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arXiv:quant-ph/0202028 · Physical Review A

Spin squeezing via quantum feedback

L. K. Thomsen, Stefano Mancini, Howard M. Wiseman

Published Jun 4, 2002• 156 citations
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Abstract

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.

DOI
10.1103/physreva.65.061801

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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.
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.
Abstract We analyze the generation of spin-squeezed states via coupling of three-level atoms to an optical cavity and continuous quantum measurement of the transmitted cavity field in order to monitor the evolution of the atomic ensemble. Using analytical treatment and microscopic simulations of the dynamics, we show that one can achieve significant spin squeezing, favorably scaling with the number of atoms N. However, contrary to some previous literature, we clarify that it is not possible to obtain Heisenberg scaling without the continuous feedback that is proposed in optimal approaches. In fact, in the adiabatic cavity removal approximation and large N limit, we find the scaling behavior N − 2 / 3 for spin squeezing and N − 1 / 3 for the corresponding protocol duration. These results can be obtained only by considering the curvature of the Bloch sphere, since linearizing the collective spin operators tangentially to its equator yields inaccurate predictions. With full simulations, we characterize how spin-squeezing generation depends on the system parameters and departs from the bad cavity regime, by gradually mixing with cavity-filling dynamics until metrological advantage is lost. Finally, we discuss the relevance of this spin-squeezing protocol to state-of-the-art optical clocks.
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 theoretically investigate the entangled states of an atomic ensemble that can be obtained via cavity feedback, varying the atom-light coupling from weak to strong, and including a systematic treatment of decoherence. In the strong-coupling regime for small atomic ensembles, the system is driven by cavity losses into a long-lived, highly entangled many-body state that we characterize analytically. In the weak-coupling regime for large ensembles, we find analytically the maximum spin-squeezing that can be achieved by optimizing both the coupling and the atom number. This squeezing is fundamentally limited by spontaneous emission to a constant value, which is independent of the atom number.
We theoretically investigate the entangled states of an atomic ensemble that can be obtained via cavity feedback, varying the atom-light coupling from weak to strong, and including a systematic treatment of decoherence. In the strong-coupling regime for small atomic ensembles, the system is driven by cavity losses into a long-lived, highly entangled many-body state that we characterize analytically. In the weak-coupling regime for large ensembles, we find analytically the maximum spin-squeezing that can be achieved by optimizing both the coupling and the atom number. This squeezing is fundamentally limited by spontaneous emission to a constant value, which is independent of the atom number.