S. Brouard

We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case, such a “weak” measurement preserves coherence between the system's alternatives. We demonstrate that in both classically and quantally the information about the scenario realized in each individual trial is lost. However, ensemble parameters such as classical path probabilities and quantum quasiprobabilities can be extracted from the obtained statistics. Both classically and quantally, causality ensures that additional postselection only redistributes individual outcomes between the system's final states. Quantum quasiprobabilities may change sign, which allows for anomalously large meter's (pointer's) reading for some final states. These, we show, result from mere “reshaping” of a broad distribution obtained earlier and provide no “experimental evidence” of quantum variables taking, albeit on rare occasions, exceptionally large or otherwise anomalous values.

We follow Kofler and Brukner [Phys. Rev. Lett., {\bf 99}, 180403 (2007)] in studying the conditions under which a classical picture emerges from the results of not too accurate quantum measurements made on large macroscopic objects. We show that for such objects, consisting of a large number of microscopic elements obeying quantum laws, the Central Limit Theorem guarantees the existence of classical values for collective variables, even if the corresponding operators do not commute. Owing to localisation of the overall wave function in any chosen representation, these values can be measured to a small relative error without significantly altering the state of the object. We study a simple model, which includes a rudimentary observer capable of detecting in the coordinate space the position of a macroscopic pointer. The pointer can be employed to measure such quantities, not directly accessible to the observer, as linear or angular momenta. A purely classical picture arises provided the measurements are made on macroscopic objects. Results of measurements, made on small quantum objects, cannot be predicted with certainty, but acquire certain objectivity when encoded in macroscopic pointers' positions accessible to all observers. Our estimates show that the classical conditions could, in principle, be realised for systems with number of constituent parts of the order of the Avogadro constant. It is possible that the approach captures the essential features of the quantum-to-classical transition, although its extension to more realistic systems is likely to be required.

The conversion of ultracold atoms to molecules via a magnetic Feshbach resonance with a sinusoidal modulation of the field is studied. Different practical realizations of this method in Bose atomic gases are analyzed. Our model incorporates many-body effects through an effective reduction of the complete microscopic dynamics. Moreover, we simulate the experimental conditions corresponding to the preparation of the system as a thermal gas and as a condensate. Some of the experimental findings are clarified. The origin of the observed dependence of the production efficiency on the frequency, amplitude, and application time of the magnetic modulation is elucidated. Our results uncover also the role of the atomic density in the dynamics, specifically, in the observed saturation of the atom–molecule conversion process.

The dynamics of a quantum anharmonic oscillator whose position is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential is studied. The (non-exponential) decoherence induced on the oscillator by the measuring device is analysed. A detailed quasiclassical and quantum analysis is presented. In the first case, for an arbitrary initial coherent state, two different decoherence regimes are observed: An initial Gaussian decay followed by a power law decay for longer times. The characteristic time scales of both regimes are reported. Analytical approximated expressions are obtained in the full quantum case where algebraic time decay of decoherence is observed.

The dynamics of a quantum anharmonic oscillator whose position is monitored by a Bose-Einstein condensate trapped in a symmetric double well potential is studied. The (nonexponential) decoherence induced on the oscillator by the measuring device is analyzed. A detailed quasiclassical and quantum analysis is presented. In the first case, for an arbitrary initial coherent state, two different decoherence regimes are observed: an initial Gaussian decay followed by a power law decay for longer times. The characteristic time scales of both regimes are reported. Analytical approximated expressions are obtained in the full quantum case where algebraic time decay of decoherence is observed.

We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double-well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a ``coherent'' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power-law) or rapid (Gaussian) decoherence of the mean values themselves.

We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a `coherent' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power law) or rapid (Gaussian) decoherence of the mean values themselves.