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Varró Sándor1,2

1) MTA Wigner Fizikai Kutatóközpont, Budapest

2) ELI Att d Li ht P l S ELI HU N fit Kft S d2) ELI Attosecond Light Pulse Source, ELI-HU Nonprofit Kft, Szeged

Fizikus Vándorgyűlés, 24‐27 augusztus 2016, Szeged

Some open fundamental questions Some open fundamental questions of attosecond physics.Sá d V óFizikus Vándorgyűlés, 24‐27 August 2016, Szeged, Hungary

Sándor Varró

Outline of the talk.

• Introduction. Few recent historical notes.

• The question of locking of the high harmonics. Quantum phase uncertainties.

• The question of the proper boundary conditions for extremely short electromagnetic radiation pulses.

• Some special subjects (pair creation, Unruh radiation, source fields versus wandering waves, entropy in the Compton process). g , py p p )

• Summary and outlook.

SV, Open questions of attosecond physics. Fizikus Vándorgyűlés, 24‐27 August 2016, Szeged, Hungary.

Challenges for technology and science.

[ F. Krausz and M. Ivanov, Attosecond physics. Rev. Mod. Phys. 81,163-234 (2009) ]


The first proposal : Farkas & Tóth [ 1992 ]The first proposal : Farkas & Tóth [ 1992 ]

Innermost Bohr orbit of H

1as1

Varro_ECLIM_2010


“Dear Drs. Farkas and Toth,

Th k f i t ti l ttThank you for your interesting letter of June 22. So far we do not have any finished paper on atoms.

Quantum mechanical computationsQuantum mechanical computations for hydrogen atoms in an intense pulsed laser field by Ken Kulander at the Lawrence Livermore Laboratory and by Peter Lambropoulos at UCS

t i di t th t th h f thseem to indicate that the phases of the high harmonics vary in some complex way, so that the atoms do not emit Fourier-limited short pulses. However, more theoretical and experimentalmore theoretical and experimental work needs to be done, before the potential of such a scheme can be fully judged. In the meantime, we have put our writing on hold. …Yours sincerely,

Prof. T. W. Hänsch” [ Münich, July 09. 1992. ]


Classical Fourier synthesis of high-order harmonics.

)12.5(.)(2

11

22

11

)/(212

12

)/(2

nn

nn

iTtinn

knn

knn

Ttinin

nn eAeeAtE

111 12 nnknn

Synthesis of N = 15 higher-harmonics of the same intensity at the plateau region,the same intensity at the plateau region, according to (5.12); Real part and modulus with phase-locking. In the last figure the phase difference of thefigure the phase difference of the components are not constant (random).


2

nnoutgoing

znEmciTtnEiT

0

20 222exp

Possible description of (higher-order) processes in interaction of electrons and ‚photons’.‚photons .

PHOTONELECTRON

Trajectory, Ray(Geometric Optics)

Field; Wave(Maxwell Theory)

Quantized Field (True Photon)

Trajectory, current [Point, charged dust, Mechanics

1. 2. ClassicalElectrodynamicsClassical EM fields Radiation

3. Classicalcurrent, Classical(Poisson) photon

Mechanics, Hidrodynamics]

fields, Radiationreaction

Field; Wave. Transition

4. 5. SemiclassicalTheory [ Both

6. Quantum Optics QuantumTransition

Currents [WaveMechanics]

Theory. [ Both Wave ] [Schrödinger, KG, Dirac, Maxwell]

Optics. Quantum transitions + General Photon

Quantized Field [Electron-Positron (Hole) Field,Solid

7. 8. QED in External EMFields [e.g. e-e+

9. Full QED, paircreation andback- reaction of

State Physics] pair creation] charges


KINEMATIC EFFECTS DUE TO QUANTIZATION. This is an example which shows that the nonclassical nature of the strong light field can even manifest itself in the

difi ti f th HHG t Th ti dditi ll difi th fmodification of the HHG spectrum. The reaction additionally modifies the frequency.

ˆ VAi rad 0])ˆ([

22

200

nn C

n

2221 200 sinn

C

Varro_ECLIM_2010NNN /)(

Implementation of ELI‐ALPS, Phase 1GOP‐1.1.1‐12/B‐2012‐0001

Coherence effects. Is the HHG radiation a quantum mechanical product state ofquantum mechanical product state of coherent states, where h ’=n h ?

tinNnn

EeEtE

ˆ)(0

ff

nnnN EeEtE

)(

0

)()1( 000 Nnnnf

t

tttdieT )(ˆ)(ˆ E ififfi tttdT ),()(0

rEx

tin 0)(ˆ)()( dd tin

nnettet 0)(ˆ)()( dxd

10ˆ1)(ˆ AtE 101~),( At if rE


Illustrations for the quantum phase and projector functions of a quantized mode, in terms of the coherent state kernel functions.

cl( )

e(ei)

)( NENFA -

., DzzzzF

Fi 2 3 [ S V R l h d SU(1 1) h f h h i ill Ph i S i 90 ( ) 0 40 3Fig. 2-3 [ S. V., Regular phase operator and SU(1,1) coherent states of the harmonic oscillator. Physica Scripta 90 (7), 074053 (2015) ]


Time evolution of the physicalphase. [Blaschke part.]

10

Time evolution of the phases at < a+a > = 200

)0()0()( tUnbounded

5

10

ysic

alph

ase )0()0()(

00 tB t

)()()(0

ttt Bdyn

0

cal,

and

phy 0 y

Sum: Periodic

-10

-5

gle,

dyna

mic

ttdyn )0()(0

Unbounded

p

-5 0 5 10 15-15

ang p

qScaled Time radians


Hanbury Brown – Twiss correlation with an attosec pulse.

The left figure is just for comparison (thermal states; usual ‘photon bunching’). The right figure refers to a multimodeThe right figure refers to a multimode phase eigenstate (as a quantum model of an attosecond pulse). [The with of the curve is expected to be of order of fs.]

attosec

curve is expected to be of order of fs.]

21NNNNK

Poisson level

21 NN


Mandel’s Q parameter (Fano factor– 1 ) of the high harmonics.

21 NNK

21 NNK

1 )1(11 Fn

K

2nnF

2

Gombkötő Á, Czirják A, Varró S and Földi P, A quantum optical model for the dynamics of high harmonic generation. To appear in Physical Review A (2016).dynamics of high harmonic generation. To appear in Physical Review A (2016). arXiv: 1605.01087 [quant-ph], 2016.


The question of the theoretical description of switching–on/ off.

)cos()(),( 000 fFt εrE

/

cztct // rn

0/ czt

1/ czt

0.0

0.5

1.0

Ft

t = 1, j = -p2

-2 -1 0 1 2-1.0

-0.5

t T

Hack Sz, Varró S and Czirják A, Interaction of relativistic electrons with an intense laser pulse: High-order harmonic generation based on Thomson scattering.

S. V & F. Ehlotzky, Z. Phys. D 22, 691-628 (1992)

laser pulse: High order harmonic generation based on Thomson scattering.Nuclear Instruments and Methods in Physics Research B 369, 45-49 (2016)


Locking of very high-order harmonics stemming from a relativistic electron bunch.

Hack Sz, Varró S and Czirják A, Nucl. Instr. Meth. in Phys. Res. B 369, 45-49 (2016). Isolated attosecond XUV-soft X-ray pulse generation via nonlinear Thomson scattering. Poster at ELI-ALPS VUVX2016 [Ultrafast D namics and Time Resol ed Interactions VUVX SatelliteALPS VUVX2016 [Ultrafast Dynamics and Time-Resolved Interactions, VUVX Satellite Workshop, 26-28 June 2016, Szeged, Hungary]


J. SCHWINGER [1954]; Kritikus tér, párkeltésS. W. Hawking [1974], P. C. W. Davies [1975], W. G. UNRUH [ 1976 ]

2)/( mcmceEeE crCcr ecmEcr /32

cmVsinEcritical /103.1~ 16%100/ UU2

2mc

0

2mc0

eExxV )(MeVmc 12 2

aT 2

0/3

22 88 rhPdkTh

Unruh

Óriási gyorsulás a lézertértől.

ck2 0/3 31r

ecdtd kTh


„Hence at very great distance from the origin the field is practically a self-conjugate field and so the energy travels with a velocity verya self-conjugate field and so the energy travels with a velocity very nearly equal to the velocity of light.” [ e.g. Bateman, 1915 ]

041/1)4( 2222222 BEBEv 2 c4

K P d A L O th ib ti i th fi ld d H t i ill t Phil K. Pearson and A. Lee, On the vibrations in the field round a Hertzian oscillator. Phil. Trans. Roy. Soc. Ser. A (1900)SV, Open questions of attosecond physics. Fizikus Vándorgyűlés, 24‐27 August 2016, Szeged, Hungary.

In 1911 Planck published his so‐called‘second theory’ in which he gave

4Energy of the oscillator : U = ne + r 0 < r < e

second theory , in which he gaveplausible arguments for the ‘emissionpostulate’: (1–)/=p·u, i.e. the ratioof the probability that the oscillatordoes not emit and the probability of

3

emission is proportional with thespectral energy density u. Hecalculated p=c3/82h=B/A, where Band A are the ‘Einstein coefficients’(1916) From this it follows that

2

Ue

(1916). From this it follows thatPlancks’s emission coefficient=A/(A+B∙u) is the ratio of the‘spontaneous’ and the complete,‘spontaneous+induced’ emission

0

1

pprobability. 0 2 4 6 8

0

time a. u.

Figure 1. Illustrates Planck’s emission law [7], where the tilted straight lines represent the continuous energy increase of a particular oscillator When a straight line crosses athe continuous energy increase of a particular oscillator. When a straight line crosses a dotted line (corresponding to integer multiples of the energy quantum e=hn), then an emission may take place abruptly by chance, and a continuous increase of the energy starts again. In 1911 Planck derived the occupation probability of the n-th level P =bn/(1+b)1+n where b=[exp(h/kT)-1]-1 The time average of the fractional energy turnsPn b /(1+b) , where b [exp(h/kT) 1] . The time average of the fractional energy turns out to be h/2, which is just the ‘zero-point energy’. The distribution Pn is the so-called ‘Bose–Einstein distribution’, rediscovered by Bose in 1924. SV, Open questions of attosecond physics. Fizikus Vándorgyűlés, 24‐27 August 2016, Szeged, Hungary.

C l iConclusions

Aacct 01 A ...

B ...pUT0

C ...

D ...


Photoelectric effect [1926-30]. Expanding electron wave.

Wentzel G 1926 Zur Theorie des photoelektrischen Effekts Zeitschrift für Physik 40 574-589 (1926).Wentzel G 1927 Über die Richtungsverteilung der Photoelektronen Zeitschrift für Physik 41, 828- (1927).Sommerfeld A, 1929 Atombau und Spektrallinien. Wellenmechanische Ergänzungsband(Druck und Verlag von Friedr. Vieweg & Sohn Akt.-Ges., Braunschweig, 1929). Kapitel II. §4. Photo-effekt .

Sommerfeld A und Schur G, 1930 Über den Photoeffekt in der K-Schale..., Ann. der Physik (5) 4, 409-Bethe H 1930 Über die nichtstationare Behandlung des Photoeffekts Annalen der Physik (5) 4 443-449

S V,, 110 years of the photon. LPHYS’15. August 21-25, 2015, Shanghai. 37

‘EPR correlation’ with entangled photon – electron systems in high-intensity Compton scattering. I.

Electron detection

nsPh

oton

Photons

Photon detection

Electrons

S. V. : Entangled photon-electron states and the number-phase minimum uncertainty states of the photon field. New Journal of

Varro_CEWQO_2009

g p p y pPhysics, 10, 053028 (35 pages) (2008). Varró S : Entangled states and entropy remnants of a photon-electron system. Physica Scripta T140 (2010) 014038 (8pp).


‘EPR correlation’ with entangled photon – electron systems in high-intensity Compton scattering. II. Photon statistics depends on the position of the detected electron after high-intensity Compton scattering.

Varró S : Entangled photon electron states and the number phase minimum uncertainty states of the photon field

Varro_CEWQO_2009

Varró S : Entangled photon-electron states and the number-phase minimum uncertainty states of the photon field.New Journal of Physics, 10, 053028 (35 pages) (2008). Varró S : Entangled states and entropy remnants of a photon-electron system.Physica Scripta T140 (2010) 014038 (8pp)


Example for ‘EPR’. ‘Összegabalyodott’ Photon – Electron States Entropy remnants after high-intensity Compton scattering III.


Summary and outlook.

• The quantum characteristics of the extreme radiation pulses to be studied in ELI-ALPS are non-trivial. Higher-order correlation measurements (like HBT) may even improve the diagnostics.measurements (like HBT) may even improve the diagnostics.

• The theoretical description should be refined (reconsidered) towards beyond the dipole approximation (which have been almost exclusively

) fused by now). Importance of causal boundary conditions. „Voreilung” and delay in photoemission are to be studied in higher order transitions.

Th ti f th t d t fi ld t if (• The propagation of the generated extrem fields are not uniform (on nanometer ~ attosecond time scale), since they are not „wandering waves”

• The details of the switching – on and off of the strong exciting fields influence the degree of entanglement (entropy, reversibility) in the multiphoton scattering process (e g high-order Compton scattering)multiphoton scattering process (e.g. high-order Compton scattering).


Acknowledgements.

I thank joint works with my group members of the Strong Field and Quantum Optics Theory Group [ Attosecond and Strong Field Science Division of ELI-ALPS]; Drs. Imre Barna, Attila Czirják, Péter Földi, Szabolcs Hack Péter Mati Mónika PolnerSzabolcs Hack, Péter Mati, Mónika Polner.

This work has been supported by the Hungarian Academy of Sciences [ K pp y g y [104260] , and by the ELI-ALPS project . The ELI-ALPS project (GOP-1.1.1-12/B-2012-0001) is supported by the European Union and co-financed by the European Regional Development Fund.


THANK YOUTHANK YOUFOR YOURATTENTION!ATTENTION!

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