Correlation in the Sequential Release Of Two Electrons from Atomic Targets by Short Laser Pulses

Collaborators: A. S. Alnaser, X. M. Tong, P. Ranitiovic, I. Litvinuyk, and C.L. CockeChakra Man Maharjan

Sub femto-second Electrons dynamicsBasic Concept ArAr2+e1-e2-Fraction of an optical periodOptical period=2.6 fstE

OUTLINE

The Goal: to directly measure the time correlation between the two electrons and explore the clock that reads electronic dynamics of the system on sub-fs scale

Tool : Measure in COINCIDENCE the highly resolved momentum distributions of electrons and doubly-charged ions produced in the circularly polarized ultra short laser pulse.

What is achieved : the full vector momentum of the singly and doubly charged recoil ions (Ar and Ne) is measured. The ion momentum distributions can also be used to map the vector sum of the two emitted electrons momenta.

Mechanism????Sequential ionizationTunneling IonizationOver barrier ionizationE=Ip2/4ZeffP =E/At high laser intensities;

How electrons and ion gain momentum in laser field?Momentum conservation.

P=E(t)/P2P1Linearly polarized pulseCircularly Polarized pulseEFor ArElectric field for over the barrierAr : 0.0841 a.u. (Io=4.95x1014W/cm2)Ar+:0.1287 a.u. (Io= 1.16 x1015 W/cm2)E=E0 e-t2/T2 (x Sinwt+ y Coswt)How P1 and P2 related to E at time of release

P1=E1/P2=E2/= cos-1(P1.P2/|p1||p2|)t= /Angular correlation between two electronsTime correlation The second hand clock!!E1P1E2P2tPhase stabilized laser.

Experimental setupIon DetectorBYXJETe detectorZLaser(COLTRIMS)qn+e-Magnetic coilMeasure: Time and positionMirror

Electron raw data( time of flight) Tof (ns)Counts

Cyclotron Periodr(0.5 mm)TOF(ns)TcCalibration of parameters used in the experimentWiggles SpectrumPx=mc (X cot(ctof/2)+Y)/2Py=mc (Y cot(ctof/2)-X)/2

YZDistribution of electrons in the plane perpendicular to the direction of the laser propagation PoIo=4x1014 W/cm2Eo=PIo=coEo2PD~ 8 fsX

Ions Tofs and positionsTarget (jet)BackgroundPosition Image Time of Flight Ar+O2+Ar2+

Single and Double Ionization of Ar Target( Circular Polarization)

Big Problem.Random electron counts

True coincidence

Two ways to decrease random counts1.Decrease counts rate2.Decrease the size of target beam

laser focusspherical mirrorjetlaserUse piezoelectrical slits to minimize Volume effectsmanipulator

FWHM=0.43a.uPze1+PzrConservation of momentum !!!!Double CoincidenceIo=4x1014 W/cm2PD = 8 fs

Triple coincidencePze1+Pze2PzrPze1+Pze2+PzrIo=1.8x1015 W/cm2

How are these spectra related to the correlation between two electrons ?Ar2+ momentum spectraModel by:X.M.Tong & C.D.Lin

Ion momentum distribution reflects the vector sum of momenta of two electronsNe2+ momentum spectrumModel by:X.M.Tong & C.D.Lin

The sum momentum spectrum:Ne as test casepzCountsNe+Ne++

Ar2+Ne2+Ar2+P1-P2P1+P2P1+P2P1-P2Ne2+Momentum of electrons at the over barrier.

a.u.P13.732.7P22.2575.0P1-P20.72.3P1+P23.77.7

P1+P2P1-P2Momentum distribution of Ne2+ and Ar2+ in the polarization planeNe2+Ar2+(Io=4.5x1015 W/cm2)(Io=1x1016 W/cm2)

At the end1.Random (false) counts is the main problem to investigate the time correlation between two electrons emitted sequentially with coincident technique.2.we are pretty much successful to get angular correlation of two electrons using the doubly charged ion momentum spectra

Thank you. The title of my talk is the sequential release of two electrons from the atomic targets like Ne and Ar.The whole presentation is consists of two part. In the first part ,I dealt with the measurement of time correlation of two electrons and in that part you will see we where we are and what are the big problem that we are facing up. In the second part, we have tried to see the angular correlation in different way by measuring the momentum of doubly charged ion.Here is the basic concept of my experiment .The target atom interacts with the circularly polarized laser pulse by emitting two electrons. If we have really few optical cycle the time difference between two emissions will be the fraction of optical cycle. Here we can have clock to read the electrons dynamics in the sub femto-second regime. The clock starts with emission of the first electron and stops at the second emission. The electric field of rotating pulse acts as second had of our clock. What is mechanism? We rule out the re-scattering phenomena. we have such intensity regime that both electrons can be emitted sequentially. The well known mechanism of sequential ionization is ADK tunneling ionization. When laser interacts with atom, the potential seen by electrons is distorted or modified in the direction of field. There is certain probability for electron to tunnel out of barrier. The ionization rate increases exponentially with the laser intensity But what happens if laser is strong enough to suppress the barrier?. Then ionization rate starts from zero to1 directly like step function.The electric field necessary for over the barrier is proportional to the square ionization of ionization potential .Thus ionization potential solely determines the electric field of laser pulse required for first and second ionization potential. The values of corresponding momentum electrons are proportional to the electric field at time of ionization.How electrons and ion gains the momentum? The people usually may think about this system as explosion case. But the present system is not isolated system and there is external force due to laser field. When electron born ,its velocity is zero but it remains some time before it leaves the pulse and during that period it gains momentum. Ion also gains momentum in same way but there are two steps. The first electron is removed at to and the ion switches its charge from1+ to 2+ at time t1.If both electrons are removed without transferring to momentum to the ion, the ion momentum at tinfinity at the end of pulse with envelope of electric field is given by above second equation.How p1 and p2 related to E at the time of release? We have linear and circularly polarized pulses. Why we use the circularly polarized pulse in our experiment? Unlike the linear pulse ,the electric field vector of circularly polarized pulse rotates rather than oscillates, with a smoothly increasing and decreasing amplitude. The angle with which electron is lunched into the field then becomes a phase marker for the time of emission and pulse becomes a clock. If the second electron is released at later in the cycle, its momentum vector will make an azimuthal angle to that of the first electron which is a direct measure of the time elapsed between the two emissions. (The envelope represents the circularly polarized pulse. The electric field required for the electron to be released by over the barrier depends on the square of ionization potential. For example in Argon ,when the value of electric field reaches 0.084 a.u.,the first electron release by over the barrier and the electron the We can imagine our system as second hand of a clock. When first electron is released, the field of pulse at that instant becomes the starting of clock. and momentum vector of second emission makes an azimuthal angle with the momentum vector first electron. This angle gives the time between two emission. How we can measured the phase angle made by electric field between two emissions? The values of momentum at the instant of emission can be determined by the magnitude of electric field at these instant. Which in turn gives the angle between the momentum vectors of two electrons and equal to angle made by rotated electric field. Ultimately it gives time elapsed between two emission. Thus we have clock to read the first and second ionization.The first diagram presents how clock works on our real experimental situation.The second diagram is ideal case and can be true if we have really very short pulse and stabilized laserIntroduction: recoil momentum spectroscopyAxis: x-direction propagation of laser Y-jet direction Z-time direction (spectrometer axis) and three are mutually perpendicular to each other. The laser beam propagating in x direction falls on the spherical mirror and it focuses the beam at the geometrically cooled supersonic jet. The ion and electron released during the interaction are driven by electric field. In order to increase the acceptance angle for electron we use uniform magnetic field and strength of filed depends on the transverse energy of electron ,which in turn depends on the intensity of laser. The electrons move in cyclotron path in magnetic field. Hence we will get the information on time and position by mcp and delay line detector. Experimentally we measure the time of flight and position of electrons and later these information are used to construct the different components of momentum ,energy and angle.This is so called wiggle spectrum. It is the 2D plot between the distance of the electron hitting at the point on the detector plane from its center and their time of flight.Special features1.This spectrum can be used to calibrate the strength of magnetic field very accurately by calculating the distance between the nodes.2.Nodes are the time of flight for those electron which reach at detector center and their time of flight is integer multiple of cyclotron frequency . This is the image of the momentum distribution in the polarization plane where y and z axis represent the direction of jet and time respectively. The radius of the donut gives the momentum of the electron in the circular polarization. The beauty of this spectrum is that we can estimate the peak intensity of laser field with less than 20% error.Let us turn to the recoil side. Similar to electron , we need at least time and position for calculating the momentum and energy of recoil ion. We can see several peaks in the first uppermost spectrum. These are time of flight for different molecules and atoms. The most pronounced two peaks are the time of flight for singly and doubly charged argon ion. Since the time of flight is directly proportional to square root of the ratio of mass to charge and hence we will expect to see the higher charged ions have shorter time of flight and vice versaTwo other graphs in inset are the zooming of the time flight of Ar+ and Ar2+ and structures clearly resembles that these ions are produced by circularly polarized pulse.Let us turn to the recoil side. Similar to electron , we need at least time and position for calculating the momentum and energy of recoil ion. We can see several peaks in the first uppermost spectrum. These are time of flight for different molecules and atoms. The most pronounced two peaks are the time of flight for singly and doubly charged argon ion. Since the time of flight is directly proportional to square root of the ratio of mass to charge and hence we will expect to see the higher charged ions have shorter time of flight and vice versaTwo other graphs in inset are the zooming of the time flight of Ar+ and Ar2+ and structures clearly resembles that these ions are produced by circularly polarized pulse.Spatial variation of laser intensity around focuses ,with different processes occurring simultaneously in various parts of the focal volume. We can see clearly that the central part is more intense that outside .the probability of producing the multiple charge depends on the intensity of the specific region. Multiple electric charged ions are produced from the central portion of target beam and weaker intensity region of focal volume mainly produce the singly charged ion from the side of target beam.This is the situation we really want to have. Here the two electrons are produced by the peak intensity from the argon atom. If we measured the doubly charged argon ion and two electron simultaneously, then we can apply our coincidence technique. we will virtually free from any kinds of random.But technically this is very tedious task to achieve this situation in our experiment. The main difficulty is that we cannot make out jet much thinner that it only passes through the peak part of intensity in focal volume.But we singnficantly success to achieve the thinnner jet.What happen if we measured the doubly charged argon ion and two electron produced from the singly charged argon ions? Clearly we cannot use the coincidence technique. Because the we cannot use momentum conservation law.In our case we have both kinds of situation at same time .We measured the electrons and the ions at same time. It is much easier to filter out doubly charged argon ion. what we need to do just put gate over the time of flight of Ar2++.But problem is we cannot separate electrons whether they come out form singly and doubly charged argon ion.One way to achieve more true counts than random is make jet thinner so that it only passes through middle part or intense part of focal part. This can be done by using piezoelectric slit before the focus. Before the slit, the size jet is 2mm and the size of jet on the focal volume can be varied any desired value from 2mm to 45 m by changing the value voltgae throuh the slits.1.This electric swithc helps in our experiment in two ways..It make our jet so thin that we can have ions from only intense part of focal volume and hereby effectively reduces the problem of volume effect.2.To make thin jet is to have less counts of ions and electrons on the detectorThis is the test of momentum conservation law before going to apply the three particle coincidence technque.The plot is the momentum of singly charged ion and electron in z direction. The statistics on the diagonal are mostly true counts and off diagonal lines are random. This picture present the beautiful picture of conservation law. Try to catch any point on the diagonal line ,one can see the good illustration of momentum conservation. At any point on the diagonal ,there will be equal and opposite momentum of electron and ion. If we project the this spectra parallel to diagonal, we will observe the peak at zero of sum of momentum.we can see that the ratio of random to true is still high.This spectrum is the plot of the sum of z component of the momentum of the two electrons released from argon atom versus the z component of momentum of doubly charged argon ion. It is dominated by random counts but the good news is that we see the events of of true counts which we can see along the diagonal of spectrum. The importance of this spectrum is that we can purify the true signals from random. In order to calculate the correlation between two electrons ,we have to make sure that the electrons are real. One possibility is that we can select electrons from the diagonal part of spectrum. Set the gate over the peak on the triple sum of momentum in z direction. But the problem is that we will loose much statistics for the distributions.This is time of flight for argon ions at different intensities.The higher the intensities ,we have higher the mulitple ionization of argon.We have very good ratio of singly and doubly charged ration of argon.This is best condition to run the experiment and the trouble is that we cannot use that much intensity For argon the difference in the first and second ionization potential is very low .The momentum gained by two electrons emitted by over the barrier, are nearly equal in magnitude. The middle peak which is almost close to zero correspond to the difference in momentum . The another peak at value corresponds to the vector sum of two momentum vectors moving in same direction. The distribution between two peaks is all possible angles between two velocity vectors of electrons. The experimental data is compared with theoretical calculations.SummaryThree possibilites1.Two electrons in release in same direction.The vector momentum of two electrons are added up-peak having Large value of momentum2.Two electrons release in oppsite direction.The difference in momentum vector peak close to zero3.The two electron release in such way that the momentum vector of them make an angle .the the resultant of the two vector- distribution between two peaks.Special featurs1.Momentum of doubly charged neon is equal to the vector sum of momentum of two electrons.2.Difference in ionization potential for the first and second ionization is large. Hence momentum gain by the two electrons are also large as according to over the barrier rule.3.First peak- corresponds to the vector difference of momentum of two electrons release in opposite direction.4.Second peak- corresponds to the vector sum of momentum of two electrons release in same direction5.Black curve-corresponds to the momentum of ion in the circularly polarized pulse in z- direction. This is the projection of circle in z direction. since the first ionization occurs usually in weak in intensity at its peak field.Since the momentum of electron release at the subsequent ionization depends upon the electric field of laser pulse at the time of ionization which in turn depends upon the ionization potential of atom. Two electrons can have vector sum of different combinations. The two peaks corresponding to the electrons having drift velocity in same and opposite directions. The distribution between two peaks corresponds to the different angles between two electrons at the time of release.The table shows the momentum gained by electron at first and second ionization for argon and neon target. The sum of vector momenta is corresponding the momentum when both electrons move in same direction. The difference is for the case when both electrons are moving in opposite direction. FeaturesFirst peak- corresponds to sum momenta vector ( =0)Second peak correspods to difference momenta vector (=)Distribution between two peaks (= between 0 and )This is another way to see the angular correlation between two electrons. The two rings give the sum and difference of momentum vectors of two electrons. The gap between two rings in neon is much higher than on argon. The difference in ionization potential in two cases explains the reason behind the difference.