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arXiv:0712.1543 · Physical Review A

Quantum-limited position measurements of a dark matter-wave soliton

Antonio Negretti, Carsten Henkel, Klaus Mølmer

Published Apr 4, 2008• 12 citations
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Abstract

We show that the position of a dark matter-wave soliton can be determined with a precision that scales with the atomic density as ${n}^{\ensuremath{-}3/4}$. This surpasses the standard shot-noise detection limit for independent particles, without use of squeezing and entanglement, and it suggests that interactions among particles may present new advantages in high-precision metrology. We also take into account quantum density fluctuations due to phonon and Goldstone modes and we show that they, somewhat unexpectedly, actually improve the resolution. This happens because the fluctuations depend on the soliton position and make a larger amount of information available.

DOI
10.1103/physreva.77.043606

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We show that the position of a dark matter-wave soliton can be determined with a precision that scales with the atomic density as n\ensuremath−3/4{n}^{\ensuremath{-}3/4}n\ensuremath−3/4. This surpasses the standard shot-noise detection limit for independent particles, without use of squeezing and entanglement, and it suggests that interactions among particles may present new advantages in high-precision metrology. We also take into account quantum density fluctuations due to phonon and Goldstone modes and we show that they, somewhat unexpectedly, actually improve the resolution. This happens because the fluctuations depend on the soliton position and make a larger amount of information available.
We show that the position of a dark matter-wave soliton can be determined with a precision that scales with the atomic density as n(−3/4). This surpasses the standard shot-noise detection limit for independent particles, without use of squeezing and entanglement, and it suggests that interactions among particles may present new advantages in high-precision metrology. We also take into account quantum density fluctuations due to phonon and Goldstone modes and we show that they, somewhat unexpectedly, actually improve the resolution. This happens because the fluctuations depend on the soliton position and make a larger amount of information available.
Abstract The nature of dark matter is unknown and calls for a systematical search. For axion dark matter, such a search relies on finding feeble random noise arising from the weak coupling between dark matter and microwave haloscopes. We model such process as a quantum channel and derive the fundamental precision limit of noise sensing. An entanglement-assisted strategy based on two-mode squeezed vacuum is thereby demonstrated optimal, while the optimality of a single-mode squeezed vacuum is found limited to the lossless case. We propose a “nulling” measurement (squeezing and photon counting) to achieve the optimal performances. In terms of the scan rate, even with 20-decibel of strength, single-mode squeezing still underperforms the vacuum limit which is achieved by photon counting on vacuum input; while the two-mode squeezed vacuum provides large and close-to-optimum advantage over the vacuum limit, thus more exotic quantum resources are no longer required. Our results highlight the necessity of entanglement assistance and microwave photon counting in dark matter search.
While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose-Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton can be obtained by just driving the impurity atoms. By controlling the driving force on the impurity, one can therefore fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.
We discuss the issue of measuring the mean position (center of mass) of a group of bosonic or fermionic quantum particles, including particle number fluctuations. We introduce a standard quantum limit for these measurements at ultralow temperatures, and discuss this limit in the context of both photons and ultracold atoms. In the case of non-interacting harmonically trapped fermions, we present evidence that the Pauli exclusion principle has a strongly beneficial effect, giving rise to a 1∕N1∕N1∕N scaling in the position standard deviation---as opposed to a 1∕N1∕\sqrt{N}1∕N​ scaling for bosons. The difference between the actual mean-position fluctuation and this limit is evidence for quantum wave-packet spreading in the center of mass. This macroscopic quantum effect cannot be readily observed for noninteracting particles, due to classical pulse broadening. For this reason, we also study the evolution of photonic and matter-wave solitons, where classical dispersion is suppressed. In the photonic case, we show that the intrinsic quantum diffusion of the mean position can contribute significantly to uncertainties in soliton pulse arrival times. We also discuss ways in which the relatively long lifetimes of attractive bosons in matter-wave solitons may be used to demonstrate quantum interference between massive objects composed of thousands of particles.
Abstract While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose–Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton state can be obtained by selectively driving the impurity atoms. This allows to fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.
Quantum metrology for frequency measurement has been used to surpass the Heisenberg scaling of the measurement uncertainty with observation time. In a single ion experiment, we show that the uncertainty in the frequency measurement scales as 1/T21/T^21/T2 for over 100 μ\muμs time scale limited by the de-phasing time of the probe state. The proof-of-principle experiment also sets a limit on the coupling strength of axion like dark matter particle wind to interact with an electron spin. Even though the limit is a weak limit, we provide feasible experiment by which the limit can be strengthened to complement the other dark matter search experiments. The scheme is based on the proposal by Pang et al.~\cite{Pang2017} implemented on a laser cooled single ion probe which has been subjected to an external time dependent field coupling.