### Abstract

We obtain an explicit solution for the stationary-state populations of a dissipative Fano model, where a discrete excited state is coupled to a continuum set of states; both excited sets of states are reachable by photoexcitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the population of the continuum states as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4×4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic-induced transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter.

Original language | English |
---|---|

Article number | 063414 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 93 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 16 2016 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*93*(6), [063414]. https://doi.org/10.1103/PhysRevA.93.063414

**Nonlinear Fano interferences in open quantum systems : An exactly solvable model.** / Finkelstein-Shapiro, Daniel; Calatayud, Monica; Atabek, Osman; Mujica, Vladimiro; Keller, Arne.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 93, no. 6, 063414. https://doi.org/10.1103/PhysRevA.93.063414

}

TY - JOUR

T1 - Nonlinear Fano interferences in open quantum systems

T2 - An exactly solvable model

AU - Finkelstein-Shapiro, Daniel

AU - Calatayud, Monica

AU - Atabek, Osman

AU - Mujica, Vladimiro

AU - Keller, Arne

PY - 2016/6/16

Y1 - 2016/6/16

N2 - We obtain an explicit solution for the stationary-state populations of a dissipative Fano model, where a discrete excited state is coupled to a continuum set of states; both excited sets of states are reachable by photoexcitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the population of the continuum states as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4×4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic-induced transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter.

AB - We obtain an explicit solution for the stationary-state populations of a dissipative Fano model, where a discrete excited state is coupled to a continuum set of states; both excited sets of states are reachable by photoexcitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the population of the continuum states as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4×4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic-induced transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter.

UR - http://www.scopus.com/inward/record.url?scp=84975159501&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975159501&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.93.063414

DO - 10.1103/PhysRevA.93.063414

M3 - Article

AN - SCOPUS:84975159501

VL - 93

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 6

M1 - 063414

ER -