Robustifying twist-and-turn entanglement with interaction-based readout

Abstract

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.

Machine-Designed Sensor to Make Optimal Use of Entanglement-Generating Dynamics for Quantum Sensing

“…TheĴ 2 z term is the source of the entanglement generation in OAT dynamics [17][18][19], and the presence of a constant, non-zeroĴ x term results in "Twist-and-Turn" (TNT) dynamics, which has been shown to create entanglement more rapidly than OAT [20][21][22][23][24]. For an initial pure state |Ψ 0 evolving under this Hamiltonian for some duration T , the precision to which the parameter ω can be estimated by making measurements on the final state |Ψ(T ) is bounded by…”

“…3, F C drops below the SNL for σ ∼ 1. It was found in previous work that robustness to detection noise could be drastically improved by adding an interaction-based readout (IBR), which is a period of evolution after the interrogation time, to convert the final probability distribution into one that is more robust to detection noise [24,27,35,36]. This often involves reversal of the initial state preparation dynamics (commonly referred to as an 'echo') to restore the initial coherent spin-state [37][38][39][40][41][42][43][44][45].…”

Detecting macroscopic indefiniteness of cat states in bosonic interferometers

“…Thus in good faith, an experimenter can believe that the density-matrix ensemble which they are observing is mostly composed of pure states with double peak amplitudes. Furthermore, one can expect to be able to account for 100% of the quantum variance by using a more optimal observable R [19,26,41,42]. For the state evolved (at t = 1.1T π ) from the high temperature distribution (β −1 = 10 τ ), the quality of indefiniteness is 5% and the reduced extensive difference is Λr q = 3 = O(1).…”

“…Interferometry in Bose Einstein condensates has led to new measurement techniques for magnetic fields [29], gravitational fields [37,38] and rotational motion [36]. In the kind of interferometry that we are considering the experiment consists of the following four steps [21,26]:…”

“…The QFI quantifies the sensitivity of the interferometer when the best projective measurement is used and is bounded from below by the CFI for any arbitrary choice of the projective measurement. The CFI and other measures of sensitivity can be measured by experiments [25,41] and many proposals exist to optimize the bound the CFI puts on the QFI [19,26,42]. The extensive difference can also be obtained in an experiment from the counting statistics of a single-particle observable [25,41].…”