Figure 1

(Color online) Schematic setup for generation of the entanglement between two caged electron spins in two distant peapods, where each fullerene is located in a SWCNT-SQD embedded in a two-mode optical cavity. We show here the cavity in photonic crystal as an example. Actually, the cavity required could also be a micropillar cavity in a substrate. The static qubits $A^{\prime }$ and $B^{\prime }$ are caged in the peapods and the auxiliary qubits $A$ and $B$ are bound in the conduction bands of the SWCNT-SQDs. The magnetic field gradient $B_0\left(x\right)=\frac{\partial B_0}{\partial x}\delta x{\widehat{e}}_z$ applied along the nanotube axis is used to entangle the static and auxiliary qubits and to define the quantization axis. The lasers with linear polarization are radiated to generate single ${\sigma }_{\pm }$ polarized photons by STIRAP. The quarter-wave plates (QWPs) transform left- and right-polarized photons to be horizontally and vertically polarized, respectively. PBS is the polarized beam splitter which transmits $|H⟩$ and reflects $|V⟩$. $M$ is the mirror and $D_i$, with $i=1,2$, are the single-photon detectors.Reuse & Permissions

Figure 2

Generation of single photons via virtually exciting excitons, where (a) describes the process from the initial state ${|1/2⟩}_{con\text{−}e}$ via the virtual exciton $|U⟩$ and (b) is for the process from the initial state ${|-1/2⟩}_{con\text{−}e}$ via the virtual exciton $|D⟩$. ${\omega }_{L_i}$ and ${\omega }_{c_i}$ $\left(i=1,2\right)$ are, respectively, frequencies of the laser and the cavity mode and ${\Delta }_i$ is the corresponding detuning. ${\sigma }_{j=0,+,-}$ denote linearly, right-, and left-polarized photons, respectively.Reuse & Permissions

Figure 3

Success probabilities $P_1$ and $P_2$ with respect to the cavity decay rate $\kappa$, where we set ${\Omega }_1=10\text{meV}\approx 15.2\text{THz}$, $g_1=1\text{meV}\approx 1.52\text{THz}$, and ${\Delta }_1=15\text{meV}\approx 22.8\text{THz}$. $P_1$ and $P_2$, defined in the text, are plotted by solid and dashed curves. Strictly considering the condition $V⪢\kappa$, we only need to show $\kappa <500\text{GHz}$. The calculation applied to the exciton $|D⟩$ is similar.Reuse & Permissions

Figure 4

(Color online) Schematic setup for achieving an $n$-qubit GHZ state of the caged electron spins, where $c_k$ with $k=1,2,\dots ,n$ includes the $k\text{th}$ peapod embedded in a photonic crystal cavity and also includes a QWP. $D_k$ is the single-photon detector. When all the detectors click, we achieve the GHZ state. Since each photon going through a PBS splits into two parts associated with different polarizations, for meeting the requirement for coincident detection, we must make sure appropriate path lengths for different polarization components of each photon.Reuse & Permissions