Spin-Mechanical Scheme with Color Centers in Hexagonal Boron Nitride Membranes

Recently observed quantum emitters in hexagonal boron nitride (hBN) membranes have a potential for achieving high accessibility and controllability thanks to the lower spatial dimension. Moreover, these objects naturally have a high sensitivity to vibrations of the hosting membrane due to its low mass density and high elasticity modulus. Here, we propose and analyze a spin-mechanical system based on color centers in a suspended hBN mechanical resonator. Through group theoretical analyses and ab initio calculation of the electronic and spin properties of such a system, we identify a spin doublet ground state and demonstrate that a spin-motion interaction can be engineered, which enables ground-state cooling of the mechanical resonator. We also present a toolbox for initialization, rotation, and readout of the defect spin qubit. As a result, the proposed setup presents the possibility for studying a wide range of physics. To illustrate its assets, we show that a fast and noise-resilient preparation of a multicomponent cat state and a squeezed state of the mechanical resonator is possible; the latter is achieved by realizing the extremely detuned, ultrastrong coupling regime of the Rabi model, where a phonon superradiant phase transition is expected to occur.

Figure 1

(a) Geometry of $V_N{N}_B$ defect in hBN monolayer in top view. (b) Ab initio results for band structure and the corresponding density of states (DOS) of a monolayer hBN with charge neutral $V_N{N}_B$ defects: spin-up polarization is in black and spin-down in red. The defect energy levels within the band gap are labeled according to their molecular symmetry [9]. The Fermi energy level is set to zero (purple dashed line). (c) Two lowest multielectron states of the defect. They are spin doublets with Zeeman splitting $\mathrm{\Delta }$ and the respective transition rates: spin-preserving decays (at rate $\kappa$), spin-flip optical drives due to spin-orbit mixing ${\mathcal{E}}_{\parallel }$, and microwave drive $\mathrm{\Omega }$.

Figure 2

(a) Scheme for the proposed setup: A suspended circular hBN membrane with radius $R$ as the mechanical resonator. A magnetic field gradient enables a spin-motion coupling. The spin qubits are driven by a microwave field, while a polarized collimated optical drive provides the spin-polarization mechanism. (b) Coupling rate to mechanical frequency ratio for the qubit at the sweet spot (blue line) and effective boson number of the mechanical mode after cooling under optimal conditions (red circles) versus radius of the membrane. The black horizontal line indicates both $g_0/{\omega }_m=1$ and ${\overline{n}}_{\mathrm{eff}}=1$ (the ground-state limit). For clarity, the explicit mechanical frequencies are given in the top axis.

Figure 3

(a) The fidelity of the prepared multicomponent Schrödinger cat state as a function of the decoherence rate. Inset: The Wigner function of the prepared state for $\tilde{\mathrm{\Gamma }}/{\omega }_m=0.2$ (black dot). (b) The minimum quadrature variance of the mechanical mode in units of dB. Inset: The Wigner function of the prepared state for $\xi =2$ and $\mathrm{\Omega }/{\omega }_m=15$ (black dot). Note that in both plots, ${\tilde{\mathrm{\Gamma }}}_o\simeq 0$ because there is no optical polarization and ${\tilde{\mathrm{\Gamma }}}_h/{\omega }_m\approx 0.1$.