# Decoherence induced by interacting quantum spin baths

## Abstract

We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, XY, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the XY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bathmore »

- Authors:

- NEST-CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa (Italy)
- Dipartimento di Fisica, Universita di Trento and BEC-CNR-INFM, I-38050 Povo (Italy)
- (United States)
- (SISSA), Via Beirut 2-4, I-34014 Trieste (Italy)

- Publication Date:

- OSTI Identifier:
- 20982279

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032333; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMS; COUPLING; DECAY; DENSITY MATRIX; HAMILTONIANS; HEISENBERG MODEL; INFORMATION THEORY; ISING MODEL; LOSSES; ONE-DIMENSIONAL CALCULATIONS; QUANTUM COMPUTERS; QUANTUM DECOHERENCE; QUANTUM ENTANGLEMENT; QUBITS; RENORMALIZATION; SPIN; TIME DEPENDENCE

### Citation Formats

```
Rossini, Davide, Giovannetti, Vittorio, Montangero, Simone, Calarco, Tommaso, ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, Fazio, Rosario, and International School for Advanced Studies.
```*Decoherence induced by interacting quantum spin baths*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032333.

```
Rossini, Davide, Giovannetti, Vittorio, Montangero, Simone, Calarco, Tommaso, ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, Fazio, Rosario, & International School for Advanced Studies.
```*Decoherence induced by interacting quantum spin baths*. United States. doi:10.1103/PHYSREVA.75.032333.

```
Rossini, Davide, Giovannetti, Vittorio, Montangero, Simone, Calarco, Tommaso, ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, Fazio, Rosario, and International School for Advanced Studies. Thu .
"Decoherence induced by interacting quantum spin baths". United States.
doi:10.1103/PHYSREVA.75.032333.
```

```
@article{osti_20982279,
```

title = {Decoherence induced by interacting quantum spin baths},

author = {Rossini, Davide and Giovannetti, Vittorio and Montangero, Simone and Calarco, Tommaso and ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138 and Fazio, Rosario and International School for Advanced Studies},

abstractNote = {We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, XY, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the XY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.},

doi = {10.1103/PHYSREVA.75.032333},

journal = {Physical Review. A},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}