# Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior

## Abstract

We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula that is applicable to models with a nondegenerate ground state is derived. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard Landau-Zener probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.

- Authors:

- Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033 (Japan)
- (Japan)
- Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany)
- Department of Mathematical Science, Graduate School of Engineering, Osaka Prefecture University, Sakai 599-8531 (Japan)

- Publication Date:

- OSTI Identifier:
- 20951520

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 21; Other Information: DOI: 10.1103/PhysRevB.75.214308; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COUPLING; FLUCTUATIONS; GROUND STATES; PROBABILITY; QUANTUM COMPUTERS; QUANTUM ELECTRODYNAMICS; QUBITS; SPIN; TEMPERATURE ZERO K; TUNNEL EFFECT

### Citation Formats

```
Saito, Keiji, Department of Physics, Graduate School of Science, 2 CREST, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Wubs, Martijn, Kohler, Sigmund, Haenggi, Peter, and Kayanuma, Yosuke.
```*Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVB.75.214308.

```
Saito, Keiji, Department of Physics, Graduate School of Science, 2 CREST, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Wubs, Martijn, Kohler, Sigmund, Haenggi, Peter, & Kayanuma, Yosuke.
```*Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior*. United States. doi:10.1103/PHYSREVB.75.214308.

```
Saito, Keiji, Department of Physics, Graduate School of Science, 2 CREST, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Wubs, Martijn, Kohler, Sigmund, Haenggi, Peter, and Kayanuma, Yosuke. Fri .
"Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior". United States.
doi:10.1103/PHYSREVB.75.214308.
```

```
@article{osti_20951520,
```

title = {Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior},

author = {Saito, Keiji and Department of Physics, Graduate School of Science, 2 CREST, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012 and Wubs, Martijn and Kohler, Sigmund and Haenggi, Peter and Kayanuma, Yosuke},

abstractNote = {We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula that is applicable to models with a nondegenerate ground state is derived. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard Landau-Zener probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.},

doi = {10.1103/PHYSREVB.75.214308},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 21,

volume = 75,

place = {United States},

year = {Fri Jun 01 00:00:00 EDT 2007},

month = {Fri Jun 01 00:00:00 EDT 2007}

}