Physical Review A

Quantum nondemolition measurement of spin via the paramagnetic Faraday rotation

Yoshiro Takahashi, Keita HONDA, N. Tanaka, K. Toyoda, Kiyoshi Ishikawa, T. Yabuzaki

Published Dec 1, 1999• 147 citations

Abstract

We propose a method for quantum nondemolition (QND) measurement of one component of spin by the measurement of polarization rotation of the off-resonant light induced by a paramagnetic Faraday rotation effect. We show that nonclassical states of spins such as the squeezed spin state, the Dicke state, and macroscopic quantum superposed state of spin can be realized corresponding to particular results of QND measurements. Furthermore, it is shown that a nonclassical state of light such as the twin photon state can also be realized with this method.

DOI: 10.1103/physreva.60.4974

Related papers

Quantum nondemolition measurement by pulsed oscillation

Guiying Zhang, Kai-Feng Zhao

Paramagnetic Faraday rotation is a quantum nondemolition measurement method that can generate spin squeezing and improve the measurement precision of a collective spin component beyond the standard quantum limit. In practice, a constant bias magnetic field is used to drive the spin precessing at sufficiently high frequency in order to lift the signal out of low-frequency technical noises. However, continuous measurement of precessing spins introduces back-action noise (BAN) due to the light-shift effect. Two types of back-action-evading (BAE) measurement of collective spin components have been demonstrated recently: continuous measurement of a two-ensemble system and stroboscopic measurement of a single ensemble. Here we propose another single ensemble BAE measurement by periodically modulating the bias field with $\ensuremath{\pi}$ pulses. Our theoretical calculation shows that under experimental settings where pulse-field modulation does not introduce significant decoherences, the proposed method can suppress the BAN and generate spin squeezing faster than the stroboscopic one at the same probe light power. Moreover, if it is combined with synchronous stroboscopic probing, light-shift BAN can be completely eliminated.

Physical Review AMar 22, 20163 citations

Hybrid measurement scheme for generating non-Gaussian spin states

Andrew Kolmer Forbes, Ivan Deutsch

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.

Physical Review AJul 31, 20251 citation

Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon

C. Y. Hu, A. B. Young, Jeremy L. O’Brien +2 more

We propose a quantum nondemolition method---a giant optical Faraday rotation near the resonant regime to measure a single-electron spin in a quantum dot inside a microcavity where a negatively charged exciton strongly couples to the cavity mode. Left-circularly and right-circularly polarized lights reflected from the cavity obtain different phase shifts due to cavity quantum electrodynamics and the optical spin selection rule. This yields giant and tunable Faraday rotation that can be easily detected experimentally. Based on this spin-detection technique, a deterministic photon-spin entangling gate and a scalable scheme to create remote spin entanglement via a single photon are proposed.

arXiv:0708.2019Physical Review BAug 13, 2008337 citations

Intrinsic quantum noise in Faraday-rotation measurements of a single-electron spin

Yanjun Ma, Jeremy Levy

Faraday rotation is one way to realize quantum nondemolition measurement of electron spin in quantum dots. To describe Faraday rotation, semiclassical models are typically used based on quantized electron-spin states and classical electromagnetic fields. Such treatments neglect the entanglement between electronic and photonic degrees of freedom that produce intrinsic quantum noise, limiting the ultimate sensitivity of this technique. We present a fully quantum-mechanical description of Faraday rotation and quantify this intrinsic noise. A method for measuring the purity of a given spin state is suggested based on this analysis.

arXiv:0810.5095Physical Review AFeb 24, 20092 citations

A Hybrid Measurement Scheme for Generating nonGaussian Spin States

Andrew Kolmer Forbes, Ivan Deutsch

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 nonGaussian 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 Cramér Rao bound in the presence of decoherence.

arXiv:2502.19527Feb 26, 20250 citations

Paramagnetic Faraday rotation with spin-polarized ytterbium atoms

Takeuchi, M, Ichihara, S, Kumakura, M +4 more

We report observation of the paramagnetic Faraday rotation of spin-polarized ytterbium (Yb) atoms. As the sample of the atoms, we used atomic beam, released atom from magneto-optical trap (MOT), and trapped atoms in far-off-resonant trap (FORT). Since Yb is diamagnetic and has spin-1/2 isotope, it is an ideal sample for the spin physics, such as quantum non-demolition measurement of spin (spin QND), for example. From the results of the rotation angle, we confirmed that the atoms were almost perfectly polarized.

Dec 7, 20059 citations