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arXiv:cond-mat/0307221 · Physical Review A

Continuous measurement of atom-number moments of a Bose-Einstein condensate by photodetection

Gilberto Aparecido Prataviera, M. C. de Oliveira

Published Jul 14, 2004• 10 citations
arXivHTMLPDF

Abstract

We propose a measurement scheme that allows determination of even moments of a Bose-Einstein condensate (BEC) atom number, in a ring cavity, by continuous photodetection of an off-resonant quantized optical field. A fast cavity photocounting process limits the heating of atomic samples with a relatively small number of atoms, being convenient for BECs on microchip scale applications. The measurement back-action introduces a counting-conditioned phase damping, suppressing the condensate typical collapse and revival dynamics.

DOI
10.1103/physreva.70.011602

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We propose a measurement scheme that allows determination of even moments of a Bose-Einstein condensate (BEC) atom number, in a ring cavity, by continuous photodetection of an off-resonant quantized optical field. A fast cavity photocounting process limits the heating of atomic samples with a relatively small number of atoms, being convenient for BECs on microchip scale applications. The measurement back-action introduces a counting-conditioned phase damping, suppressing the condensate typical collapse and revival dynamics.
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We investigate a nondestructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from an atomic resonance, and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunneling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop due to measurement backaction noise alone.
Off-resonant optical imaging is a popular method for continuous monitoring of a Bose–Einstein condensate. However, the disturbance caused by scattered photons places a serious limitation on the lifetime of such continuously monitored condensates. In this paper, we demonstrate that a new choice of feedback control can overcome the heating effects of the measurement backaction. In particular, we show that the measurement backaction caused by off-resonant optical imaging is a multi-mode quantum-field effect, as the entire heating process is not seen in single-particle or mean-field models of the system. Simulating such continuously monitored systems is possible with the number-phase Wigner particle filter, which currently gives both the highest precision and largest timescale simulations amongst competing methods. It is a hybrid between the leading techniques for simulating non-equilibrium dynamics in condensates and particle filters for simulating high-dimensional non-Gaussian filters in the field of engineering. The new control scheme will enable long-term continuous measurement and feedback on one of the leading platforms for precision measurement and the simulation of quantum fields, allowing for the possibility of single-shot experiments, adaptive measurements and robust state-preparation and manipulation.
We investigate a non-destructive homodyne measurement of atomic condensates using off-resonant optical laser beam that interacts with atomic Bose-Einstein condensate (BEC). The interaction between laser beam and the atomic BEC creates entangled states of atom and light that are destroyed in a homodyne detection of light. The destruction of the entangled states causes back-action on the atomic states. We derive expression for the measurement operator on the atomic states due to the photon measurement. We characterize the back-action by calculating quantities such as the Q-function and observe the variation of the measured state with the strength of the light-BEC interaction.
Abstract A fundamental tenet of quantum mechanics is that measurements change a system’s wavefunction to that most consistent with the measurement outcome, even if no observer is present. Weak measurements produce only limited information about the system, and as a result only minimally change the system’s state. Here, we theoretically and experimentally characterize quantum back-action in atomic Bose-Einstein condensates interacting with a far-from resonant laser beam. We theoretically describe this process using a quantum trajectories approach where the environment measures the scattered light and present a measurement model based on an ideal photodetection mechanism. We experimentally quantify the resulting wavefunction change in terms of the contrast of a Ramsey interferometer and control parasitic effects associated with the measurement process. The observed back-action is in good agreement with our measurement model; this result is a necessary precursor for achieving true quantum back-action limited measurements of quantum gases.
A model of photodetection using a Bose-Einstein condensate in an atom-chip-based microtrap is analyzed. Atoms absorb photons from the incident light field, receive part of the photon momentum, and leave the trap potential. Upon counting escaped atoms within predetermined time intervals, the photon statistics of the incident light is mapped onto the atom-count statistics. Whereas traditional photodetection theory treats the emission centers of photoelectrons as distinguishable, here the centers of escaping atoms are condensed and thus indistinguishable atoms. From this, an enhancement of the photon-number resolution as compared to the commonly known counting formula is derived for the case of low saturation.