Coherence protection by the quantum Zeno effect and nonholonomic control in a Rydberg rubidium isotope

The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error correction (ancilla adding, coding and decoding) and the quantum Zeno effect. A demonstration of our method on a simple atomic system—namely, a rubidium isotope—is proposed.

Figure 1

Multidimensional QZE: (a) a simple projection fails to recover the initial vector, (b) the sequence coding-decoding-projection protects the initial vector.

Figure 2

Spectrum of ${}^{78}\mathrm{Rb}$: The useful part of the spectrum of rubidium is represented.

Figure 3

Ancilla adding by pumping. Photon polarization and involved sub-Zeeman levels are represented. The fine structure of the Rydberg level $60f$ is not resolvable.

Figure 4

Coding step through the nonholonomic control technique. The two Hamiltonians ${\widehat{H}}_a$ and ${\widehat{H}}_b$ are alternately applied to the system during pulses of timings $\left\{t_i\left(\mathrm{ns}\right)\right\}=\{3.9763,$ 6.4748, 4.2274, 3.6259, 2.8717, 3.6281, 7.2263, 6.4260, 4.8070, 5.0394, 6.5242, 4.8890, 4.2400, 7.3834, 4.8653, 5.4799, 4.5341, 4.3099, 6.2959, 3.7346, 6.5293, 6.8586, 6.0749, 5.1213, 4.6806, 3.4985, 3.9909, 4.6701, 4.5168, 6.4702, 4.7787, 5.3476, 3.4567, 3.8009}. The frequencies of the laser fields involved in the encoding step are represented on the spectrum of the rubidium atom. The fine structure of the Rydberg level $60f$ is not represented.

Figure 5

Decoding step by the nonholonomic control technique. We reverse the magnetic field and the detunings of the electric fields, as represented on the spectrum of the rubidium atom, and apply the same control sequence as for coding (same timings) backwards. The fine structure of the level $60f$ is not represented.

Figure 6

Projection path. The lasers involved are marked by solid arrows; the spontaneous photon is represented by a dashed arrow. The different polarizations are specified. The fine structure of the level $60f$ is not represented.