## Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance

## Abstract

We consider a localized electronic spin controlled by a circularly polarized optical beam and an external magnetic field. When the frequency of the beam is tuned near an optical resonance with a continuum of higher energy states, effective magnetic fields are induced on the two-level system via the inverse Faraday effect. We explore the process in which the frequency of the beam is made linearly time-dependent so that it sweeps through the optical resonance, starting and ending at the values far away from it. In addition to changes of spin states, Kramers-Kronig relations guarantee that a localized electron can also escape into a continuum of states. We argue that probabilities of transitions between different possible electronic states after such a sweep of the optical frequency can be found exactly, regardless the shape of the resonance. In conclusion, we also discuss extension of our results to multistate systems.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Texas A & M Univ., College Station, TX (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1329893

- Alternate Identifier(s):
- OSTI ID: 1239010

- Report Number(s):
- LA-UR-15-26180

Journal ID: ISSN 1751-8113

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Physics. A, Mathematical and Theoretical

- Additional Journal Information:
- Journal Volume: 48; Journal Issue: 50; Journal ID: ISSN 1751-8113

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; material science; inverse Faraday effect; qubit control; Kramers-Kronig; scattering theory; Landau-Zener; Stokes phenomenon

### Citation Formats

```
Sun, Chen, and Sinitsyn, Nikolai A. Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance. United States: N. p., 2015.
Web. doi:10.1088/1751-8113/48/50/505202.
```

```
Sun, Chen, & Sinitsyn, Nikolai A. Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance. United States. doi:10.1088/1751-8113/48/50/505202.
```

```
Sun, Chen, and Sinitsyn, Nikolai A. Thu .
"Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance". United States. doi:10.1088/1751-8113/48/50/505202. https://www.osti.gov/servlets/purl/1329893.
```

```
@article{osti_1329893,
```

title = {Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance},

author = {Sun, Chen and Sinitsyn, Nikolai A.},

abstractNote = {We consider a localized electronic spin controlled by a circularly polarized optical beam and an external magnetic field. When the frequency of the beam is tuned near an optical resonance with a continuum of higher energy states, effective magnetic fields are induced on the two-level system via the inverse Faraday effect. We explore the process in which the frequency of the beam is made linearly time-dependent so that it sweeps through the optical resonance, starting and ending at the values far away from it. In addition to changes of spin states, Kramers-Kronig relations guarantee that a localized electron can also escape into a continuum of states. We argue that probabilities of transitions between different possible electronic states after such a sweep of the optical frequency can be found exactly, regardless the shape of the resonance. In conclusion, we also discuss extension of our results to multistate systems.},

doi = {10.1088/1751-8113/48/50/505202},

journal = {Journal of Physics. A, Mathematical and Theoretical},

number = 50,

volume = 48,

place = {United States},

year = {2015},

month = {11}

}

*Citation information provided by*

Web of Science

Web of Science