High-Efficiency Detection of a Single Quantum of Angular Momentum by Suppression of Optical Pumping

We propose and demonstrate experimentally the discrimination between two spin states of an atom purely on the basis of their angular momentum. The discrimination relies on angular momentum selection rules and does not require magnetic effects such as a magnetic dipole moment of the atom or an applied magnetic field. The central ingredient is to prevent by coherent population trapping an optical pumping process which would otherwise relax the spin state before a detectable signal could be obtained. We detected the presence or absence of a single quantum ($1\hslash$) of angular momentum in a trapped calcium ion in a single observation with success probability 0.86. As a practical technique, the method can be applied to read out some types of quantum computer.

Figure 1

(a)  Basic concept of the spin measurement. A weak probe laser ${\Omega }_S$ causes fluorescence which is detected. A strong pump laser ${\Omega }_D$ selectively suppresses the excitation from $|-\rangle$ which would otherwise cause optical pumping from $|-\rangle$ to $|+\rangle$. (b) Low-lying energy levels of the ${\mathrm{C}\mathrm{a}}^{+}$ ion used in the experiment, with laser wavelengths indicated in nm. The pump and probe transitions are $3D_{3/2}\leftrightarrow 4P_{3/2}$ (850 nm) and $4S_{1/2}\leftrightarrow 4P_{3/2}$ (393 nm), respectively.

Figure 2

Experimental sequence to prepare and measure the spin once. First the 397 and 866 nm beams cool the ion, and the PMT collects fluorescence (typical signal 100 counts), while the 854 nm beam serves to depopulate $D_{5/2}$, should the ion have been shelved in the previous sequence. Next a weak circularly polarized 397 nm beam is used to prepare the spin state by optical pumping. For ${\sigma }^{+}$ polarization the prepared state is a a mixture expected to be 99.9% $|+\rangle$, $0.1$% $|-\rangle$, owing to the 3° between this beam and the quantisation axis set by the 850 nm beam. (We confirmed the preparation to 1% uncertainty in a separate experiment by observing the reduction in fluorescence as a waveplate was rotated.) All beams are then shut off, and the intense ${\sigma }^{+}$-polarized 850 nm pump beam is introduced. Then the ${\sigma }^{-}$-polarized 393 probe beam, propagating at angle 6° to the 850 beam, is introduced for a precisely timed pulse of duration $\tau$. The optimum pulse time was found experimentally to be $\tau =150\mu \mathrm{s}$; this was consistent with our calculations discussed in the text. Finally the 850 nm beam is extinguished, and then the 397 nm and 866 nm beams are reintroduced and fluorescence detected during 10 ms. Absence of fluorescence indicates that the ion has been shelved.

Figure 3

Example data set. The proportion of times no fluorescence was observed in a set of 100 repetitions is shown versus detuning $\delta$ of the 393 nm laser. Circles: population prepared in $|+\rangle$; triangles: population prepared in $|-\rangle$. The lines show theoretical fits obtained from a full solution of the OBEs, with parameters ${\Omega }_S=2\pi \times 0.82\mathrm{M}\mathrm{H}\mathrm{z},{\Omega }_D=2\pi \times 85\mathrm{M}\mathrm{H}\mathrm{z},{\gamma }_{393}={\gamma }_{850}=2\pi \times 1.5\mathrm{M}\mathrm{H}\mathrm{z},B=7\mathrm{G}$. The fitted curve allows for 1% polarization impurity in the 850 nm beam. The angular momentum state is detected with $(1+ϵ)/2=86\%$  reliability in a single shot (for equal prior probabilities of $|-\rangle$, $|+\rangle$).