We experimentally investigate three methods, utilizing different atomic observables and entangled states, to increase the sensitivity of rotation angle measurements beyond the "standard quantum limit" for nonentangled states. All methods use a form of quantum mechanical "squeezing." In a system of two entangled trapped (9)Be(+) ions we observe a reduction in uncertainty of rotation angle below the standard quantum limit for all three methods including all sources of noise. As an application, we demonstrate an increase in precision of frequency measurement in a Ramsey spectroscopy experiment.
We experimentally investigate three methods, utilizing different atomic observables and entangled states, to increase the sensitivity of rotation angle measurements beyond the "standard quantum limit" for nonentangled states. All methods use a form of quantum mechanical "squeezing." In a system of two entangled trapped (9)Be(+) ions we observe a reduction in uncertainty of rotation angle below the standard quantum limit for all three methods including all sources of noise. As an application, we demonstrate an increase in precision of frequency measurement in a Ramsey spectroscopy experiment.
Experiments with two entangled trapped 9Be+ ions are discussed. In one type of experiments we used entanglement to increase the precision of rotation angle measurements. For “spin-squeezed" and maximally entangled states we observed a reduction in uncertainty of rotation angle below the standard quantum limit. In a second experiment we demonstrate a decoherence-free quantum memory of one qubit. By encoding the qubit into the decoherence-free subspace of two ions, we protect it from environment-induced dephasing. We increased the storage time by up to an order of magnitude compared to an unprotected qubit.
Aided by quantum sources, quantum metrology helps to enhance measurement precision. Here, we introduce a method to enhance the measurement of a rotation angle. As a proof of principle, assisted by a quantum state called the squeezed orbital-angular-position (OAP) state and balance homodyne detection, we demonstrate in experiments 3 dB-enhanced measurements of a rotation-angle beyond the shot noise limit. A precision of up to 17.7 nrad/Hz is obtained. Furthermore, we discuss means to further improve the measurement with a high-order precision OAP squeezed state. The method holds promise for future practical applications, such as in high-sensitive Sagnac interferometry.
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.
Quantum metrology employs entanglement to enhance measurement precision [V. Giovannetti et al., Quantum-enhanced measurements: Beating the standard quantum limit, Science 306, 1330 (2004)SCIEAS0036-807510.1126/science.1104149, V. Giovannetti et al., Advances in quantum metrology, Nat. Photonics 5, 222 (2011)NPAHBY1749-488510.1038/nphoton.2011.35, and L. Pezzè et al., Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018)RMPHAT0034-686110.1103/RevModPhys.90.035005]. The focus and progress so far have primarily centered on estimating a single parameter. In diverse application scenarios, estimation of more than one single parameter is often required. Joint estimation of multiple parameters can benefit from additional advantages for further enhanced precision. Here we report quantum-enhanced estimation of simultaneous spin rotations around two orthogonal axes, making use of spin-nematic squeezing in an atomic Bose-Einstein condensate. Aided by the F=2 atomic ground hyperfine manifold coupled to the nematic-squeezed F=1 states as an auxiliary field through a sequence of microwave (MW) pulses, multiple spin-1 observables are simultaneously measured, reaching an enhancement factor 3.3 to 6.3 decibels (dB) beyond the classical limit over a wide range of rotation angles. Our work realizes the first quantum enhanced multiparameter estimation using entangled massive particles. The techniques developed and the protocols implemented also highlight the application of two-mode squeezed vacuum states in quantum-enhanced sensing of noncommuting spin rotations simultaneously.
This thesis describes new results on the entanglement of atomic spins in Ramsey interferometry, optical atomic clocks and trapped ions. It is divided into three parts: First, we investigate improvements to conventional Ramsey interferometry with entanglement and adding only rotations of the collective spin to adjust the signal and measurement directions. The geometric degrees of freedom, connected to the rotations, are analytically optimized for a large class of generalized Ramsey protocols to allow efficient optimization of all parameters. Besides a unification of existing approaches, the main result is that there is only one new protocol, where a previously unused double inversion is applied. Studies of the local sensitivity show that this protocol reaches the fundamental quantum Fisher information limit and is yet robust against errors during preparation and measurement. In the second section we investigate the conditions under which optical atomic clocks exhibit increased long-term stability when applying weakly entangled, spin squeezed states. We discuss the common case of an atomic clock with a single ensemble, typical Brownian frequency noise and finite dead time. Theoretical modelling of the servo loop allows quantitative predictions of the optimal stability for given values of dead time and laser noise, in very good agreement with numerical simulations of the closed feedback loop. The main result is that, even with the current most stable lasers, the clock stability can only be improved for ensembles below a critical atom number of about one thousand in optical Sr lattice clocks. Even with a future improvement of the laser performance by one order of magnitude, the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers. Thus the last section considers the robust generation of entanglement in ion traps. An error budget including relevant experimental error sources is calculated for state-of-the-art quantum gates, driven by oscillating microwave gradients in surface traps. Amplitude modulation of the driving fields is shown to efficiently counteract the current limitations from motional mode instability. The predicted increase of the gate quality was demonstrated by the group of C. Ospelkaus at PTB Braunschweig, who measured gates with errors as low as ~ 10^(-3). In a similar approach, interactions between spin and motion can also be generated by combining oscillating rf-fields with a static magnetic field gradient. Penning traps designed for precision spectroscopy already feature large magnetic field gradients at the edge of a magnetic bottle configuration. We present parameters and conditions under which laser-free coupling of spin and quantized motion for (anti-)protons is possible at these points, in a step towards quantum logic spectroscopy for (anti-)protons.
Summary form only given. The use of entangled states can provide an increased sensitivity in quantum-limited spectroscopic measurements, leading to an uncertainty that is inversely proportional to the number of particles instead of the usual square-law dependence. In this contribution, we show that spectroscopy with maximally entangled states of atoms also offers significant advantages over experiments done with single atoms. As a first example, we demonstrate that entanglement can be used to effectively eliminate first-order Zeeman shifts in spectroscopy with 40Ca+ even though there are no m=0 -> m=0 transitions. Secondly, we discuss how maximally correlated states of two 40Ca+ could be used for measuring tiny frequency shifts of the S1/2 - D5/2 transition arising from second-order Zeeman shifts and electric quadrupole shifts due to the trapping potential.