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arXiv:1201.5036 · Physical Review B

Hyperfine induced electron spin and entanglement dynamics in double quantum dots: The case of separate baths

B. Erbe, John Schliemann

Published Apr 16, 2012• 6 citations
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Abstract

We consider a system of two strongly coupled electron spins in zero magnetic field, each of which is interacting with an individual bath of nuclear spins via the hyperfine interaction. Applying the long-spin approximation that we introduced in a previous paper [Europhys. Lett. 95, 47009 (2011)] (here each bath is replaced by a single long spin), we numerically study the electron spin and entanglement dynamics. We demonstrate that the decoherence time is scaling with the bath size according to a power law. As expected, the decaying part of the dynamics decreases with increasing bath polarization. However, surprisingly it turns out that, under certain circumstances, combining quantum dots of different geometry to the double dot setup has a very similar effect on the magnitude of the spin decay. Finally, we show that even for a comparatively weak exchange coupling the electron spins can be fully entangled.

DOI
10.1103/physrevb.85.155127

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We consider a system of two strongly coupled electron spins in zero magnetic field, each of which is interacting with an individual bath of nuclear spins via the hyperfine interaction. Applying the long-spin approximation that we introduced in a previous paper [Europhys. Lett. 95, 47009 (2011)] (here each bath is replaced by a single long spin), we numerically study the electron spin and entanglement dynamics. We demonstrate that the decoherence time is scaling with the bath size according to a power law. As expected, the decaying part of the dynamics decreases with increasing bath polarization. However, surprisingly it turns out that, under certain circumstances, combining quantum dots of different geometry to the double dot setup has a very similar effect on the magnitude of the spin decay. Finally, we show that even for a comparatively weak exchange coupling the electron spins can be fully entangled.
We numerically study the hyperfine induced nuclear spin dynamics in a system of two coupled quantum dots in zero magnetic field. Each of the electron spins is considered to interact with an individual bath of nuclear spins via homogeneous coupling constants (all coupling coefficients being equal). In order to lower the dimension of the problem, the two baths are approximated by two single long spins. We demonstrate that the hyperfine interaction allows to utilize the nuclear baths for quantum information purposes. In particular, we show that it is possible to swap the nuclear ensembles on time scales of seconds and indicate that it might even be possible to fully entangle them. As a key result, it turns out that the larger the baths are, the more useful they become as a resource of quantum information. Interestingly, the nuclear spin dynamics strongly benefits from combining two quantum dots of different geometry to a double-dot setup.
We numerically study the hyperfine induced nuclear spin dynamics in a system of two coupled quantum dots in zero magnetic field. Each of the electron spins is considered to interact with an individual bath of nuclear spins via homogeneous coupling constants (all coupling coefficients being equal). In order to lower the dimension of the problem, the two baths are approximated by two single long spins. We demonstrate that the hyperfine interaction allows to utilize the nuclear baths for quantum information purposes. In particular, we show that it is possible to swap the nuclear ensembles on time scales of seconds and indicate that it might even be possible to fully entangle them. As a key result, it turns out that the larger the baths are, the more useful they become as a resource of quantum information. Interestingly, the nuclear spin dynamics strongly benefits from combining two quantum dots of different geometry to a double-dot setup.
We study the dynamics of entanglement of two electron spins in two quantum dots, in which each electron is interacting with its nuclear spin environment. Focusing on the case of uncoupled dots, and starting from either Bell or Werner states of two qubits, we calculate the decay of entanglement due to the hyperfine interaction with the nuclei. We mostly focus on the regime of magnetic fields in which the bath-induced electron spin flips play a role, for example, their presence leads to the appearance of entanglement sudden death at finite time for two qubits initialized in a Bell state. For these fields, the intrabath dipolar interactions and spatial inhomogeneity of hyperfine couplings are irrelevant on the time scale of coherence (and entanglement) decay, and most of the presented calculations are performed using the uniform-coupling approximation to the exact hyperfine Hamiltonian. We provide a comprehensive overview of entanglement decay in this regime, considering both free evolution of the qubits, and an echo protocol with simultaneous application of $\ensuremath{\pi}$ pulses to the two spins. All the currently relevant for experiments bath states are considered: the thermal state, narrowed states (characterized by diminished uncertainty of one of the components of the Overhauser field) of two uncorrelated baths, and a correlated narrowed state with a well-defined value of the zzz component of the Overhauser field interdot gradient. While we mostly use concurrence to quantify the amount of entanglement in a mixed state of the two electron spins, we also show that their entanglement dynamics can be reconstructed from measurements of the currently relevant for experiments entanglement witnesses and the fidelity of quantum teleportation, performed using a partially disentangled state as a resource.
We investigate in detail, using both analytical and numerical tools, the decoherence of electron spins in quantum dots (QDs) coupled to a bath of nuclear spins in magnetic fields or with various initial bath polarizations, focusing on the longitudinal relaxation in low and moderate field and polarization regimes. An increase of the initial polarization of nuclear-spin bath has the same effect on the decoherence process as an increase of the external magnetic field, namely, the decoherence dynamics changes from smooth decay to damped oscillations. This change can be observed experimentally for a single QD and for a double-QD setup. Our results indicate that substantial increase of the decoherence time requires very large bath polarizations, and the use of other methods (dynamical decoupling or control of the nuclear spins distribution) may be more practical for suppressing decoherence of QD-based qubits.
We investigate hyperfine induced electron spin and entanglement dynamics in a system of two quantum dot spin qubits. We focus on the situation of zero external magnetic field and concentrate on approximation-free theoretical methods. We give an exact solution of the model for homogeneous hyperfine coupling constants (with all coupling coefficients being equal) and varying exchange coupling, and we derive the dynamics therefrom. After describing and explaining the basic dynamical properties, the decoherence time is calculated from the results of a detailed investigation of the short-time electron-spin dynamics. The result turns out to be in good agreement with experimental data.
The time evolution of spin states of two electrons interacting with a nuclear spin bath in a quantum dot system is studied. The hyperfine interaction between the electrons and the nuclear spins is modeled by an isotropic Heisenberg interaction, and the interaction between the electron spins by Heisenberg exchange. Depending on the extent of the overlap between the spatial wave functions of the electrons, there are two physically different cases, namely, the two qubits either interact with the same set of nuclear spins or they see different nuclear spin environments. In the two cases, the decoherence of the two-qubit state is studied analytically. We have identified a class of two-qubit states that have a rich dynamics when the exchange interaction between the qubits becomes large in comparison to the hyperfine interaction strengths. The decoherence time scale is determined as a function of the bath-spin distribution and the polarizations of the initial two-qubit state. States with large decoherence times are identified by performing a minimization over all the two-qubit pure states.