Electrically Switchable Entanglement Channel in van der Waals Magnets

Two-dimensional layered van der Waals (vdW) magnets demonstrate their potential to allow the study of both fundamental and applied physics due to their remarkable electronic properties. However, the connection of vdW magnets to spintronics and quantum information science is not clear. In particular, it remains elusive whether there are interesting magnetic phenomena belonging only to vdW magnets but absent in widely studied crystalline magnets. Here, we consider the quantum correlations of magnons in a layered vdW magnet and identify an entanglement channel of magnons across the magnetic layers, which can be effectively tuned and even deterministically switched on and off by both magnetic and electric means. This is a unique feature of vdW magnets, in which the underlying physics is well understood in terms of the competing roles of exchange and anisotropy fields that contribute to magnon excitation. Furthermore, we show that such a tunable entanglement channel can mediate the electrically controllable entanglement of two distant qubits, which also provides a protocol to indirectly measure the entanglement of magnons. Our findings provide an avenue to electrically manipulate qubits and further open up opportunities to utilize vdW magnets for quantum information science.

Figure 1

(a) Schematic illustration of bilayer van der Waals magnets subject to an in-plane magnetic field ($\mathbf{H}$) and a normal electric field ($\mathbf{E}$) (b) Entanglement of magnons and occupation of Fock space in the ground state as a function of magnetic field. Magnetic parameters of ${\mathrm{Cr}\mathrm{I}}_3$ [19] are used with $2J=0.83\mathrm{T}$ and $2K=1.73\mathrm{T}$. We take the truncation $N=19$ in the numerical calculation of magnon entanglement (red line) and a further increase of $N$ does not change the entanglement significantly. Red dashed line indicates the magnetic transition field at $H_{cm}=2.46\mathrm{T}$, and blue dashed line is the local minimum of entanglement at $H_{ce}=2.16\mathrm{T}$. (c) Energy levels of the two-magnon system.

Figure 2

(a) Steady magnon-magnon entanglement in the $(H,J/K)$ plane. (b) Steady entanglement as a function of external field for $J/K=0.48$ (red line), 0.96 (blue line), and 1.92 (black line). Dashed lines indicate the transition fields $H_{cm}$ located at $2(J+K)S$. ${\gamma }_1={\gamma }_2=0.01$. (c) Entanglement at the transition field ($E_{cm}$) and critical field for zero entanglement ($H_{ce}/H_{cm}$) as a function of $J/K$. Symbols are full numerical results based on the Hamiltonian [Eq. (2)] and lines depict Eqs. (9) and (11).

Figure 3

Entanglement of magnons at different temperatures (a) and magnon dissipation (b). Here, $n_{\mathrm{th}}=0.3$ corresponds to $T=1.6\mathrm{K}$ with $\omega /2\pi =50\mathrm{GHz}$ [19]. $\gamma =0.01$ for (a) and $n_{\mathrm{th}}=0.01$ for (b).

Figure 4

Entanglement of magnons (solid lines) and qubits (dashed lines) as a function of gate voltage for $H=1.5\mathrm{T}$ (red line), 1.75 T (blue line), 2.0 T (black line), and 2.25 T (purple line). Gray line at $E_N=0.085$ is a threshold of magnon-magnon entanglement to switch the qubit-qubit entanglement on and off. Parameters are $J_0=0.865\mathrm{T}$, $b_J=9.5\times {10}^{-3}\mathrm{T/V}$, $K_0=0.415\mathrm{T}$, and $b_K=5.5\times {10}^{-3}\mathrm{T/V}$ [19]. ${\omega }_1=-{\omega }_2=0.01\mathrm{T}$, $g_{qm}={10}^{-4}\mathrm{T}$ [30, 31]. (b) Density of states for the steady states of two qubits when $E=-20\mathrm{V}$ (left panel) and 19 V (right panel). $H=1.5\mathrm{T}$.