The full analysis of the superconductor diamond hybrid system is very difficult, especially if we wish to consider the effect of noise. To overcome this problem, we developed a new theoretical model to analyze this system by using an appropriate approximation, and succeeded to simulate this system efficiently. Using our new theoretical prediction of this system, we found an improvement in the lifetime of the electron spin in diamond via the hybridization within this model.
(1) Mechanism to improve the lifetime of the electron spin in diamond via a coupling with the superconducting flux qubit (Fig.3)
A defect that consists of a Nitrogen atom and a vacancy in diamond lattice is called a Nitrogen-Vacancy (NV) center, which has single electron spins (
Fig.1). The NV center has two excited states in a ground-state manifold. It is known that, since these two excited states have almost the same energy, even a small perturbation from the environment can induce an unwanted transition between these two states, which decreases the lifetime of the NV center (
Fig.3).
We have theoretically shown that a coupling with the superconducting flux qubit can energetically separate these two excited states in the NV center. One of the exited states in the NV center can be directly coupled with the superconducting flux qubit so that a finite energy shift occurs, while the other excited states cannot be affected by the superconducting qubit. This mechanism provides a protection of this system from low-energy noise induced by the environment, leading to an improvement in the lifetime of the NV center.
(2) Numerical simulation to estimate the lifetime of the NV center (Fig.4).
We show that the coupling with the superconducting flux qubit can make the NV center robust against noise due to the energy separation between the excited states of the NV centers. We perform a numerical simulation of the dynamics of the NV center coupled with the superconducting flux qubit, and predict that the lifetime of the NV center, which is 100 micro seconds without the superconducting flux qubit, becomes 950 micro seconds after the hybridization with the superconducting flux qubit (
Fig.4). This means that the accuracy of the NV center sensor becomes 10 times better than the sensor using the NV center alone.
Our research team has found that it is possible to improve the lifetime of the electron spin in diamond via a coupling with a superconducting flux qubit. Although the lifetime of the superconducting flux qubit is ten times worse than that of the electron spin, such hybridization can actually enhance the lifetime of the electron spin by an order of magnitude.
Also, it was believed that the coupling of the single NV center might be too weak to hybridize the superconducting flux qubit. However, we reveal that, even if this hybrid system is in a
regime of a weak coupling, it is possible to observe the improvement of the lifetime of the NV center. So the necessary requirement to demonstrate our theoretical prediction is within a reach of the current technology.
It is difficult to simulate the superconductor diamond hybrid system, and a full analysis of this system is considered impossible even if we use the fastest existing computers, because of the large freedom of the environment to induce noise. We have experimentally succeeded to hybridize a superconducting flux qubit and an ensemble of NV centers, we are familiar with the analysis of this system. We generalize our previous model to describe the ensemble of NV centers coupled with the superconducting flux qubit to a new model to describe a single NV center coupled with it. Especially, we simplify the environmental effect on this hybrid system and so succeed in simulating this system using an ordinary desktop computer. This advantage led us to obtain the results described here.