Zeno and Anti-Zeno Polarization Control of Spin Ensembles by Induced Dephasing

We experimentally and theoretically demonstrate the purity (polarization) control of qubits entangled with multiple spins, using induced dephasing in nuclear magnetic resonance setups to simulate repeated quantum measurements. We show that one may steer the qubit ensemble towards a quasiequilibrium state of a certain purity by choosing suitable time intervals between dephasing operations. These results demonstrate that repeated dephasing at intervals associated with the anti-Zeno regime leads to ensemble purification, whereas those associated with the Zeno regime lead to ensemble mixing.

Figure 1

Time evolution of the $S$-spin polarization. (a) The main panel compares $S$-spin polarization interrupted by repeated measurements at intervals of ${\tau }_c^{\exp }=1\mathrm{ms}$ (blue upper triangles) and the evolution interrupted at ${\tau }_h=0.2\mathrm{ms}$ (red circles), respectively. A quasiequilibrium state is achieved for the ${\tau }_c^{\exp }$ measurements, stopped after 8 ms and followed by free evolution at later times (green lower triangles). The $S$ spin free evolution is shown with black squares. The inset zooms the dynamics for short times. The theoretical curves (dashed lines) are obtained by exact diagonalization of the Hamiltonian (1) for the experimental parameters above. (b) Schematic representation of the QZE and AZE in thermalized qubits. The white line is the $S$-spin quantum dynamics steered by $n=20$ measurements upon varying the time interval $\tau$. It evidences the predicted amplifications compared with the free evolution (black line). For short times (QZE regime), the levels are unresolved and their transition rates are equal (lower inset), while for long times (AZE regime) they are resolved and the downward transitions dominate (upper inset).

Figure 2

System polarization evolution under matching (${\omega }_S={\omega }_I$) and off-matching (${\omega }_S\ne {\omega }_I$) conditions. (a) Free evolution (black solid line) of the system ($S$) spin polarization and its evolution interrupted by measurements at time intervals $\tau$ of $346\mu \mathrm{s}$ (orange circles) and $692\mu \mathrm{s}$ (green upper triangles) for off-resonant fields with high detuning. $\tau$ values were chosen to optimize the transfer. The quasiequilibrium state corresponding to measurements (at time intervals of $692\mu \mathrm{s}$) stopped after 31.14 ms ($n=45$), followed by the free evolution for the later times, is marked by blue lower triangles. (b) For resonant rf fields, we plotted the free evolution (black line) of $S$-spin polarization, interrupted by measurements at time intervals 1.82 ms (green upper triangle). The quasiequilibrium state corresponding to measurements (at time intervals of 1.82 ms) stopped after 14.56 ms ($n=8$), followed by free evolution at later times, is marked by blue lower triangles. The maximal polarization transfer attained by resonant fields (black line) is almost the same as that achieved and maintained (blue lower triangles) by measurements for all later times.