We investigate the properties of angular-momentum states which yield high sensitivity to rotation. We discuss the application of these ``squeezed-spin'' or correlated-particle states to spectroscopy. Transitions in an ensemble of N two-level (or, equivalently, spin-1/2) particles are assumed to be detected by observing changes in the state populations of the particles (population spectroscopy). When the particles' states are detected with 100% efficiency, the fundamental limiting noise is projection noise, the noise associated with the quantum fluctuations in the measured populations. If the particles are first prepared in particular quantum-mechanically correlated states, we find that the signal-to-noise ratio can be improved over the case of initially uncorrelated particles. We have investigated spectroscopy for a particular case of Ramsey's separated oscillatory method where the radiation pulse lengths are short compared to the time between pulses. We introduce a squeezing parameter ${\ensuremath{\xi}}_{\mathit{R}}$ which is the ratio of the statistical uncertainty in the determination of the resonance frequency when using correlated states vs that when using uncorrelated states. More generally, this squeezing parameter quantifies the sensitivity of an angular-momentum state to rotation. Other squeezing parameters which are relevant for use in other contexts can be defined. We discuss certain states which exhibit squeezing parameters ${\ensuremath{\xi}}_{\mathit{R}}$\ensuremath{\simeq}${\mathit{N}}^{\mathrm{\ensuremath{-}}1/2}$. We investigate possible experimental schemes for generation of squeezed-spin states which might be applied to the spectroscopy of trapped atomic ions. We find that applying a Jaynes-Cummings--type coupling between the ensemble of two-level systems and a suitably prepared harmonic oscillator results in correlated states with ${\ensuremath{\xi}}_{\mathit{R}}$1.
It is known that a partially entangled state gives improved sensitivity in generalized Ramsey spectroscopy in the presence of decoherence, whereas a maximally entangled state does not. However, it has been an open question whether the known decoherence limit in the improvement is achievable. We show that every spin-squeezed state possesses pairwise entanglement, thereby improving the spectroscopic sensitivity, and that even suboptimal entanglement in its easiest implementation suffices to asymptotically reach the decoherence limit without any measurement optimization.
It is known that partially entangled state gives improved sensitivity of Ramsey spectroscopy in the presence of decoherence, whereas maximally entangled state gives no improvement. However it has been an open question whether the absolute limit in the improvement is attainable by optimal entanglement alone or via measurement optimization. In this Paper, we answer this question by showing that even sub-optimal entanglement generated by the simplest spin squeezing can asymptotically attain the absolute improvement with increasing number of atoms.
We report quantum enhancement of Faraday rotation spin noise spectroscopy by polarization squeezing of the probe beam. Using natural abundance Rb in 100 Torr of
N2 buffer gas and squeezed light from a subthreshold optical parametric oscillator stabilized 20 GHz to the blue of the
D1 resonance, we observe that an input squeezing of 3.0 dB improves the signal-to-noise ratio by 1.5 to 2.6 dB over the combined (power)$\ensuremath{\bigotimes}$(number density) ranges (0.5--4.0 mW)$\ensuremath{\bigotimes}(1.5\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ to $1.3\ifmmode\times\else\texttimes\fi{}{10}^{13} {\mathrm{cm}}^{\ensuremath{-}3}$), covering the ranges used in optimized spin noise spectroscopy experiments. We also show that squeezing improves the tradeoff between statistical sensitivity and broadening effects, a previously unobserved quantum advantage.
Ramsey interferometry allows the estimation of the phase
phi of rotation of the pseudospin vector of an ensemble of two-state quantum systems. For
phi small, the noise-to-signal ratio scales as the spin-squeezing parameter
xi, with
xi<1 possible for an entangled ensemble. However states with minimum
xi are not optimal for single-shot measurements of an arbitrary phase. We define a phase-squeezing parameter,
zeta, which is an appropriate figure-of-merit for this case. We show that (unlike the states that minimize
xi), the states that minimize
zeta can be created by evolving an unentangled state (coherent spin state) by the well-known 2-axis counter-twisting Hamiltonian. We analyse these and other states (for example the maximally entangled state, analogous to the optical "NOON" state
∣psi>=(∣N,0>+∣0,N>)/sqrt2) using several different properties, including
xi,
zeta, the coefficients in the pseudo angular momentum basis (in the three primary directions) and the angular Wigner function
W(theta,phi). Finally we discuss the experimental options for creating phase squeezed states and doing single-shot phase estimation.
We propose a hybrid quantum-classical atomic clock where the interrogation of atoms prepared in a spin-coherent (or weakly squeezed) state is used to feed back one or more highly spin-squeezed atomic states toward their optimal phase-sensitivity point. The hybrid clock overcomes the stability of a single Ramsey clock using coherent or optimal spin-squeezed states and reaches a Heisenberg-limited stability while avoiding nondestructive measurements. When optimized with respect to the total number of particles, the protocol surpasses the state-of-the-art proposals that use Greenberger-Horne-Zeilinger or NOON states. We compare analytical predictions with numerical simulations of clock operations, including correlated 1/f local oscillator noise.