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Spin squeezing via continuous QND feedback

L. K. Thomsen, Howard M. Wiseman

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Conditional spin squeezing can be achieved by continuous quantum-nondemolition measurement of an atomic sample. We show that simultaneous feedback of the measurement results can control the quantum state such that the squeezing becomes unconditional. For very strong cavity coupling, the squeezing approaches the Heisenberg limit. Squeezing is also produced at weaker couplings and even in free space, thus presenting a simple experimental test for quantum feedback.

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arXiv:1301.1016•Physical Review Letters•Apr 15, 2013•70 citations
Conditional spin squeezing can be achieved by continuous quantum-nondemolition measurement of an atomic sample. We show that simultaneous feedback of the measurement results can control the quantum state such that the squeezing becomes unconditional. For very strong cavity coupling, the squeezing approaches the Heisenberg limit. Squeezing is also produced at weaker couplings and even in free space, thus presenting a simple experimental test for quantum feedback.
We discuss the theory and experimental considerations of a quantum feedback scheme for producing deterministically reproducible spin squeezing. Continuous nondemolition atom number measurement from monitoring a probe field conditionally squeezes the sample. Simultaneous feedback of the measurement results controls the quantum state such that the squeezing becomes unconditional. We find that for very strong cavity coupling and a limited number of atoms, the theoretical squeezing approaches the Heisenberg limit. Strong squeezing will still be produced at weaker coupling and even in free space (thus presenting a simple experimental test for quantum feedback). The measurement and feedback can be stopped at any time, thereby freezing the sample with a desired amount of squeezing.
We propose a quantum feedback scheme for producing deterministically reproducible spin squeezing. The results of a continuous nondemolition atom number measurement are fed back to control the quantum state of the sample. For large samples and strong cavity coupling, the squeezing parameter minimum scales inversely with atom number, approaching the Heisenberg limit. Furthermore, ceasing the measurement and feedback when this minimum has been reached will leave the sample in the maximally squeezed spin state.
A weak measurement approach is proposed to entangle and squeeze atoms. We show that even for very small coupling strength between light and atoms, one can achieve large squeezing unattainable with normal measurement-based squeezing. Post-selecting the photons interacting with spins via a weak off-resonant quantum nondemolition interaction (QND) in a state nearly orthogonal to its initial state can strengthen the entanglement among elementary spins and thus enhance spin squeezing. The squeezing process is probabilistic but the created state is unconditionally determined. Further control of the post-selection parameter and the detection process can transform the QND-like spin squeezing into the one-axis-twisting or even two-axis-twisting type.
This chapter describes recent experiments involving continuous measurement and quantum feedback control of collective spin in a cloud of cold alkali atoms. While measurement by itself can generate entanglement between different atoms in the sample by virtue of conditional spin-squeezing, the squeezed state produced in any individual instance of the measurement is randomly distributed. Incorporating real-time feedback control into the observation process suppresses the statistical dispersion of the measurement outcome so that the same a posteriori state is achieved in every instance of the feedback-stabilized measurement.
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.