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Spin-squeezing and Dicke state preparation through single-photon heterodyne measurement

Thomas Vanderbruggen, Simon Bernon, Andréa D Bertoldi, Arnaud Landragin, Philippe Bouyer

Published Feb 22, 2010• 1 citation
OpenAlex

Abstract

We investigate the collapse of a coherent superposition of two-level atoms induced by a single-photon heterodyne quantum non-demolition (QND) measurement, and show that such a measurement process leads to the generation of spin-squeezed and Dicke states. We describe the stochastic process of the measurement and the associated atomic evolution in a wavevector formalism. Analytical formulas of the atomic distribution momenta are derived in the weak coupling regime for both short and long time behavior and are in good agreement with those from a Monte-Carlo simulation.

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We investigate the collapse of a coherent superposition of two-level atoms induced by a single-photon heterodyne quantum non-demolition (QND) measurement, and show that such a measurement process leads to the generation of spin-squeezed and Dicke states. We describe the stochastic process of the measurement and the associated atomic evolution in a wavevector formalism. Analytical formulas of the atomic distribution momenta are derived in the weak coupling regime for both short and long time behavior and are in good agreement with those from a Monte-Carlo simulation.
We investigate the quantum nondemolition (QND) measurement of an atomic population based on a heterodyne detection and show that the induced back-action allows for the preparation of both spin-squeezed and Dicke states. We use a wave-vector formalism to describe the stochastic process of the measurement and the associated atomic evolution. Analytical formulas of the atomic distribution momenta are derived in the weak-coupling regime both for short- and long-time behavior, and they are in good agreement with those obtained by a Monte Carlo simulation. The experimental implementation of the proposed heterodyne detection scheme is discussed. The role played in the squeezing process by the spontaneous emission is considered.
We report on a novel experiment to generate non-classical atomic states via quantum non-demolition (QND) measurements on cold atomic samples prepared in a high-finesse ring cavity. The heterodyne technique developed for QND detection exhibits an optical shot-noise limited behavior for local oscillator optical power of a few hundred μW, and a detection bandwidth of several GHz. This detection tool is used in a single pass to follow non-destructively the internal state evolution of an atomic sample when subjected to Rabi oscillations or a spin-echo interferometric sequence.
We present a protocol for generating nonclassical states of atomic spin ensembles through the backaction induced by a hybrid measurement of light that is entangled with atoms, combining both homodyne and single-photon detection. In phase I of the protocol we create a spin-squeezed state by measuring the light's polarization rotation due to the Faraday effect in a balanced polarimeter, equivalent to a homodyne measurement. In phase II we send a second probe beam through the sample and detect single photons scattered into the signal mode. Before doing so, we rotate the uncertainty bubble to increase the projection fluctuations of the measured spin component. This increases the coupling strength between the atoms and photons and thus the rate of scattering of single photons into the signal mode. In the ideal case, the result is a squeezed Dicke state, with substantial quantum advantage for sensing spin rotations. We benchmark the protocol's utility in the presence of inevitable decoherence due to optical pumping using the Fisher information as a measure of quantum advantage. We show that in the presence of decoherence, the quantum Fisher information associated with the non-Gaussian mixed state we prepare is substantially larger than the classical Fisher information obtained from the standard measurement of spin rotations. We deduce a measurement basis that is close to optimal for achieving the quantum Cram\'er-Rao bound in the presence of decoherence.
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.
We demonstrate spin squeezing and entanglement in a large-spin system via quantum non-demolition measurement. We make non-destructive, projection-noise-limited collective spin measurements on an ensemble of up to in 8.4 × 105 laser-cooled 87Rb atoms in the f = 1 hyperfine ground state. A dynamically-decoupled probing scheme [Phys. Rev. Lett. 105, 093602 (2010)] prevents probe-induced decoherence. Repeated measurements show correlations beyond the standard quantum limit, indicating generation of a spin-squeezed state with up to −3.6 dB of noise reduction and −2.6 dB of metrologically-relevant squeezing.