# Incoherent time evolution of Rydberg level populations in a Landau-Zener grid

## Abstract

The time evolution of two intersecting groups of parallel energy levels, E{sub m} ({tau}) = p{tau} - m{epsilon} and E{sub m {prime}({tau}) = p{tau} + m{prime}{epsilon} = 0,1,2,..., p and {epsilon} constants), is considered as a model of state mixing of interacting Rydberg manifolds by a ramped electric field. Each intersection [m,m{prime}] of the triangular grid of level crossings is treated as an isolated 2-level Landau-Zener anticrossing at energy {1/2} (m{prime}-m){epsilon} with probabilities D and A = 1-D for diabatic and adiabatic transitions, respectively (interference effects are ignored here.) Beginning on the upward-going m = 0 level and following successive time steps {tau}{sup N} = {1/2} N{epsilon}/p (N = 0,1,2,...), a path analysis leads to a distribution of probabilities for arriving at an intersection [m,m{prime}] after N = m +m{prime} previous steps via ({sub m}{sup n}) possible paths. The fastest ramp rates (D {r_arrow} 1} evolve purely diabatically, remaining on the m = 0 level with probability D{sup N}; the slowest ramps (A {r_arrow} 1) follow a purely adiabatic path that switches between mid-grid levels m, m{prime} {approx} {1/2}N with probability A{sup N}. For any but the fastest ramps, however, there is a broad single-humped distribution with average energy E{supmore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 281217

- Report Number(s):
- CONF-9305421-

Journal ID: BAPSA6; ISSN 0003-0503; TRN: 96:019142

- Resource Type:
- Journal Article

- Journal Name:
- Bulletin of the American Physical Society

- Additional Journal Information:
- Journal Volume: 38; Journal Issue: 3; Conference: 1993 American Physical Society annual meeting on atomic, molecular, and topical physics, Reno, NV (United States), 16-19 May 1993; Other Information: PBD: May 1993

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; RYDBERG STATES; LANDAU-ZENER FORMULA; TIME DEPENDENCE; ELECTRIC FIELDS

### Citation Formats

```
Price, P N, and Harmin, D A.
```*Incoherent time evolution of Rydberg level populations in a Landau-Zener grid*. United States: N. p., 1993.
Web.

```
Price, P N, & Harmin, D A.
```*Incoherent time evolution of Rydberg level populations in a Landau-Zener grid*. United States.

```
Price, P N, and Harmin, D A. Sat .
"Incoherent time evolution of Rydberg level populations in a Landau-Zener grid". United States.
```

```
@article{osti_281217,
```

title = {Incoherent time evolution of Rydberg level populations in a Landau-Zener grid},

author = {Price, P N and Harmin, D A},

abstractNote = {The time evolution of two intersecting groups of parallel energy levels, E{sub m} ({tau}) = p{tau} - m{epsilon} and E{sub m {prime}({tau}) = p{tau} + m{prime}{epsilon} = 0,1,2,..., p and {epsilon} constants), is considered as a model of state mixing of interacting Rydberg manifolds by a ramped electric field. Each intersection [m,m{prime}] of the triangular grid of level crossings is treated as an isolated 2-level Landau-Zener anticrossing at energy {1/2} (m{prime}-m){epsilon} with probabilities D and A = 1-D for diabatic and adiabatic transitions, respectively (interference effects are ignored here.) Beginning on the upward-going m = 0 level and following successive time steps {tau}{sup N} = {1/2} N{epsilon}/p (N = 0,1,2,...), a path analysis leads to a distribution of probabilities for arriving at an intersection [m,m{prime}] after N = m +m{prime} previous steps via ({sub m}{sup n}) possible paths. The fastest ramp rates (D {r_arrow} 1} evolve purely diabatically, remaining on the m = 0 level with probability D{sup N}; the slowest ramps (A {r_arrow} 1) follow a purely adiabatic path that switches between mid-grid levels m, m{prime} {approx} {1/2}N with probability A{sup N}. For any but the fastest ramps, however, there is a broad single-humped distribution with average energy E{sup (N)}= {1/2} {epsilon} {Sigma}{sub k}{sup N}=1 (D-A){sup k}- population is always concentrated near the center of the interaction region. Its spread in energy grows as N{sup 1/2} at large N but is narrower the larger is A.},

doi = {},

url = {https://www.osti.gov/biblio/281217},
journal = {Bulletin of the American Physical Society},

number = 3,

volume = 38,

place = {United States},

year = {1993},

month = {5}

}