Demonstration of geometric diabatic control of quantum states

Geometric effects can play a pivotal role in streamlining quantum manipulation. We demonstrate a geometric diabatic control, that is, perfect tunneling between spin states in a diamond by a quadratic sweep of a driving field. The field sweep speed for the perfect tunneling is determined by the geometric amplitude factor and can be tuned arbitrarily. Our results are obtained by testing a quadratic version of Berry's twisted Landau-Zener model. This geometric tuning is robust over a wide parameter range. Our work provides a basis for quantum control in various systems, including condensed-matter physics, quantum computation, and nuclear magnetic resonance.

Figure 1

Comparison of the Landau-Zener (LZ) transition and the twisted Landau-Zener (TLZ) transition. (a) Tunneling at level anticrossing. (b) Sweeping of the driving field. The fields at $t=0$ and $t=T$ for the LZ (TLZ) model are indicated by solid and dashed blue (red) arrows, respectively. Predicted (c) LZ transition probability and (d) TLZ transition probability are plotted as a function of the speed $F$. Dynamics of the field (black arrow) and spin (blue arrow) in the LZ model are plotted in the (e) adiabatic and (f) diabatic limits [see also (b) and (c)]. Dynamics of the field (black arrow) and spin (red arrow) in the TLZ model are plotted at (g) $F=F_{\text{PT}}$ and (h) $F=-F_{\text{PT}}$ [see also (b) and (d)]. The solid black line indicates the field amplitude in the $xy$ plane in (e) and (f) and in the $yz$ plane in (g) and (h). The origin of each arrow corresponds to the field amplitude at each instant.

Figure 2

Demonstration of the TLZ transition at $m=0.5$ MHz. (a) Measurement sequence. Laser and microwave pulses are used for initialization and readout of the NV center. (b) Dependence of tunneling probability $P$ on speed $F$. The squares and circles indicate experimental results, black solid lines indicate the TLZ formula [Eq. (2)], and vertical black dotted lines indicate $F=F_{\text{PT}}$. The blue dashed lines indicate the LZ formula [TLZ with $R_{12}\left(0\right)=0$]. (c) Tunneling probability at $F=F_{\text{PT}}$ in the range of ${\kappa }_{\parallel }=0$–$1\mu \mathrm{s}$. The error bars indicate 65% confidence intervals estimated from the shot noise of the PL measurement.

Figure 3

Gap parameter and curvature dependence of the TLZ transition probability. (a) The left (right) panels denote the results at $m=0.5\mathrm{MHz}$ ($m=2.0\mathrm{MHz}$). The black solid (green dashed) line indicates the PT condition in the TLZ formula (simulation). (b) Tunneling probability at ${\kappa }_{\parallel }=1.4\mu \mathrm{s}$ [white line in (a i) and (a ii)]. The black arrow in (ii) indicates the PT condition.

Figure 4

Sweep speed dependence of the transition probability of the gapless ($m=0.0\mathrm{MHz}$) system. (a) The LZ transition (${\kappa }_{\parallel }=0$). The inset is a schematic of the energy change. (b) The TLZ transition (${\kappa }_{\parallel }=2.5\mu \mathrm{s}$).