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arXiv:1206.6702 · Physical Review A

Unsharp continuous measurement of a Bose-Einstein condensate: Full quantum state estimation and the transition to classicality

Moritz Hiller, Magnus Rehn, Francesco Petruccione, Andreas Buchleitner, Thomas Konrad

Published Sep 24, 2012• 11 citations

Abstract

We study a Bose-Einstein condensate (BEC) in a double-well potential subject to an unsharp continuous measurement of the atom number in one of the two wells. We investigate the backaction of the measurement on the quantum dynamics and the viability to monitor the ensuing time evolution. For vanishing interatomic interactions, mainly the expectation values of the measured local observable can be inferred from the measurement record. Conversely, in the presence of moderate interatomic interactions, the entire many-body state---modified by the measurement---is monitored with unit fidelity and, at the same time, the measurement effects a transition from quantum to mean-field (classical) behavior of the BEC. We show that this perfect state estimation is possible because the interatomic interactions enhance the information gained via the measurement.

DOI: 10.1103/physreva.86.033624

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We study a Bose-Einstein condensate (BEC) in a double-well potential subject to an unsharp continuous measurement of the atom number in one of the two wells. We investigate the backaction of the measurement on the quantum dynamics and the viability to monitor the ensuing time evolution. For vanishing interatomic interactions, mainly the expectation values of the measured local observable can be inferred from the measurement record. Conversely, in the presence of moderate interatomic interactions, the entire many-body state---modified by the measurement---is monitored with unit fidelity and, at the same time, the measurement effects a transition from quantum to mean-field (classical) behavior of the BEC. We show that this perfect state estimation is possible because the interatomic interactions enhance the information gained via the measurement.

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For the dynamics of Bose-Einstein condensates (BECs), differences between mean-field (Gross-Pitaevskii) physics and

N

-particle quantum physics often disappear if the BEC becomes larger and larger. In particular, the time scale for which both dynamics agree should thus become larger if the particle number increases. For BECs in a double-well potential, we find both examples for which this is the case and examples for which differences remain even for huge BECs on experimentally realistic short time scales. By using a combination of numerical and analytical methods, we show that the differences remain visible on the level of expectation values even beyond the largest possible numbers realized experimentally for BECs with ultracold atoms.

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.

This thesis aims to investigate the dynamic properties of ultra-cold Bose-Einstein condensates (BEC) trapped in a deep double well potential. Despite its simplicity, this system shows a rich variety of dynamical behaviors: Josephson oscillations, self-trapping behavior and critical dynamics. In contrast to previous studies, we aim to understand not only the first moment of the evolving occupation probability, but all its moments. This is known in mesoscopic physics as the "counting statistics" problem. Using the quantum dimer, we are the first to address the effects of interatomic interactions on counting statistics. We expect that our predictions will be easily tested in recent experimental realizations of the BEC double well trap.

We investigate fidelity for the quantum evolution of a Bose-Einstein condensate (BEC) and reveal its general property with a simple two-component BEC model. We find that, when the initial state is a coherent state, the fidelity decays with time in the ways of exponential, Gaussian, and power law, depending on the initial location, the perturbation strength, as well as the underlying mean-field classical dynamics. In this case we find a clear correspondence between the fast quantum fidelity decay and the dynamical instability of the mean-field system. With the initial state prepared as a maximally entangled state, we find that the behavior of fidelity has no classical correspondence and observe an interesting behavior of the fidelity: periodic revival, where the period is inversely proportional to the number of bosons and the perturbation strength. An experimental observation of the fidelity decay is suggested.