Improving the Coherence Time of a Quantum System via a Coupling to a Short-Lived System

In this Letter, we propose a counterintuitive use of a hybrid system where the coherence time of a quantum system can be significantly improved by coupling it with a system of a shorter coherence time. Coupling a two-level system with a single nitrogen-vacancy (${\mathrm{NV}}^{-}$) center, a dark state of the ${\mathrm{NV}}^{-}$ center naturally forms after the hybridization. We show that this dark state becomes robust against noise due to the coupling even when the coherence time of the two-level system is much shorter than that of the ${\mathrm{NV}}^{-}$ center. Our proposal opens a new way to use a quantum hybrid system for the realization of robust quantum information processing.

Figure 1

Hybrid system composed of a superconducting FQ and a ${\mathrm{NV}}^{-}$ center. Since the ${\mathrm{NV}}^{-}$ has a three-level system, we can naturally define a bright state and a dark state. The dark state can be driven using polarized microwave fields.

Figure 2

Energy diagram of a single ${\mathrm{NV}}^{-}$ center and a hybrid system composed of a ${\mathrm{NV}}^{-}$ center and superconducting FQ. For a single ${\mathrm{NV}}^{-}$ center, low-frequency magnetic noise can induce an unwanted transition between $|\mathcal{B}⟩$ and $|\mathcal{D}⟩$. However, once the ${\mathrm{NV}}^{-}$ center is coupled with the FQ, low-frequency magnetic noise cannot induce such transition due to the energy splitting of the hybrid system. This mechanism makes the coherence time of the states much longer than that of a single ${\mathrm{NV}}^{-}$ center alone.

Figure 3

Fidelity $F=⟨{\psi }_0|\rho (t)|{\psi }_0⟩$ against time where $\rho (0)=|{\psi }_0⟩⟨{\psi }_0|$ and $|{\psi }_0⟩=[(1/\sqrt{2})|D⟩+(1/\sqrt{2})|0⟩]|\downarrow ⟩$. We use $G_{\perp }=2\pi \times 10\mathrm{kHz}$, $T_{\mathrm{FID}}^{(\mathrm{NV})}=100\mu \mathrm{s}$, and $T_{\text{echo}}^{(\mathrm{NV})}=2\mathrm{ms}$. We fit the decay by $f(t)=[1+e^{-(t/T_{\text{dark}})}/2]$, and obtain $T_{\text{dark}}=471,609,730,839\mu \mathrm{s}$.