yudin_2001
==========

G\. L\. Yudin and M\. Yu\. Ivanov, "Nonadiabatic tunnel ionization\: Looking inside a laser cycle", Phys\. Rev\. A 64, 013409 \(2001\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/yudin_2001.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/physreva\.64\.013409 <https://doi.org/10.1103/physreva.64.013409>`__

**Source kind:** theory

**Recorded technique:** Analytic theory\: the instantaneous \(sub\-cycle\) ionisation rate for arbitrary Keldysh gamma in the strong\-field approximation, from the Dykhne saddle\-point method; the pre\-exponential factor matched to the cycle\-averaged PPT rate; linear and circular polarization\. Atomic units \(pp\. 1\-4\)\.

**Materials in structured entries:** None recorded.

**Dataset quantities:** None recorded.

**Contents:** 0 datasets; 0 formulas.

Curation notes
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Pages are pdf pages \(1\-4 = 013409\-1 to \-4\)\. Identity checked against pdf p\. 1\.

WHY NOTHING IS TAKEN\. A formula paper with no rate table\: Fig\. 1 \(p\. 3\), Phi\(gamma, theta\)/Phi\(gamma, 0\) against theta for gamma = 0\.25, 0\.5, 1 and 2 \(the dashed curve is 1/cos theta, captioned 'the quasistatic limit gamma/cos theta \<\< 1'\); Fig\. 2 \(p\. 3\), Gamma\(theta\)/Gamma\(0\) for He at 780 nm, 5 x 10^13 W/cm^2 \(gamma ~ 2\), quasistatic against nonadiabatic\. Text value \(p\. 3\)\: at those conditions the multiphoton contribution is 'approximately 3\.3% in the total rate integrated over a half\-cycle'\. No quantity holds these\.

KEY FORMULAS \(atomic units; for review; the formulas were compared with the page images and Eq\. \(12\) at theta = 0 reproduces the Keldysh/PPT exponent \(computed 2026\-09\-26\)\)\: \- Definitions \(p\. 1\)\: gamma^2 = I\_p/\(2 U\_p\), U\_p = script\-E^2/\(4 omega\_L^2\); the field script\-E f\(t\) cos\(omega\_L t \+ phi0\); phi\(t\) = omega\_L t \+ phi0; n\* = Z/sqrt\(2 I\_p\), Z the ion charge\. \- Eq\. \(1\), quasistatic rate \(p\. 1\), 'rigorously valid only in the limit gamma \<\< 1'\: Gamma\_qs\(t\) = A\_n\*,l\* B\_l,\|m\| I\_p \(2 \(2I\_p\)^\(3/2\)/\(script\-E f\(t\) \|cos phi\(t\)\|\)\)^\(2n\* \- \|m\| \- 1\) exp\(\-2 \(2I\_p\)^\(3/2\)/\(3 script\-E f\(t\) \|cos phi\(t\)\|\)\)\. \- Eq\. \(2\) \[8\-10\]\: A\_n\*,l\* = 2^\(2n\*\)/\(n\* Gamma\(n\* \+ l\* \+ 1\) Gamma\(n\* \- l\*\)\); B\_l,\|m\| = \(2l \+ 1\)\(l \+ \|m\|\)\!/\(2^\|m\| \|m\|\! \(l \- \|m\|\)\!\)\. Averaging Eq\. \(1\) over a half\-cycle gives the tunnelling formula of \[8\-10\]\. \- Eq\. \(11\) \(p\. 2\)\: Gamma\(t\) ~ exp\(\-\(script\-E^2 f^2\(t\)/omega\_L^3\) Phi\(gamma\(t\), theta\(t\)\)\), gamma\(t\) = gamma/f\(t\); theta\(t\) = phi\(t\) \- pi k, \-pi/2 \<= theta \<= pi/2 \(Eqs\. \(8\)\-\(9\)\)\. \- Eq\. \(12\) \(p\. 2\)\: Phi\(gamma, theta\) = \(gamma^2 \+ sin^2 theta \+ 1/2\) ln c \- \(3 sqrt\(b \- a\)/\(2 sqrt 2\)\) sin\|theta\| \- \(sqrt\(b \+ a\)/\(2 sqrt 2\)\) gamma; a = 1 \+ gamma^2 \- sin^2 theta; b = sqrt\(a^2 \+ 4 gamma^2 sin^2 theta\); c = sqrt\(\(sqrt\(\(b \+ a\)/2\) \+ gamma\)^2 \+ \(sqrt\(\(b \- a\)/2\) \+ sin\|theta\|\)^2\)\. \- Eq\. \(13\)\: omega\_L tau\_tun = \-Im\[arcsin\(sin theta \- i gamma\)\] \(the envelope need be constant only over tau\_tun\)\. \- Eq\. \(15\), gamma \>\> 1\: Phi ~ Phi\(gamma, \+\-pi/2\) = \(gamma^2 \+ 3/2\) ln\(2 gamma\) \- gamma^2/2 \- 1 \+ 35/\(16 gamma^2\) \+ \.\.\.; Eq\. \(16\), 'for gamma \<= 2'\: Phi\(gamma, pi/2\) ~ \(4/5\) gamma^2 sqrt\(gamma\) \(1 \+ 3 gamma/50 \- gamma^2/80\), the leading term exact for gamma \<\< 1 and within 5 % up to gamma = 1 \(p\. 3\)\. \- Eq\. \(17\) \(p\. 3\)\: Gamma\(t\) = N\(t\) exp\(\-\(script\-E^2 f^2\(t\)/omega\_L^3\) Phi\(gamma\(t\), theta\(t\)\)\), the sub\-cycle dependence of N\(t\) ignored except through the envelope\. \- Eq\. \(18\) \(p\. 4\), N matched to the cycle\-averaged PPT rate of \[8\]\: N\(t\) = A\_n\*,l\* B\_l,\|m\| \(3 kappa/gamma^3\)^\(1/2\) C I\_p \(2 \(2I\_p\)^\(3/2\)/\(script\-E f\(t\)\)\)^\(2n\* \- \|m\| \- 1\), kappa = ln\(gamma \+ sqrt\(gamma^2 \+ 1\)\) \- gamma/sqrt\(gamma^2 \+ 1\) \(this kappa is not sqrt\(2 I\_p\)\); C = \(1 \+ gamma^2\)^\(\|m\|/2 \+ 3/4\) A\_m\(omega\_L, gamma\), the PPT correction, A\_m from Eqs\. \(55\)\-\(56\) of Perelomov, Popov and Terent'ev \[8\]; C = 1 for gamma \<\< 1, and for gamma \>\> 1, m = 0, A\_0 ~ 1\.2/gamma^2, C ~ 1\.2/sqrt\(gamma\) \(p\. 4\)\. \- Eqs\. \(19\)\-\(20\), circular polarization\: Gamma\_circ ~ exp\(\-\(script\-E^2 f^2/omega\_L^3\) Phi\_circ\(gamma\)\), Phi\_circ = \(gamma^2 \+ 2\) cosh^\-1\(1 \+ gamma^2/2\) \- 2 gamma sqrt\(1 \+ gamma^2/4\)\.

VALIDITY AND CITED ACCURACY \(p\. 1\)\: cycle\-averaged tunnelling rates are accurate up to gamma ~ 0\.5 \[11\] \(Ilkov, Decker and Chin 1992\: ilkov\_1992\); the PPT cycle\-averaged formula's accuracy 'is excellent for many atoms \(He, Ne, Ar, Kr, Xe\) up to gamma = 3\-4' \[12\] \(Larochelle, Talebpour and Chin, J\. Phys\. B 31, 1215 \(1998\)\) 'and even many small molecules' \[13\] \(Cornaggia and Hering, Phys\. Rev\. A 62, 023403 \(2000\)\), restricted only by omega\_L \<\< omega\_exc\. \[12\] is curated as larochelle\_1998 \(figures only\); \[11\] and \[13\] are not in the library\.

**Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

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No datasets are recorded.

Formulas
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No formulas are recorded.

Corrections
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No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register </register>` for the checks and decisions.