Photon-mediated entanglement between spin qubits beyond the dispersive regime

Abstract

Dispersively coupled distant qubits in a shared cavity can become entangled through virtual photon exchange with energy-conserving phase evolution of their quantum states. This interaction can potentially be accelerated by operating on resonance, allowing for the exchange of real photons. In this theoretical study, we examine photon-mediated entanglement between two distant spins of electrons confined in double quantum dots formed in a Si/SiGe heterostructure. We calculate the dynamics of the combined system comprised of both spin qubits and the cavity, assuming that both spin qubits can be tuned into and out of resonance with the host cavity. We demonstrate that the exchange of real photons between the two spin qubits can result in rapid entanglement that is robust against decoherence. These results pave the way for the development of quantum gates on resonantly coupled distant semiconductor spin qubits.

Figures (9)

• Figure 1: Two electrons (green clouds) are confined within the DQDs in the shared cavity. A strong magnetic field $B_z$ lifts the spin degeneracy, while a relatively weak non-uniform field $\pm B_x$ hybridizes the spin and charge electronic states. A real photon with energy $\omega$ is transferred from one spin qubit to another and induces spin flips of both electrons whose energy levels are tuned to fulfill the resonance condition $E_\sigma = \omega$.
• Figure 2: Two-step entanglement scheme for the initial state $\ket{\Psi_0} = \ket{\text{SQ}_1 \text{SQ}_2}_0 = \ket{\uparrow \downarrow}_0$ with empty cavity, the first spin qubit (SQ$_1$) prepared in the excited $\ket{\uparrow}$ state and the second spin qubit (SQ$_2$) in the ground $\ket{\downarrow}$ state. In the first step, the ground-state spin qubit (SQ$_2$) is decoupled, whereas the $\sqrt{i\mathrm{SWAP}}$ operation is performed between the initially excited spin qubit (SQ$_1$) and the cavity. The second step is the subsequent $i\mathrm{SWAP}$ between SQ$_2$ and the cavity, leaving the cavity empty.
• Figure 3: The process of entangling the two spin qubits. The panel (a) depicts the probabilities of the two-qubit system to occupy different basis states, while the panel (b) shows the temporal evolution of the entanglement measured via the concurrence $C$. The parameters used in the computation are $\omega / 2\pi = 10$ GHz, $\Delta / 2\pi = 2$ GHz, $g / 2\pi = 100$ MHz, $\phi = \pi/6$.
• Figure 4: The concurrence from Eq. \ref{['eq:Concurrence']} as a function of two time intervals, during which SQ$_{1,2}$ are activated/deactivated. The maximum concurrence $C_\mathrm{max} = 0.9$ is found at $\tau_1 = 2.48$ ns and $\tau_2 = 4.82$ ns. The parameters used in the computation are $\omega / 2\pi = 10$ GHz, $\Delta / 2\pi = 2$ GHz, $g / 2\pi = 100$ MHz, $\phi = \pi/6$, $\kappa / 2 \pi = 2$ MHz, $\gamma / 2 \pi = \gamma_\phi / 2 \pi = 3$ MHz.
• Figure 5: The temporal dependences of state probabilities for the initial condition $\ket{\Psi_0} = \ket{\uparrow \downarrow}_0$. The spin-charge angle is $\phi = \pi / 6$.