harmonic is IP + 3.17UP. This coherent light source has a number of potential applications such as lithography and biological imaging. At energies just above the carbon K shell edge at 284 eV (harmonic order 183), the photons are relatively transparent to water but are strongly absorbed by biological structures (the “water window”). Emission of photons with energies greater than 1 keV has already been demonstrated in the laboratory [6]. Closed shell noble gases like He and Xe do not have a permanent dipole moment, but when an electric field is applied, a dipole is induced which can become large if the electron is drawn away from the atom as in the re-collision process. The expectation value of the induced dipole yields the time evolution of emitted radiation field, and the square of its Fourier transform yields the intensity spectrum. As Xe has a larger polarizability than He, the harmonic emission is stronger for Xe, but He can produce higher harmonics as it is more resistant to depletion through ionization and can experience a higher intensity. The HHG generation process is inefficient as the phase properties of the emission depend strongly on the intensity, which varies across the laser focus. Therefore, only a small part of the interaction volume results in coherent emission. To maximise the emission, a pulsed gas jet is injected at high pressure into the vacuum chamber. Conversion efficiencies of around 10-5 have been achieved. 2.5 Attosecond Pulses In the HHG process, the highest harmonics can only be emitted for a small range of phases of the laser cycle where the re-collision energy is at its highest. For a laser pulse with many cycles, if the lower energy harmonics are removed, the emission is a train of short attosecond (< 1 fs) pulses separated by half the period of the driving frequency (Figure 16). As the classical orbital time of an electron in the ground state of a H atom is about 150 as, this opens up the possibility for direct imaging of the motion of electrons in atoms, molecules and surfaces. However, to use attosecond pulses to generate “movies” of electronic phenomena, it is necessary to use a single attosecond pulse at a time. To generate one attosecond pulse per laser pulse the emission of the high harmonics must be limited to a single laser half-cycle. This can be achieved by either making the laser pulse very short, or by dynamically altering the laser polarization during the laser pulse so that it varies from circularly polarized to linear to circular. In the latter case, elliptically polarization causes the electron to orbit the core rather than collide and high harmonics are suppressed. For the former, producing pulses as short as 5 fs (approximately 2 cycles long) as described in section 1.6 is necessary but not sufficient for the production of a single attosecond pulse. Electron “born” 18 after peak 2.67 fs @ 800 nm Phase 0 180 360 Electron returns 235 after “birth” E field of highest harmonics Time Figure 16: Electron trajectories yielding maximum re-collision energies and hence highest harmonics The phase of the carrier frequency with respect to the pulse envelope must be considered. In Figure 17(a), the electric field is strongest at the centre, resulting in the highest harmonics being produced for the trajectory shown. In Figure 17(b), an electron can be accelerated by the maximum electric field at two points in the laser pulse producing two attosecond pulses. Stabilizing this carrier-envelope phase is an essential part of the attosecond generation process. When a phase of zero (or 180) is achieved, as the pulse produced is very short it has a very broad bandwidth and indeed can no longer be considered a harmonic. The signature of the attosecond pulse is a continuum in the spectrum (Figure 18). By isolating the continuum emission with a filter, attosecond pulses in the extreme ultraviolet (XUV) of energy around 100 eV, bandwidth 10 eV, and duration about 200as, have been produced [7]. Carrier-envelope phase = 0 Single attosecond pulse (a) Carrier-envelope phase = 90 2 attosecond pulses produced (b) Figure 17: 5 fs pulses with different carrier-envelope phases with electron trajectories which produce the highest harmonics Intensity Lower harmonics removed by filter Continuum emission Attosecond radiation Frequency Figure 18: High harmonic spectrum obtained from an ultrashort pulse with = 0 2.6 Attosecond Physics This field is in its infancy, but the first task is to measure the length of the attosecond pulse. An autocorrelation process is not possible as there are no efficient non-linear processes in the extreme ultra-violet. Alternatively, a cross correlation with the parent laser pulse can be performed. Although the parent pulse is about 5 fs long and the laser cycle is 2.6 fs, the electric field changes significantly on the attosecond timescale and can used as a diagnostic. The non-linear process at work is the photoionization of an atom in the presence of this electric field. The apparatus used to perform the measurement is shown in Figure 18. The ultrashort, phase stabilised ( = 0) laser pulses are focussed into an atomic gas jet to produce the attosecond XUV pulses. The XUV beam has a smaller angular divergence than the laser beam. A filter which transmits XUV but absorbs optical photons is used to generate a hollow laser beam copropagating with the XUV beam at the centre. Both are focussed by a multi-layer mirror into another gas jet. The mirror has two components with the central portion capable of being driven in 30 nm steps to introduce delays to the XUV pulses at 100as intervals. The energy spectrum of the electrons ejected along the polarization direction is obtained by s field-free time of flight spectrometer (TOF). Figure 18: Experimental apparatus used to produce attosecond pulses and perform pump-probe measurements of ionization [8], see www.attoworld.de A free electron in a laser field will gain no momentum, unless it is injected into the field instantaneously. This is the situation when the attosecond XUV pulse ionizes an electron from an atom. In the field free case the electron has momentum p0 2m X I P where IP is the binding energy of the electron and X is the energy of the XUV photon. With a time-dependent electric field present E0 f t ' cost ' , where E0 is the peak electric field, f(t’) is the pulse envelope function (-1 > f(t’) > +1)and is the carrier-envelope phase, the electron will gain additional momentum p along the direction of polarization of the laser pulse. If the electron is born at a time t, t t p mx dt ' eE0 f t ' cos t ' dt ' If the rate of change of the pulse envelope is much less than that of the carrier wave (a good approximation even for ultrashort pulses), then eE f t p 0 sin t Only electrons ejected along the polarization direction, which is parallel to the axis of a time of flight spectrometer, are detected. The measured energy of these electrons is given by 2 p 2 p 0 p T T0 T 2m 2m where T0 X I P T p 0 p m T eV 2T0 E 0 f t sin t m T eV 2.5 10 10 T0 eV E 0 f t sin t For a peak intensity of 6.5 1014 Wcm-2, E0 = 7 109 Vm-1 and T0 = 71.5 eV, T 15 f t sin t eV Therefore the time evolution of the electric field f t cos t can be directly re-produced by differentiation the electron energy spectrum. This demonstration of the fastest measurements ever made is shown in Figure 19(a). The reconstructed electric field shown in Figure 19(b) can be seen to have the zero phase expected for the production of the single attosecond pulse. Figure 19: (a) Electron energy distribution produced from ionization of Ne with a 93 eV attosecond pulse in the presence of an ultrashort laser pulse. (b) Electric field of the laser pulse reconstructed from differentiation of (a), see reference [9] These techniques have already been used to directly measure the lifetime of an M-shell vacancy in Kr [10]. This shows the future potential for measuring electronic quantum phenomena with unprecedented time resolution. 2.7 Femtosecond and Attosecond Resources in the UK The UK is at the fore-front of the study of ultra-fast processes. Attosecond sources are under development through an RCUK Basic Technology programme led by Imperial College(IC) with Reading, Oxford, University College London (UCL), Birmingham and the Rutherford Appleton Laboratory (RAL) as partners www.attosecond.org. The Central Laser Facility in UK is located at RAL and intense, femtosecond pulses are available at the ASTRA laser. Current specifications of this laser system are given below and through involvement in the attosecond programme, will be upgraded to include carrier-envelope phase stabilized pulses and an attosecond XUV source. Laser ASTRA TA2 ASTRA TA1 Repetition Rate 1kHz 1kHz 10Hz 10Hz 10 Hz Compressor Prism Prism then Fibre Grating Grating then Fibre Grating Pulse Length 30fs 10fs 35fs 10fs 40 fs Energy per Pulse 0.8mJ 0.3mJ 16mJ 0.5mJ 500 mJ Max Intensity Wcm-2 1016 1016 1017 1016 1019 Current specifications of the ASTRA laser at RAL http://www.clf.rl.ac.uk/Facilities/AstraWeb/AstraMainPage.htm There are a number of other University based high power femtosecond laser systems in the UK. These include (not an exclusive list) IC www.imperial.ac.uk/research/qols Strathclyde tops.phys.strath.ac.uk/main.html Reading www.ull.rdg.ac.uk/ UCL and Queen’s University Belfast also have systems in development. References [1] Quantum control of gas-phase and liquid-phase femtochemistry T. Brixner and G. Gerber, ChemPhysChem 4, 418 (2003) [2] Magnetic field paralleliser for 2 electron-spectrometer and electron-image magnifier P. Kruit and F.H. Read, J. Phys. E, 16, 313 (1983) [3] Ionization Dynamics in Strong Laser Fields L. F. DiMauro and P. Agostini, Adv. At. Mol. Opt. Phys., 35, 79 (1995) [4] Multiple Ionization in Strong Laser Fields R. Dörner et al., Adv. At. Mol. Opt. Phys., 48, (2002) [5] Multiple fragmentation of atoms in femtosecond laser pulses A. Becker, R. Dörner and R. Moshammer, J. Phys. B,. 38, S753 (2005) [6] Source of coherent kiloelectronvolt X-rays J. Seres et al., Nature, 433, 596 (2005) [7] Attosecond Metrology Comes of Age R. Kienberger and F. Krausz, Physica Scripta., T110, 32 (2004) [8] X-ray Pulses Approaching the Attosecond Frontier M. Drescher et al., Science 291, 1923 (2001) [9] Direct Measurement of Light Waves E. Goulielmakis et al., Science, 305, 1267 (2004) [10] Time-resolved atomic inner-shell spectroscopy M. Drescher et al., Nature, 419, 803, (2002)