Broadband noise-free optical quantum memory with neutral nitrogen-vacancy centers in diamond

It is proposed that the ground-state manifold of the neutral nitrogen-vacancy center in diamond could be used as a quantum two-level system in a solid-state-based implementation of a broadband noise-free quantum optical memory. The proposal is based on the same-spin $\Lambda$-type three-level system created between the two $E$ orbital ground states and the $A_1$ orbital excited state of the center, and the cross-linear polarization selection rules obtained with the application of a transverse electric field or uniaxial stress. Possible decay and decoherence mechanisms of this system are discussed, and it is shown that high-efficiency, noise-free storage of photons as short as a few tens of picoseconds for at least a few nanoseconds could be possible at low temperature.

Figure 1

(a) [(b)] Electronic configurations (left) and schematic level structure (right) of the ${\text{NV}}^{-}$ (${\text{NV}}^0$) under electric field along the $\widehat{x}$ direction in the NV coordinate system (see text). VB (CB) denotes the valence (conduction) band. An upward- (downward-) pointing arrow represents an electron with spin $\frac{1}{2}(-\frac{1}{2})$. The ellipses in (a) represent spin-triplet configurations. Only one of the three states is presented. The ellipse in (b) represents a symmetric superposition of both electrons occupying the $E_x$ state or the $E_y$ state. Only the spin $\frac{1}{2}$ states are presented. The double-headed arrows on the right represent allowed optical transitions. The transition dipole direction is specified next to each arrow.

Figure 2

(a) ${\text{NV}}^0$ energy levels vs transverse electric field. The NV axis is along $\left[111\right]\left(\widehat{z}\right)$. The field is along $\left[\overline{1}\overline{1}2\right]\left(\widehat{x}\right)$. The solid line presents the case of ${\rm Y}=0$. The dashed, dotted, and dashed-dotted lines present the case of ${\rm Y}=12\text{GHz}$ for $\alpha =0^{\circ }$, $\pm {90}^{\circ }$, and ${180}^{\circ }$, respectively. The same convention is used also in (b)–(d). (b) Linear polarization degree [equal to 1 ($-1$) for $\widehat{x}\left(\widehat{y}\right)$ polarization] of the optical transitions related to the lower [blue (dark gray) lines] and the higher [green (light gray) lines] ground state. (c) The product of the Raman coupling and the detuning, detuning-independent in the large-detuning regime, in cross-linear polarizations [higher- (lower-) energy light polarized along $\widehat{x}\left(\widehat{y}\right)$]. (d) Relative probability of $\widehat{x}$-polarized light to couple to the higher ground state.

Figure 3

(a) All possible orientations of the NV center. The nitrogen atom is in the middle. The direction of the applied field (optical axis) is denoted by a red horizontal (black vertical) arrow. (b) ${\text{NV}}^0$ energy levels vs electric field along [100]. The solid line presents the case of ${\rm Y}=0$. The dashed, dotted, thick dotted, and dashed-dotted lines present the case of ${\rm Y}=12\text{GHz}$ for $\alpha =0^{\circ }$, ${90}^{\circ }$, $-{90}^{\circ }$, and ${180}^{\circ }$, respectively. (c) The allowed transitions' $\left[100\right]\text{−}\left[010\right]$ linear polarization degree. The blue (dark gray) [green (light gray)] lines present the polarization of the transition coupled to the lower (higher) ground state. (d) Raman coupling [the higher- (lower-) energy light is polarized along $\left[100\right]$ ($\left[010\right]$)]. (e) Relative probability of the higher-energy light to couple to the higher-energy ground state, summed over all orientations.

Figure 4

(a) Optical pumping, (b) memory read-in, and (c) memory readout, for an NV oriented along $\left[111\right]$ under electric field along [100]. The transition dipole direction is stated next to each ground state. The polarization directions of the optical fields are indicated next to the relevant arrows. The right diagram in (c) corresponds to a readout attempt where no photon was initially stored. The control pulse couples only to one ground state, and no noise photon is emitted. The same external field directions induce the same effects for all other NV orientations as well (not shown).

Figure 5

(a) ${\text{NV}}^0$ ZPL spectrum at 5.7 K. The circles present the measured data. The solid black line is a single Gaussian fit convolved with the measured response function. The latter is presented by the green dotted line. (b) Fitting quality (sum of squared residuals, left axis) and fitted width (one standard deviation, right axis) of a double Gaussian model, vs the splitting between the two Gaussians. The splitting at which the fitting quality is twice as bad as the best achievable one is marked by the dotted lines. The corresponding fit is presented in (a) by the red dashed-dotted line.