Non-Demolition Measurement and Control in Quantum Dynamical Systems

Abir U. Igamberdiev

V. P. Belavkin

Sergey Victorovich Ulyanov, Fumihito Arai, K. Yamafuji +3 more

The possible accuracy limit of micro control of dynamic systems in which the dominating disturbances are thermal and quantum noises is considered. The optimal control with a Kalman-Bucy filter (KBF) and physical limits of micro control of a macro object are studied. For the individual control of a micro object a quantum prototype of KBF with non-demolition observation on the basis of quantum filtering equation is introduced.

Peng Zhang, Qing Ai, Yong Li +2 more

We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation (Nature {\bf 405}, 546 (2000)). The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly {\it enhanced} by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with {\it arbitrary} temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.

H. Ezawa