Influence of an external magnetic field on the decoherence of a central spin coupled to an antiferromagnetic environment

Abstract

Using the spin wave approximation, we study the decoherence dynamics of a central spin coupled to an antiferromagnetic environment under the application of an external global magnetic field. The external magnetic field affects the decoherence process through its effect on the antiferromagnetic environment. It is shown explicitly that the decoherence factor which displays a Gaussian decay with time depends on the strength of the external magnetic field and the crystal anisotropy field in the antiferromagnetic environment. When the values of the external magnetic field is increased to the critical field point at which the spin-flop transition (a first-order quantum phase transition) happens in the antiferromagnetic environment, the decoherence of the central spin reaches its highest point. This result is consistent with several recent quantum phase transition witness studies. The influences of the environmental temperature on the decoherence behavior of the central spin are also investigated.

Tailoring Quantum Correlations of a Coupled Central Two Qubits Soaked in a Finite Temperature Antiferromagnetic Environment with Frequency Gap

“…This behavior is related to the overall increase in magnon excitation number difference and fluctuations as magnetic field increases; a situation similarly witnessed in [21] where these fluctuations leads to a decrease in the decoherence time of a central electron spin in an AF environment. The finite time death of entanglement after the peak value is reached is a manifestation of Markovian (memory less) effects that dominates the dynamics of entanglement as the two modes completely lost their information following their interaction with the rest of the thermal environment.…”

Quantum Spin Baths Induced Transition of Decoherence and Entanglement

“…But the inclusion of intra-spin interaction in the bath make the problem complicated and exact reduced dynamics is only available for some limited models with high symmetry. [7] Approximated method such as mean-field theory [8] or perturbation theory [9] have been used to handle more generic models.…”

Geometric phase of a central spin coupled to an antiferromagnetic environment

“…The anisotropy field B A is assumed to be positive, which approximates the effect of the crystal anisotropy energy, with the property of tending for positive magnetic moment µ B to align the spins on sublattice a in the positive z direction and the spins on sublattice b in the negative z direction. Using the Holstein-Primakoff transformation to map the spin operators of the AF environment onto bosonic operators, considering the situation that the environment is in the lowtemperature and low-excitation limits, then transforming the resultant Hamiltonians to the momentum space, and finally using the Bogoliubov transformation, we obtain in the spinwave approximation [15] …”

“…The reduced density matrix of the qubit in the thermodynamics limit (i.e., N → ∞) can be obtained, following the calculation in Ref. [15], to be…”

“…When the strength of the magnetic field is increased further toward the critical point where the spin-flop transition occurs, B = B c ≈ 2.83 Tesla for the parameters used in Figs. 2 and 3, the decoherence time approaches zero abruptly [15]. An analytical expression for the decoherence time near the critical field can be found in Eq.…”