{{Short description|Rapid removal of two electrons from an atom}} '''Double ionization''' is a process of formation of doubly charged ions when laser radiation or charged particles like electrons,<ref>{{Cite journal |last1=Berakdar |first1=J. |last2=Lahmam-Bennani |first2=A. |last3=Dal Capello |first3=C. |date=2003 |title=The electron-impact double ionization of atoms: an insight into the four-body Coulomb scattering dynamics |url=https://www.sciencedirect.com/science/article/abs/pii/S037015730200515X |journal=Physics Reports |volume=374 |issue=2 |pages=91–164 |doi=10.1016/S0370-1573(02)00515-X|bibcode=2003PhR...374...91B |url-access=subscription }}</ref> positrons<ref>{{Cite journal |last1=Simonović |first1=N. |last2=Lukić |first2=D. |last3=Grujić |first3=P. |date=2005 |title=Double ionization by positrons near threshold |url=https://iopscience.iop.org/article/10.1088/0953-4075/38/17/006 |journal=J. Phys. B |volume=38 |issue=17 |pages=3147–3161 |doi=10.1088/0953-4075/38/17/006|bibcode=2005JPhB...38.3147S |url-access=subscription }}</ref> or heavy ions<ref>{{Cite journal |last1=DuBois |first1=R.D. |last2=Santos |first2=A.C.F. |last3=Manson |first3=S.T. |date=2014 |title=Empirical formulas for direct double ionization by bare ions: 𝑍=−1 to 92 |url=https://journals.aps.org/pra/abstract/10.1103/PhysRevA.90.052721 |journal=Physical Review A |volume=90 |article-number=052721 |doi=10.1103/PhysRevA.90.052721}}</ref> are exerted on neutral atoms or molecules. Double ionization is usually less probable than single-electron ionization. Two types of double ionization are distinguished: sequential and non-sequential.

==Sequential double ionization== Sequential double ionization is a process of formation of doubly charged ions consisting of two single-electron ionization events: the first electron is removed from a neutral atom/molecule (leaving a singly charged ion in the ground state or an excited state) followed by detachment of the second electron from the ion.<ref name=Delone_2000> {{Cite book | last1=Delone | first1=N. B. | author2-link=Vladimir P. Krainov | last2=Krainov | first2=V. P. | title=Multiphoton Processes in Atoms | publisher=Springer | year=2000 | isbn=3-540-64615-9| author1-link=Nikolai Borisovich Delone }}, chapter 8. </ref>

{{Gallery |title=Examples of sequential double ionization |align=center |width=320 |height=320 |File:Sequential double ionization.pdf|Sequential double ionization |File:NSDI through the ionic ground state.pdf|Sequential double ionization via an ionic exited state }}

==Non-sequential double ionization== Non-sequential double ionization is a process whose mechanism differs (in any detail) from the sequential one. For example, both the electrons leave the system simultaneously (as in alkaline earth atoms, see below), the second electron's liberation is assisted by the first electron (as in noble gas atoms, see below), etc.

The phenomenon of non-sequential double ionization was experimentally discovered by Suran and Zapesochny for alkaline earth atoms as early as 1975.<ref name=Suran_1975>{{Cite journal | last1=Suran | first1=V. V. | last2=Zapesochny | first2=I. P. | volume=1 | year = 1975 | journal = Sov. Tech. Phys. Lett. | page = 420 | title=Observation of Sr<sup>2+</sup> in multiple-photon ionization of strontium|issue=11}} </ref> Despite extensive studies, the details of double ionization in alkaline earth atoms remain unknown. It is supposed that double ionization in this case is realized by transitions of both the electrons through the spectrum of autoionizing atomic states, located between the first and second ionization potentials.<ref name=Lambropoulos_1988> {{Cite journal | last1 = Lambropoulos | first1 = P. | last2 = Tang | first2 = X. | last3 = Agostini | first3 = P. | last4 = Petite | first4 = G. | last5 = L'Huillier | first5 = A. | title = Multiphoton spectroscopy of doubly excited, bound, and autoionizing states of strontium | doi = 10.1103/PhysRevA.38.6165 | journal = Physical Review A | volume = 38 | issue = 12 | pages = 6165–6179 | year = 1988 | pmid = 9900374|bibcode = 1988PhRvA..38.6165L }} </ref> <ref name=Bondar_1993>{{Cite journal | last1=Bondar' | first1=I. I. | last2=Suran | first2=V. V. | journal=JETP | volume=76 | issue=3 | year=1993 | page=381 | title=The two-electron mechanism of Ba<sup>2+</sup> ion formation in the ionization of Ba atoms by YAG-laser radiation | url=http://www.jetp.ac.ru/cgi-bin/e/index/e/76/3/p381?a=list | archive-url=https://archive.today/20121221095534/http://www.jetp.ac.ru/cgi-bin/e/index/e/76/3/p381?a=list | archive-date=December 21, 2012 | bibcode=1993JETP...76..381B }}</ref> <ref name=Bondar_1998>{{Cite journal | last1 = Bondar' | first1 = I. I. | last2 = Suran | first2 = V. V. | doi = 10.1134/1.567802 | title = Resonance structure of doubly-charged-ion production during laser dielectronic ionization of atoms | journal = Journal of Experimental and Theoretical Physics Letters | volume = 68 | issue = 11 | page = 837 | year = 1998 |bibcode = 1998JETPL..68..837B | s2cid = 120658599 }}</ref> <ref name=Bondar_2000>{{Cite journal | last1 = Bondar | first1 = I. I. | last2 = Suran | first2 = V. V. | last3 = Dudich | first3 = M. I. | doi = 10.1088/0953-4075/33/20/304 | title = Resonant structure in doubly charged ion formation during multiphoton ionization of Sr and Ba atoms by infrared laser radiation | journal = Journal of Physics B: Atomic, Molecular and Optical Physics | volume = 33 | issue = 20 | page = 4243 | year = 2000 |bibcode = 2000JPhB...33.4243B | s2cid = 250826815 }}</ref> <ref name=Liontos2004>{{Cite journal | last1 = Liontos | first1 = I. | last2 = Bolovinos | first2 = A. | last3 = Cohen | first3 = S. | last4 = Lyras | first4 = A. | title = Single and double ionization of magnesium via four-photon excitation of the 3p^{2}^{1}S_{0} autoionizing state: Experimental and theoretical analysis | doi = 10.1103/PhysRevA.70.033403 | journal = Physical Review A | volume = 70 | issue = 3 | article-number = 033403 | year = 2004 |bibcode = 2004PhRvA..70c3403L }}</ref> <ref name=Liontos2010>{{Cite journal | last1 = Liontos | first1 = I. | last2 = Cohen | first2 = S. | last3 = Lyras | first3 = A. | doi = 10.1088/0953-4075/43/9/095602 | title = Multiphoton Ca2+production occurring before the onset of Ca+saturation: Is it a fingerprint of direct double ionization? | journal = Journal of Physics B: Atomic, Molecular and Optical Physics | volume = 43 | issue = 9 | article-number = 095602 | year = 2010 |bibcode = 2010JPhB...43i5602L | s2cid = 119869086 | url = https://hal.archives-ouvertes.fr/hal-00630010/document }}</ref>

[[File:Simultaneous photo-detachment of two electrons.pdf|thumb|center|300px|Non-sequential double ionization in alkaline earth atoms]]

For noble gas atoms, non-sequential double ionization was first observed by L'Huillier.<ref name="L'Huillier_1982"> {{Cite journal | last1 = l'Huillier | first1 = A. | last2 = Lompre | first2 = L. | last3 = Mainfray | first3 = G. | last4 = Manus | first4 = C. | title = Multiply Charged Ions Formed by Multiphoton Absorption Processes in the Continuum | doi = 10.1103/PhysRevLett.48.1814 | journal = Physical Review Letters | volume = 48 | issue = 26 | page = 1814 | year = 1982 |bibcode = 1982PhRvL..48.1814L }} </ref><ref name="L'Huillier_1983"> {{Cite journal | last1 = l'Huillier | first1 = A. | last2 = Lompre | first2 = L. A. | last3 = Mainfray | first3 = G. | last4 = Manus | first4 = C. | title = Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 μm | doi = 10.1103/PhysRevA.27.2503 | journal = Physical Review A | volume = 27 | issue = 5 | page = 2503 | year = 1983 |bibcode = 1983PhRvA..27.2503L }} </ref>&nbsp; The interest to this phenomenon grew rapidly after it was rediscovered<ref name=Walker_1993> {{Cite journal | last1 = Walker | first1 = B. | last2 = Mevel | first2 = E. | last3 = Yang | first3 = B. | last4 = Breger | first4 = P. | last5 = Chambaret | first5 = J. | last6 = Antonetti | first6 = A. | last7 = Dimauro | first7 = L. | last8 = Agostini | first8 = P. | doi = 10.1103/PhysRevA.48.R894 | title = Double ionization in the perturbative and tunneling regimes | journal = Physical Review A | volume = 48 | issue = 2 | pages = R894–R897 | year = 1993 | pmid = 9909791|bibcode = 1993PhRvA..48..894W }} </ref><ref name=Walker_1994> {{Cite journal | last1 = Walker | first1 = B. | last2 = Sheehy | first2 = B. | last3 = Dimauro | first3 = L. | last4 = Agostini | first4 = P. | last5 = Schafer | first5 = K. | last6 = Kulander | first6 = K. | doi = 10.1103/PhysRevLett.73.1227 | title = Precision Measurement of Strong Field Double Ionization of Helium | journal = Physical Review Letters | volume = 73 | issue = 9 | pages = 1227–1230 | year = 1994 | pmid = 10057657|bibcode = 1994PhRvL..73.1227W }} </ref> in infrared fields and for higher intensities. Multiple ionization has also been observed.<ref name=Rudenko_2004> {{Cite journal | last1 = Rudenko | first1 = A. | last2 = Zrost | first2 = K. | last3 = Feuerstein | first3 = B. | last4 = De Jesus | first4 = V. | last5 = Schröter | first5 = C. | last6 = Moshammer | first6 = R. | last7 = Ullrich | first7 = J. | title = Correlated Multielectron Dynamics in Ultrafast Laser Pulse Interactions with Atoms | doi = 10.1103/PhysRevLett.93.253001 | journal = Physical Review Letters | volume = 93 | issue = 25 | year = 2004 | pmid = 15697894|arxiv = physics/0408065 |bibcode = 2004PhRvL..93y3001R | article-number=253001| s2cid = 40450686 }} </ref><ref name=Zrost_2006> {{Cite journal | last1 = Zrost | first1 = K. | last2 = Rudenko | first2 = A. | last3 = Ergler | first3 = T. | last4 = Feuerstein | first4 = B. | last5 = Jesus | first5 = V. L. B. D. | last6 = Schröter | first6 = C. D. | last7 = Moshammer | first7 = R. | last8 = Ullrich | first8 = J. | doi = 10.1088/0953-4075/39/13/S10 | title = Multiple ionization of Ne and Ar by intense 25 fs laser pulses: Few-electron dynamics studied with ion momentum spectroscopy | journal = Journal of Physics B: Atomic, Molecular and Optical Physics | volume = 39 | issue = 13 | pages = S371 | year = 2006 |bibcode = 2006JPhB...39S.371Z | s2cid = 122414336 }} </ref>&nbsp; The mechanism of non-sequential double ionization in noble gas atoms differs from the one in alkaline earth atoms. For noble gas atoms in infrared laser fields, following one-electron ionization, the liberated electron can recollide with the parent ion.<ref name=Corkum_1993> {{Cite journal | last1 = Corkum | first1 = P. | title = Plasma perspective on strong field multiphoton ionization | doi = 10.1103/PhysRevLett.71.1994 | journal = Physical Review Letters | volume = 71 | issue = 13 | pages = 1994–1997 | year = 1993 | pmid = 10054556|bibcode = 1993PhRvL..71.1994C | s2cid = 29947935 | url = https://nrc-publications.canada.ca/eng/view/accepted/?id=c16dde3a-0d05-4437-bca6-3292fdd9d9ff }} </ref><ref name=Kuchiev_1987>{{Cite journal | last1 = Kuchiev | first1 = M. Y. | title = Atomic Antenna | journal = JETP Letters | year = 1987 | volume = 45 | page = 404 | url = http://www.jetpletters.ac.ru/ps/1241/article_18763.shtml | archive-url = https://archive.today/20121221145821/http://www.jetpletters.ac.ru/ps/1241/article_18763.shtml | archive-date = December 21, 2012 | bibcode = 1987JETPL..45..404K }}</ref> This electron acts as an "atomic antenna",<ref name=Kuchiev_1987/> absorbing the energy from the laser field between ionization and recollision and depositing it into the parent ion. Inelastic scattering on the parent ion results in further collisional excitation and/or ionization. This mechanism is known as the three-step model of non-sequential double ionization, which is also closely related to the three step model of high harmonic generation.

Dynamics of double ionization within the three-step model strongly depends on the laser field intensity. The maximum energy (in atomic units) gained by the recolliding electron from the laser field is <math>\sim 3.2 U_p</math>,<ref name=Corkum_1993/> where <math>U_p=\frac{F^2}{4\omega^2}</math> is the ponderomotive energy, <math>F</math> is the laser field strength, and <math>\omega</math> is the laser frequency. Even when <math>3.2 U_p</math> is far below ionization potential <math>I_p</math> experiments have observed correlated ionization.<ref name=Rudenko_2004/><ref name=Zrost_2006/><ref name=Zeidler_2005> {{Cite journal | last1 = Zeidler | first1 = D. | last2 = Staudte | first2 = A. | last3 = Bardon | first3 = A. B. | last4 = Villeneuve | first4 = D. M. | last5 = Dörner | first5 = R. | last6 = Corkum | first6 = P. B. | doi = 10.1103/PhysRevLett.95.203003 | title = Controlling Attosecond Double Ionization Dynamics via Molecular Alignment | journal = Physical Review Letters | volume = 95 | issue = 20 | year = 2005 | pmid = 16384053|bibcode = 2005PhRvL..95t3003Z | article-number=203003| url = https://nrc-publications.canada.ca/eng/view/accepted/?id=8ca16c24-5317-4a60-80fc-b6e55f674b9f }} </ref><ref name=Weckenbrock_2004> {{Cite journal | last1 = Weckenbrock | first1 = M. | last2 = Zeidler | first2 = D. | last3 = Staudte | first3 = A. | last4 = Weber | first4 = T. | last5 = Schöffler | first5 = M. | last6 = Meckel | first6 = M. | last7 = Kammer | first7 = S. | last8 = Smolarski | first8 = M. | last9 = Jagutzki | first9 = O. | last10 = Bhardwaj | first10 = V. | last11 = Rayner | first11 = D. | last12 = Villeneuve | first12 = D. | last13 = Corkum | first13 = P. | last14 = Dörner | first14 = R. | title = Fully Differential Rates for Femtosecond Multiphoton Double Ionization of Neon | doi = 10.1103/PhysRevLett.92.213002 | journal = Physical Review Letters | volume = 92 | issue = 21 | year = 2004 | pmid = 15245277|bibcode = 2004PhRvL..92u3002W | article-number=213002| url = https://nrc-publications.canada.ca/eng/view/accepted/?id=b728bd1f-4973-4371-934c-fa42311be1e8 }} </ref><ref name=Liu_2008> {{Cite journal | last1 = Liu | first1 = Y. | last2 = Tschuch | first2 = S. | last3 = Rudenko | first3 = A. | last4 = Dürr | first4 = M. | last5 = Siegel | first5 = M. | last6 = Morgner | first6 = U. | last7 = Moshammer | first7 = R. | last8 = Ullrich | first8 = J. | doi = 10.1103/PhysRevLett.101.053001 | title = Strong-Field Double Ionization of Ar below the Recollision Threshold | journal = Physical Review Letters | volume = 101 | issue = 5 | article-number = 053001 | year = 2008 | pmid = 18764387|bibcode = 2008PhRvL.101e3001L | url = http://www.repo.uni-hannover.de/handle/123456789/3326 }} </ref>&nbsp; As opposed to the high-<math>U_p</math> regime (<math>3.2 U_p > I_p</math>)<ref name=Yudin2001> {{Cite journal | last1 = Yudin | first1 = G. | last2 = Ivanov | first2 = M. | doi = 10.1103/PhysRevA.63.033404 | title = Physics of correlated double ionization of atoms in intense laser fields: Quasistatic tunneling limit | journal = Physical Review A | volume = 63 | issue = 3 | article-number = 033404 | year = 2001 |bibcode = 2001PhRvA..63c3404Y | url = https://nrc-publications.canada.ca/eng/view/accepted/?id=7a64c29b-0090-4152-9f57-034a305a9246 }} </ref><ref name=Becker2005> {{Cite journal | last1 = Becker | first1 = A. | last2 = Faisal | first2 = F. H. M. | s2cid = 14675241 | doi = 10.1088/0953-4075/38/3/R01 | title = Intense-field many-body S-matrix theory | journal = Journal of Physics B: Atomic, Molecular and Optical Physics | volume = 38 | issue = 3 | pages = R1 | year = 2005 |bibcode = 2005JPhB...38R...1B }} </ref><ref name=Staudte_2007> {{Cite journal | last1 = Staudte | first1 = A. | last2 = Ruiz | first2 = C. | last3 = Schöffler | first3 = M. | last4 = Schössler | first4 = S. | last5 = Zeidler | first5 = D. | last6 = Weber | first6 = T. | last7 = Meckel | first7 = M. | last8 = Villeneuve | first8 = D. | last9 = Corkum | first9 = P. | last10 = Becker | first10 = A. | last11 = Dörner | first11 = R. | title = Binary and Recoil Collisions in Strong Field Double Ionization of Helium | doi = 10.1103/PhysRevLett.99.263002 | journal = Physical Review Letters | volume = 99 | issue = 26 | article-number = 263002 | year = 2007 | pmid = 18233574|bibcode = 2007PhRvL..99z3002S | url = https://nrc-publications.canada.ca/eng/view/accepted/?id=77cdbaab-c33b-4925-881e-5c68e1054226 }} </ref><ref name=Rudenko_2007> {{Cite journal | last1 = Rudenko | first1 = A. | last2 = De Jesus | first2 = V. | last3 = Ergler | first3 = T. | last4 = Zrost | first4 = K. | last5 = Feuerstein | first5 = B. | last6 = Schröter | first6 = C. | last7 = Moshammer | first7 = R. | last8 = Ullrich | first8 = J. | doi = 10.1103/PhysRevLett.99.263003 | title = Correlated Two-Electron Momentum Spectra for Strong-Field Nonsequential Double Ionization of He at 800 nm | journal = Physical Review Letters | volume = 99 | issue = 26 | year = 2007 | pmid = 18233575|bibcode = 2007PhRvL..99z3003R | article-number=263003}} </ref> in the low-<math>U_p</math> regime (<math>3.2 U_p < I_p</math>) the assistance of the laser field during the recollision is vital.

Classical and quantum analysis<ref name=Haan_2006> {{Cite journal | last1 = Haan | first1 = S. | last2 = Breen | first2 = L. | last3 = Karim | first3 = A. | last4 = Eberly | first4 = J. | title = Variable Time Lag and Backward Ejection in Full-Dimensional Analysis of Strong-Field Double Ionization | doi = 10.1103/PhysRevLett.97.103008 | journal = Physical Review Letters | volume = 97 | issue = 10 | year = 2006 | pmid = 17025816|bibcode = 2006PhRvL..97j3008H | article-number=103008}} </ref><ref name=Ho_2006> {{Cite journal | last1 = Ho | first1 = P. | last2 = Eberly | first2 = J. | doi = 10.1103/PhysRevLett.97.083001 | title = In-Plane Theory of Nonsequential Triple Ionization | journal = Physical Review Letters | volume = 97 | issue = 8 | year = 2006 | pmid = 17026298|arxiv = physics/0605026 |bibcode = 2006PhRvL..97h3001H | article-number=083001| s2cid = 8978621 }} </ref><ref name=deMorissonFaria_2006> {{Cite journal | last1 = Figueira De Morisson Faria | first1 = C. | last2 = Liu | first2 = X. | last3 = Becker | first3 = W. | title = Classical aspects of laser-induced non-sequential double ionization above and below the threshold | doi = 10.1080/09500340500227869 | journal = Journal of Modern Optics | volume = 53 | issue = 1–2 | pages = 193–206 | year = 2006 |bibcode = 2006JMOp...53..193F | s2cid = 120011073 }} </ref> of the low-<math>U_p</math> regime demonstrates the following two ways of electron ejection after the recollision: First, the two electrons can be freed with little time delay compared to the quarter-cycle of the driving laser field. Second, the time delay between the ejection of the first and the second electron is of the order of the quarter-cycle of the driving field. In these two cases, the electrons appear in different quadrants of the correlated spectrum. If following the recollision, the electrons are ejected nearly simultaneously, their parallel momenta have equal signs, and both electrons are driven by the laser field in the same direction toward the detector.<ref name=Bondar2009> {{Cite journal | last1 = Bondar | first1 = D. | last2 = Liu | first2 = W. K. | last3 = Ivanov | first3 = M. | title = Two-electron ionization in strong laser fields below intensity threshold: Signatures of attosecond timing in correlated spectra | doi = 10.1103/PhysRevA.79.023417 | journal = Physical Review A | volume = 79 | issue = 2 | article-number = 023417 | year = 2009 |arxiv = 0809.2630 |bibcode = 2009PhRvA..79b3417B | s2cid = 119275628 }} </ref> If after the recollision, the electrons are ejected with a substantial delay (quarter-cycle or more), they end up going in the opposite directions. These two types of dynamics produce distinctly different correlated spectra (compare experimental results <ref name=Rudenko_2004/><ref name=Zrost_2006/><ref name=Zeidler_2005/><ref name=Weckenbrock_2004/><ref name=Liu_2008/> with .<ref name=Staudte_2007/><ref name=Rudenko_2007/>

{{Gallery |title=Non-sequential double ionization of noble gas atoms |align=center |width=320 |height=320 |File:NSDI in high-Up regime.pdf|The high-<math>U_p</math> regime |File:NSDI in low-Up regime.pdf|The low-<math>U_p</math> regime }}

==See also== * List of laser articles * Nonlinear optics * Photoionization * Ionization * High harmonic generation * Above threshold ionization {{portal-inline|Physics}}<br /> {{portal-inline|Science}}

==References== {{Reflist|2}}

Category:Atomic, molecular, and optical physics Category:Quantum mechanics Category:Nonlinear optics