Useful quantum metrology requires nonclassical states with a high particle number and (close to) the optimal exploitation of the state's quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cramér-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. "Interaction-based readout" protocols have been shown to allow optimal interferometry or to provide robustness against detection noise at the expense of optimality. In this Letter, we prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal and robust quantum metrology is achievable in current spin-squeezing experiments.Nonclassical states enable precision measurements below the shot-noise limit (SNL) [1, 2]. However, despite many proof-of-principle experiments [3][4][5][6][7], a useful (i.e., highprecision) quantum-enhanced measurement has yet to be performed. This is partially due to the fragility of nonclassical states to typical noise sources [8] and the difficulty in marrying quantum-state-generation protocols with the practical requirements of high-precision metrology [9,10]; addressing these issues is an active research area [11][12][13][14][15][16][17][18]. A key limitation is detection noise [7,[19][20][21][22][23][24][25], which makes n and n ± σ particles indistinguishable. Quantum-enhanced measurements typically require single-particle resolution (σ ∼ 1), which restricts them to small particle numbers, since the requisite counting efficiency rapidly becomes unattainable as particle number increases.Another challenge is that many protocols are suboptimal, as they do not fully exploit the state's quantum correlations. Specifically, an estimate of classical parameter φ obtained from measurement signalŜ has a precision ∆φ2 . A quantum-enhanced estimate surpasses the SNL ∆φ 2 = 1/N for particle number N , however it is only optimal if it saturates the quantum Cramér-Rao bound (QCRB) ∆φ 2 = 1/F Q , where F Q is the quantum Fisher information (QFI) [8,[26][27][28]. For example, consider the nonclassical N -qubit states generated via the one-axis twisting (OAT) Hamiltonian [29][30][31][32]. Typical spin-squeezing procedures use the expectation of pseudospin as the signal, yielding a minimuim sensitivity ∆φ 2 ∼ N −5/3 . However, OAT can produce entangled non-Gaussian states (ENGS), which can achieve the Heisenberg limit (HL) F Q = N 2 and the...

We show that the inherently large interatomic interactions of a Bose-Einstein condensate (BEC) can enhance the sensitivity of a high precision cold-atom gravimeter beyond the shot-noise limit (SNL). Through detailed numerical simulation, we demonstrate that our scheme produces spin-squeezed states with variances up to 14 dB below the SNL, and that absolute gravimetry measurement sensitivities between two and five times below the SNL are achievable with BECs between 10 4 and 10 6 in atom number. Our scheme is robust to phase diffusion, imperfect atom counting, and shot-to-shot variations in atom number and laser intensity. Our proposal is immediately achievable in current laboratories, since it needs only a small modification to existing state-of-the-art experiments and does not require additional guiding potentials or optical cavities.

The use of multi-particle entangled states has the potential to drastically increase the sensitivity of atom interferometers and atomic clocks. The twist-and-turn (TNT) Hamiltonian can create multiparticle entanglement much more rapidly than the ubiquitous one-axis twisting (OAT) Hamiltonian in the same spin system. In this paper, we consider the effects of detection noise -a key limitation in current experiments -on the metrological usefulness of nonclassical states generated under TNT dynamics. We also consider a variety of interaction-based readouts to maximize their performance. Interestingly, the optimum interaction-based readout is not the obvious case of perfect time reversal.

We present a model of a spin-squeezed rotation sensor utilizing the Sagnac effect in a spin-1 Bose-Einstein condensate in a ring trap. The two input states for the interferometer are seeded using Raman pulses with LaguerreGauss beams and are amplified by the bosonic enhancement of spin-exchange collisions, resulting in spinsqueezing and potential quantum enhancement of the interferometry. The ring geometry has an advantage over separated beam path atomic rotation sensors due to the uniform condensate density. We model the interferometer both analytically and numerically for realistic experimental parameters and find that significant quantum enhancement is possible, but this enhancement is partially degraded when working in a regime with strong atomic interactions.

Bayesian estimation is a powerful theoretical paradigm for the operation of the approach to parameter estimation. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its use to systems that can be explicitly modeled. In this theoretical study, we formulate parameter estimation as a classification task and use artificial neural networks to efficiently perform Bayesian estimation. We show that the network’s posterior distribution is centered at the true (unknown) value of the parameter within an uncertainty given by the inverse Fisher information, representing the ultimate sensitivity limit for the given apparatus. When only a limited number of calibration measurements are available, our machine-learning-based procedure outperforms standard calibration methods. Our machine-learning-based procedure is model independent, and is thus well suited to “black-box sensors”, which lack simple explicit fitting models. Thus, our work paves the way for Bayesian quantum sensors that can take advantage of complex nonclassical quantum states and/or adaptive protocols. These capabilities can significantly enhance the sensitivity of future devices.