Abstract
We present a theoretical study of a hybrid circuit-quantum electrodynamics system composed of two semiconducting charge-qubits confined in a microwave resonator. The qubits are defined in terms of the charge states of two spatially separated double quantum dots (DQDs) which are coupled to the same photon mode in the microwave resonator. We analyse a transport setup where each DQD is attached to electronic reservoirs and biased out-of-equilibrium by a large voltage, and study how electron transport across each DQD is modified by the coupling to the common resonator. In particular, we show that the inelastic current through each DQD reflects an indirect qubit–qubit interaction mediated by off-resonant photons in the microwave resonator. As a result of this interaction, both charge qubits stay entangled in the steady (dissipative) state. Finite shot noise cross-correlations between currents across distant DQDs are another manifestation of this nontrivial steady-state entanglement.
Highlights
We show the current in the double quantum dots (DQDs) as a function of its level detuning ε1
We studied theoretically photon-mediated transport and the generation of steady-state correlations between two open charge qubits defined in spatially separated DQDs which are coupled to a common transmission line resonator
Our results demonstrate that the qubits are entangled due to the indirect coupling induced by photons in the microwave resonator
Summary
We turn to our original model in which two DQDs are coupled to the same photon mode of the microwave resonator, but uncoupled to each other. Are brought in resonance with each other, 1 = 2, with opposite detuning, ε1 = −ε2, but slightly out of resonance with the photon mode, 1 = 2 = hωr It is a result of an indirect qubit–qubit interaction induced by the common coupling to the microwave resonator and we refer to it as the two-qubits (2qb) peak. A strong coupling to the right reservoir in, say, qubit 2 induces a transport version of the quantum Zeno effect which tends to freeze the dynamics of the second qubit by effectively localizing the charge in the left dot of the DQD2, with σz2 → 1 We demonstrate this effect in figure 5(b) where the current through the first DQD as a function of R,2 is shown for the two-qubit resonance condition ε1 = −ε2, with β,1 = L,2 =. As the coupling with the resonator increases, such features, and more generally the overall behaviour as a function of level detuning, can become rather intricate
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