Collective Quantum Feedback of Many-Atom Systems

遼太郎 井上, Ryotaro Inoue, 義朗 高橋 +1 more

Joerg, Evers

D. A. Ivanov, T. Yu. Ivanova, Igor B. Mekhov

It is well known that in the presence of a ring cavity the light scattering from a uniform atomic ensemble can become unstable resulting in the collective atomic recoil lasing. This is the result of a positive feedback due to the cavity. We propose to add an additional electronic feedback loop based on the photodetection of the scattered light. The advantage is a great flexibility in choosing the feedback algorithm, since manipulations with electric signals are very well developed. In this paper we address the application of such a feedback to atoms in the Bose-Einstein condensed state and explore the quantum noise due to the incoherent feedback action. We show that although the feedback based on the photodetection does not change the local stability of the initial uniform distribution with respect to small disturbances, it reduces the region of attraction of the uniform equilibrium. The feedback-induced nonlinearity enables quantum fluctuations to bring the system out of the stability region and cause an exponential growth even if the uniform state is globally stable without the feedback. Using numerical solution of the feedback master equation we show that there is no feedback-induced noise in the quadratures of the excited atomic and light modes. The feedback loop, however, introduces additional noise into the number of quanta of these modes. Importantly, the feedback opens an opportunity to position the modulated BEC inside a cavity as well as tune the phase of scattered light. This can find applications in precision measurements and quantum simulations.

Peter Rabl, Viktor Steixner, P. Zoller

We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven $\ensuremath{\Lambda}$-system based on electromagnetically induced transparency. In the ideal limit of unit collection efficiency this provides a quantum-limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit the steady state energies are close to the ground state, limited only by the photon collection efficiency. Outside of the Lamb-Dicke regime the predicted temperatures are well below the Doppler limit.

Alexander Pitchford

Ryotaro Inoue, Shin-Ichi-Ro Tanaka, Ryo Namiki +2 more

We demonstrate unconditional quantum-noise suppression in a collective spin system via feedback control based on quantum nondemolition measurement. We perform shot-noise limited collective spin measurements on an ensemble of 3.7×10(5) laser-cooled (171)Yb atoms in their spin-1/2 ground states. Correlation between two sequential quantum nondemolition measurements indicates -0.80(-0.12)(+0.11) dB quantum-noise suppression in a conditional manner. Our feedback control successfully converts the conditional quantum-noise suppression into the unconditional one without significant loss of the noise reduction level.