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# Rabi oscillations, decoherence, and disentanglement in a qubit-spin-bath system: exact dynamics

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### Abstract

We examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one-dimensional spin bath. In contrast to previous studies, both the qubit-bath coupling and the nearest neighbor intrabath couplings are taken as the spin-flip XX-type. We first study the Rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state, finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics. Next, we discuss the bath-induced decoherence of the qubit when the bath is initially in the ground state, and show that the decoherence properties depend on the internal phases of the spin bath. By considering two independent copies of the qubit-bath system, we finally probe the disentanglement dynamics of two noninteracting entangled qubits. We find that entanglement sudden death appears when the spin bath is in its critical phase. We show that the single-qubit decoherence factor is an upper bound for the two-qubit concurrence.

### Most cited references44

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### Entanglement of Formation of an Arbitrary State of Two Qubits

(1997)
The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state is defined as the minimum average entanglement of an ensemble of pure states that represents the given mixed state. An earlier paper [Phys. Rev. Lett. 78, 5022 (1997)] conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula to be true for a special class of mixed states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing pure-state decompositions.
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### Cold bosonic atoms in optical lattices

(1998)
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap, and in optical superlattices are presented.
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### Finite-Time Disentanglement via Spontaneous Emission

(2004)
We show that under the influence of pure vacuum noise two entangled qubits become completely disentangled in a finite time, and in a specific example we find the time to be given by $$\ln \Big(\frac{2 +\sqrt 2}{2}\Big)$$ times the usual spontaneous lifetime.
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### Author and article information

###### Journal
2014-03-19
2014-05-19
###### Article
10.1103/PhysRevA.89.062105
1403.4900

15 pages, 9 figures. Ning Wu and Arun Nanduri equally contributed to this work
quant-ph

Quantum physics & Field theory