Distributed quantum sensing with mode-entangled spin-squeezed atomic states

Abstract

In "Distributed quantum sensing with mode-entangled spin-squeezed atomic states" Nature (2022) [1], Malia et. al. claim to improve the precision of a network of clocks by using entanglement. In particular, by entangling a clock network with up to four nodes, a precision 11.6 dB better than the quantum projection noise limit (i.e. precision without any entanglement) is reported. These claims are incorrect, Malia et. al. do not achieve an improved precision with entanglement. Here we show their demonstration is more than two orders of magnitude worse than the quantum projection noise limit.The central message in "Distributed quantum sensing with mode-entangled spin-squeezed atomic states" Nature (2022) [1] is that by entangling atoms in an atomic clock network, a precision is demonstrated that is impossible to attain using the same number of atoms and time without entanglement. Should we accept this message? Putting aside the impressive technical achievements in the paper, we can objectively assess whether the experimental data are in agreement with the claim.The final two figures of the paper present the supporting data. In Fig. 3, ∆( θ) is plotted as a function of the number of clocks M, each with N = 45, 000 atoms, where the black line (1/ √ MN ) is supposed to denote a limit that cannot be surpassed without entanglementthe quantum projection noise limit (QPN). One point should be made clear, ∆( θ) > 1/ √ MN is very definitively not the limit without entanglement. To see this requires an explanation of what ∆( θ) is. Despite the authors calling ∆( θ) the 'measured sensitivity', it is not a sensitivity at all. θ is simply the difference in values between two measurements (for M = 1).

Quantum-enhanced differential atom interferometers and clocks with spin-squeezing swapping

“…To conclude, we notice that, after the completion of this work, a related sub-SQL differential scheme appeared [87]. There, an atomic distributed quantum sensing protocol is demonstrated experimentally by squeezing the total spin of the two interferometers, e.g.…”

Quantum-enhanced multiparameter estimation and compressed sensing of a field

“…Although we considered the case of one atom per site, our results can be easily generalized to the case of N non-interacting atoms distributed on M sites with N /M atoms per site. Configurations of this type can be realized by splitting a previously spin-squeezed Bose-Einstein condensate [9,10] or with cold atoms in a cavity, where cavity-mediated interactions [11] or non-local quantum non demolition measurements [12] are used to entangle the atoms in the different modes.…”

“…where we used the symmetry of the state |ψ t 〉. Equation (12) shows that the MAI technique allows the estimation of the linear combination Θ = k ε k θ k /N . In an estimation protocol based on the method of moments, the uncertainty on this combination is given by [27] (∆Θ)…”

“…Two possible schemes, that directly yield the spin-squeezed state with one atom per site, consist in (i) adiabatically raising a lattice in a two-component Bose-Enstein condensate [4,5] or (ii) entangling fermionic atoms located at the lattice sites via virtual tunneling processes plus an external laser which imprints a site-dependent phase [6][7][8]. Similar configurations but with more than one spin on each site can be obtained by splitting a spin-squeezed Bose-Einstein condensate into addressable modes [9,10], or with atoms in a cavity where cavity-mediated interactions [11] or non-local quantum non demolition measurements [12] are used to entangle the modes. Using this last method, squeezing-enhanced distributed quantum sensing with a few modes has been recently experimentally demonstrated [12].…”

“…Similar configurations but with more than one spin on each site can be obtained by splitting a spin-squeezed Bose-Einstein condensate into addressable modes [9,10], or with atoms in a cavity where cavity-mediated interactions [11] or non-local quantum non demolition measurements [12] are used to entangle the modes. Using this last method, squeezing-enhanced distributed quantum sensing with a few modes has been recently experimentally demonstrated [12].…”