Near-field levitated quantum optomechanics with nanodiamonds

We theoretically show that the dipole force of an ensemble of quantum emitters embedded in a dielectric nanosphere can be exploited to achieve near-field optical levitation. The key ingredient is that the polarizability from the ensemble of embedded quantum emitters can be larger than the bulk polarizability of the sphere, thereby enabling the use of repulsive optical potentials and consequently the levitation using optical near fields. In levitated cavity quantum optomechanics, this could be used to boost the single-photon coupling by combining larger polarizability to mass ratio, larger field gradients, and smaller cavity volumes while remaining in the resolved sideband regime and at room temperature. A case study is done with a nanodiamond containing a high density of silicon-vacancy color centers that is optically levitated in the evanescent field of a tapered nanofiber and coupled to a high-finesse microsphere cavity.

Figure 1

Ratio $N\eta$ (solid dark line) of the total quantum polarizability over the dielectric polarizability for a nanodiamond with a high density of SiV. Larger intensities both increase the saturation of the quantum emitters and the internal temperature (solid light line) leading to a reduction of the quantum polarizability. The properties of the nanodiamond and the SiV are listed in Appendixes pp1-s1 and pp1-s2, respectively. We remark that since the SiV centers are embedded in the ND, we accounted for the Lorentz local field correction [51], $(n^2+2)/3$, for the field inside the ND.

Figure 2

Trapping potential for a 30 nm ND accounting for the dipolar forces acting on the quantum emitters and the ND along with gravity and the Casimir-Polder forces (see Appendix pp1-s3 for the experimental parameters). The trapping potential obtained using the dipole force for the bichromatic field using the second order in the Floquet analysis (solid line) shows an important deviation from considering the dipole force from the two evanescent fields independently (light solid line). For reference, the force without accounting for the Casimir-Polder forces is represented with the dashed line.

Figure 3

Schematic illustration of the general scenario that is considered: a dielectric nanosphere with a set of two-level quantum emitters is trapped using a bichromatic evanescent field at a distance $z$ from a surface. In the inset of the figure the level structure of an individual quantum emitter of transition frequency ${\omega }_0$ and excited-state linewidth $\gamma$ is illustrated. The transition is driven by a bichromatic field with symmetric red and blue detuning $\mp \mathrm{\Delta }>\gamma$, with Rabi frequencies ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$, respectively. The cavity field mode with vacuum Rabi frequency ${\mathrm{\Omega }}_c$ is detuned by ${\mathrm{\Delta }}_c>\gamma$.

Figure 4

Optomechanical coupling for a 30 nm ND while in the resolved sideband regime. The best optomechanical coupling is obtained at low intensity as it provides a small excited-state population [minimizing the cavity scattering losses; see Eq. (34)] and low inhomogeneous broadening thanks to a moderate internal temperature [maximizing the coupling; see Eq. (33)]. For the parameters see Appendix pp1-s5.

Figure 5

Optomechanical coupling and ND position. By varying the intensity ratio $I_2/(I_1+I_2)$, the position of the 30 nm ND can be controlled in order to the reach the optimum optomechanical coupling. As the ND is brought close the cavity, the cavity scattering losses are greatly increased by the presence of the quantum emitters.

Figure 6

Trapping potential for a 30 nm ND using two blue-detuned fields. Two blue-detuned fields, one from the nanofiber and from the cavity are used to trap the ND. The large detuning, $\left|\mathrm{\Delta }\right|=1\times {10}^{15}\text{Hz}$, allows one to maintain a very small excited-state population (see Appendix pp1-s6 for the experimental parameters). To provide confinement on the transversal dimensions, an additional weak red-detuned field from the nanofiber can be used.