Abstract
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.
Highlights
We demonstrate that the effects of the spontaneous-emission noise can be cancelled with the application of an active feedback control that is tailored to the measurement being applied
The number-phase Wigner (NPW) particle filter allows for the simulation of a feedback controlled, continuously monitored BEC that includes the quantum statistics ignored by the Hartree–Fock method
With additional measurement-induced disruption to the condensate that are not included in single-mode and semiclassical models, and cannot be counteracted with simple linear and/or quadratic feedback controls
Summary
It has been shown that the linewidth of an outcoupled atom laser can be improved by continuously monitoring the BEC with off-resonant light and applying active feedback [11,12,13,14,15,16] These prior analyses used single-particle or meanfield models of the system, and did not fully incorporate the multi-mode quantum-field effects of the measurement backaction. Most relevant to this paper, previous analyses by Szigeti et al [14, 15], who considered the semiclassical limit of a multi-mode quantum filtering model for an off-resonantly imaged, feedback-cooled BEC, suggested that active feedback could remove the disruption caused by off-resonant imaging entirely These models were analysed under the Hartree–Fock approximation, which assumes the condensate has a fixed number of atoms all in the same single-particle state, which in turn neglects part of the spontaneous-emission noise, making this analysis incomplete.
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