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atom interacting with the intense laser field ( ilf ) can absorb more than one photon and then emits photons at harmonics of the laser frequency , which is well known as high - order harmonic generation ( hhg ) @xcite .
the harmonic spectrum has the following characteristics as a function of increasing frequency : a rapid decrease in harmonic intensity at first , followed by a plateau region with the harmonics having similar intensities ; and then a rapid drop in harmonic strength beyond the plateau region .
recently , lots of theoretical works have studied this multiphoton phenomenon , including solving the time - dependent schrdinger equation @xcite , the semiclassical trajectory methods , such as the three - step model @xcite and the feynman s path - integral approach in the strong field approximation @xcite , and even the classical trajectory method @xcite .
bohmian mechanics ( bm ) @xcite , or called quantum trajectory method @xcite , is another alternative formalism of quantum mechanics . in the early years
, bm has been used to study some fundamental quantum phenomena such as the scattering by a square potential barrier @xcite and the diffraction through two slits @xcite .
recently , it has been applied to study and analyze many different processes and phenomena in physics and chemistry , such as atom - surface scattering @xcite , electron transport in mesoscopic systems @xcite , photodissociation of nocl and no@xmath0 @xcite , and the chemical reactions @xcite .
also , bm in terms of quantum trajectory has been considered to study chaos @xcite .
recently , it has been successfully applied to the intense laser - atom physics to study the dynamics of the above - threshold ionization ( ati ) photoelectron by authors @xcite .    in this paper ,
bm is introduced to the intense laser - atom physics to study hhg , which allows us to follow the time evolution of individual electron trajectory in atomic system first .
we then calculate the power spectrum with the electron trajectory and find the corresponding spectrum is irregular .
next , we consider the power spectrum associated with an atom ensemble . in the atom ensemble , harmonic generation is determined by the maxwell equation , where the electronic polarization of the atom ensemble plays a key role for the harmonic generation .
we will show the electronic polarization of the atom ensemble gained from bm is equivalent to that obtained from quantum mechanics . on this condition ,
the power spectrum from bm is regular and consistent with that obtained from quantum mechanics .
finally , we will briefly discuss the reason why an individual electron trajectory generates the irregular spectrum .
this paper is organized as follow : we will briefly introduce quantum trajectory method first .
then we show the hamiltonian for the hydrogen atom in ilf . in sec .
iv , we calculate the harmonic spectrum from a single electron trajectory , following by harmonic generation associated with an ensemble of atoms interacting with the ilf in sec .
v. finally , we briefly discuss the reason of the generation of the irregular spectrum with an individual electron trajectory and then conclude .
quantum trajectory method comes from the following transformation of the time - dependent schrdinger equation @xcite .
firstly a wave function can be written in the polar form @xmath1 .
secondly @xmath2 is substituted into the time - dependent schrdinger equation .
then the real part of the resulting equation is@xmath3 and the imaginary part has the form @xmath4 where @xmath5 , @xmath6 , and @xmath7 .
these two equations look like the classical hamilton - jacobi equation and the equation of continuity , respectively , except eq .
( [ h1 ] ) has an extra term @xmath8 which is usually called quantum potential in bm .
( [ h1 ] ) is called the quantum hamilton - jacobi equation governed by an external potential @xmath9 and the quantum potential @xmath8 .
the motion of particle is guided by the bohm - newton equation of motion , @xmath10 , or , equivalently , by @xmath11 in practice , we solve the time - dependent schrdinger equation to obtain @xmath2 , and then @xmath12 . in this way
, the quantum trajectory of the particle can be gained by integrating eq .
( [ eq ] ) .
the schrdinger equation for hydrogen atom in ilf can be written as ( atomic units are used throughout ) @xmath13\psi(\mathbf{r},t).\ ] ] here @xmath14 is the field - free hydrogen atom hamiltonian and @xmath15 is the intense laser - atom interaction : @xmath16 @xmath17 where the laser field is the linearly polarized field ( @xmath18 ) and @xmath19 is the laser field profile . due to the linearly polarized laser field ,
magnetic quantum number @xmath20 of hydrogen atom is a good quantum number , so that the problem of solving the time - dependent schrdinger here can be simplified into a two - dimensional problem ( see the inset in fig .
1 ) . in this work
the solution of the time - dependent schrdinger equation @xmath2 is obtained by the grid method and the second - order split - operator method , which has been detailedly introduced by tong _ et al _ @xcite .
the laser field profile is @xmath21 where @xmath22 , and @xmath23 and @xmath24 are the electric field amplitude and angular frequency , respectively .
we choose @xmath25 a.u .
( i.e. , @xmath26w/@xmath27 ) , and @xmath28 a.u .
( i.e. , @xmath29 nm ) .
the initial wave function @xmath30 of the system is in the ground state of the field - free hydrogen atom .
after obtaining the wavefunction @xmath2 , we can follow the time evolution of electron trajectory @xmath31 by integrating eq . ( [ eq ] ) with the electron initial position @xmath32 . according to bm @xcite ,
the initial electron distribution is @xmath33 . in this work
, @xmath30 is the ground state of the field - free hydrogen atom .
thus we can obtain an ensemble of electron trajectories with the corresponding electron initial positions .
for an individual electron trajectory , the atomic dipole moment @xmath34 along the laser polarization direction is @xmath35 .
the corresponding power spectrum is gained by the fourier transformation of the dipole moment @xcite : @xmath36 where @xmath37 and the propagation time @xmath38 is @xmath39 in this work .
explicitly , we take one atomic electron as an example with the initial position @xmath40 a.u . , @xmath41 in polar coordinates .
the electron trajectory @xmath31 is calculated by integrating eq .
( [ eq ] ) . the corresponding power spectrum is shown in fig . 1 from eq . ( [ fd ] ) .
the spectrum has even harmonics , which is dominated by a rayleigh scattering component at the laser frequency @xmath42 .
we have obtained lots of electron trajectories with different initial position @xmath32 according to the initial electron distribution @xmath43 .
the corresponding power spectra have the similar character described above . in the following ,
however , we will show the even harmonics of the power spectrum are coherently removed in an ensemble of atoms and the corresponding power spectrum is consistent with that obtained from quantum mechanics .
the harmonic generation of an atom ensemble can be gained with the maxwell equation @xcite:@xmath44 where @xmath45 is the electronic polarization of the atom ensemble at the point @xmath46 and @xmath47 describes the electromagnetic field ( involving the fundamental and the harmonic fields ) .
obviously , the electronic polarization @xmath45 plays a key role for the harmonic generation from the ensemble of atoms .
we will show that the electronic polarization @xmath45 gained from bm is , approximately , equivalent to that obtained from quantum mechanics , i.e. , both of their harmonic spectra from the atom ensemble are consistent .
we first assume the number of atoms is @xmath48 in a small volume @xmath49 near the point @xmath46 in the atom ensemble ( @xmath50 , where @xmath51 is the focal spot size of laser ) . the electronic polarization @xmath52 is defined as the atomic dipole moment per unit volume : @xmath53 , where @xmath54 is the atomic dipole moment of each atom in the small volume @xmath55 . from the view point of quantum mechanics ,
the dipole moment of each atom is @xmath56 in the @xmath57 direction , where @xmath58 is the electron coordinate of atomic system and @xmath2 is the electron wavefunction .
thus the electronic polarization of the atom ensemble obtained from quantum mechanics is @xmath59 in the @xmath57 direction .
[ 2 ]     on the other hand , we calculate the electronic polarization of the atom ensemble from bm . according to bm @xcite , the probability that an electron lies between @xmath58 and @xmath60 in the atomic system at the time @xmath61 is given by @xmath62 , where the corresponding atomic dipole moment is @xmath58 ( in atomic units ) .
then in the small volume @xmath55 of the atom ensemble , the number of atoms with atomic dipole moment @xmath58 is @xmath63 .
the sum of all kinds of atomic dipole moments in the volume @xmath55 is @xmath64 .
thus the electronic polarization @xmath45 at the point @xmath46 in the atom ensemble is @xmath65 ( see fig .
2 ) . for an atom ensemble
, we can replace the sum by an integral , @xmath66 further , because the laser field is the linearly polarized field ( @xmath18 ) , the time - dependent wavefunction @xmath2 is symmetrical along @xmath57 axis .
thus in the @xmath57 direction , @xmath67 where the last term equals eq .
( [ s ] ) . in this way ,
the electronic polarization @xmath45 gained from bm is , approximately , equivalent to that obtained from quantum mechanics , i.e. , both of their harmonic spectra from the atom ensemble are the same .
figure 3 shows the harmonic spectrum from an ensemble of hydrogen atoms interacting with ilf ( laser confocal parameter @xmath68 mm , gas density @xmath69 atoms/@xmath70 described by a truncated lorentzian in the @xmath71 direction with @xmath72 mm @xcite ) , which has a clear plateau region and cutoff at the @xmath73th order .
in bm , harmonic spectrum from a single electron trajectory has even harmonics ( see fig .
1 ) , but they are removed in the spectrum associated with an ensemble of atoms ( see fig .
the reason is that an individual electron trajectory does not possess an inversion center @xcite , but the electron trajectories of the atom ensemble have such centre . here
we will numerically show that two electron trajectories are enough to get rid of the unphysical even harmonics if the initial positions @xmath32 of the two electrons are centrally symmetric .
let s take two electrons as an example with the initial positions @xmath74 a.u . , @xmath41 and @xmath75 a.u . , @xmath76 , respectively .
the corresponding atomic dipole moment @xmath34 along the laser polarization direction is @xmath77 $ ] and the power spectrum gained from eq .
( 4 ) is shown in fig .
4 ( solid curve ) , which has only odd - order harmonics .
in addition , we calculate the hhg power spectrum in the length form from the time - dependent schrdinger equation ( dotted curve in fig .
4 ) @xcite .
note that these two curves can basically overlap if the value of the power spectrum from bm is multiplied by a factor of 0.4 , i.e. , both of them have the same relative intensity .
this is an interesting result , but the reason why hhg power spectra from bm and the time - dependent schrdinger equation have the same relative intensity should be studied in the future .
in summary , we introduce bm into the intense laser - atom physics to discuss hhg .
it allows us to follow the time evolution of each electron trajectory in an atomic system .
we find that the power spectrum from an individual electron trajectory has the even unphysical harmonics .
but the even harmonics are coherently removed in the ensemble of atoms and the power spectrum is consistent with that obtained from quantum mechanics .
the reason of the appearance of the even harmonics is an individual electron trajectory does not possess an inversion center , but the electron trajectories of the atom ensemble have such centre .
sanz a s , borondo f and miret - arts s 2004 _ phys .
b _ * 69 * 115413 ; 2004 _ j. chem .
phys . _ * 120 * 8794 ; 2002 _ j. phys . : condens
* 14 * 6109 ; 2001 _ europhys .
lett . _ * 55 * 303 ; 2000 _ phys . rev .
b _ * 61 * 7743
this paper introduces bohmian mechanics ( bm ) into the intense laser - atom physics to study high - order harmonic generation . in bm 
 , the trajectories of atomic electrons in intense laser field can be obtained with the bohm - newton equation . the power spectrum with the trajectory of an atomic electron 
 is calculated , which is found to be irregular . 
 next , the power spectrum associated with an atom ensemble from bm is considered , where the power spectrum becomes regular and consistent with that from quantum mechanics . finally , the reason of the generation of the irregular spectrum is discussed .