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arXiv:1303.5888 · Physical Review A

Dissipative versus conditional generation of Gaussian entanglement and spin squeezing

Denis V. Vasilyev, Christine A. Muschik, Klemens Hammerer

Published May 15, 2013• 9 citations
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Abstract

Spin squeezing of collective atomic spins can be achieved conditionally via probing with light and subsequent homodyne detection, as is done in a quantum nondemolition measurement. Recently it has been shown that squeezing can also be created unconditionally by a properly designed dissipative dynamics. We compare the two approaches in a Gaussian description and optimize over all Gaussian light-matter interactions. We find that in the optimal unconditional scheme based on dissipation the level of squeezing scales with optical depth as ${d}^{\ensuremath{-}1/2}$. In contrast, the optimal conditional scheme based on measurement of light---which in fact is not a quantum nondemolition measurement---can provide squeezing which scales as ${d}^{\ensuremath{-}1}$. Our results apply directly also to the creation of entanglement in the form of nonlocal spin squeezing of two atomic ensembles.

DOI
10.1103/physreva.87.053820

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We propose a scheme for producing entangled spin-squeezed states of an atomic ensemble inside an optical cavity by backaction of a detuned quantum-nondemolition (QND) measurement. By illuminating the atoms with bichromatic light, an interaction Hamiltonian of the cross-Kerr effect between the cavity and atoms is generated to implement QND measurements. The feedback effect is obtained through mixing the phase and amplitude quadratures of the cavity field, due to the detuning of the optical cavity. Therefore the continuous nondemolition measurements are fed back to correct the quantum state of the atomic sample such that unconditional spin squeezing is produced without requiring the use of any external electronics.
Squeezing of collective atomic spins has been shown to improve the sensitivity of atomic clocks and magnetometers to levels significantly below the standard quantum limit. In most cases the requisite atom-atom entanglement has been generated by dispersive interaction with a quantized probe field or by state-dependent collisions in a quantum gas. Such experiments typically use complex multilevel atoms like Rb or Cs, with the relevant interactions designed so that atoms behave like pseudospin-12\frac{1}{2}21​ particles. We demonstrate the viability of spin squeezing for collective spins composed of the physical angular momenta of 106{10}^{6}106 Cs atoms, each in an internal spin-4 hyperfine state. A peak metrological squeezing of at least 5dB is generated by quantum backaction from a dispersive quantum nondemolition (QND) measurement, implemented using a two-color optical probe that minimizes tensor light shifts without sacrificing measurement strength. Other significant developments include the successful application of composite pulse techniques for accurate dynamical control of the collective spin, enabled by broadband suppression of background magnetic fields inside a state-of-the-art magnetic shield. The absence of classical noise allows us to compare the observed quantum projection noise and squeezing to a theoretical model that properly accounts for both the relevant atomic physics and the spatial mode of the collective spin, finding good quantitative agreement and thereby validating its use in other contexts. Our work sets the stage for experiments on quantum feedback, deterministic squeezing, and closed-loop magnetometry. The implementation of real-time feedback may also create an opportunity for new types of quantum simulation, wherein the evolution of a quantum system is conditioned on the outcome of a time-continuous QND measurement. Such a scheme has the potential to access new regimes near the quantum-classical boundary, with opportunities to study long-standing issues related to quantum-classical correspondence in chaotic systems.