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Physical Review A

Heisenberg-scaled magnetometer with dipolar spin-1 condensates

Haijun Xing, Anbang Wang, Qing-Shou Tan, Wenxian Zhang, Su Yi

Published Apr 18, 2016• 31 citations
Publisher

Abstract

We propose a scheme to realize a Heisenberg-scaled magnetometer using dipolar spin-1 condensates. The input state of magnetometer is prepared by slowly sweeping a transverse magnetic field to zero, which yields a highly entangled spin state of $N$ atoms. We show that this process is protected by a parity symmetry such that the state preparation time is within the reach of the current experiment. We also propose a parity measurement with a Stern-Gerlach apparatus which is shown to approach the optimal measurement in the large atom number limit. Finally, we show that the phase estimation sensitivity of the proposed scheme roughly follows the Heisenberg scaling.

DOI
10.1103/physreva.93.043615

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We propose a scheme to realize a Heisenberg-scaled magnetometer using dipolar spin-1 condensates. The input state of magnetometer is prepared by slowly sweeping a transverse magnetic field to zero, which yields a highly entangled spin state of NNN atoms. We show that this process is protected by a parity symmetry such that the state preparation time is within the reach of the current experiment. We also propose a parity measurement with a Stern-Gerlach apparatus which is shown to approach the optimal measurement in the large atom number limit. Finally, we show that the phase estimation sensitivity of the proposed scheme roughly follows the Heisenberg scaling.
Mach-Zehnder interferometer, a powerful tool for a wide variety of measurements, has been realized with Bose-Einstein condensates in recent experiments. In this report, we propose and analyze a realizable scheme for performing a Heisenberg-limited Mach-Zehnder interferometry with dipolar spin-1 condensate. Based upon adiabatic processes of sweeping the transverse magnetic field, we demonstrate a perfect phase transition, which accomplishes the beam splitter, phase shifter and recombiner as for a Mach-Zehnder interferometer. The attractive dipolar interaction ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. We also discuss the spin-111 squeezing induced in the adiabatic passage and show that the squeezing parameter attains its minimal value near the point of saturation field.
We propose a state preparation protocol based on sequential measurements of a central spin coupled with a spin ensemble, and investigate the usefulness of the generated multi-spin states for quantum enhanced metrology. Our protocol is shown to generate highly entangled spin states, devoid of the necessity for non-linear spin interactions. The metrological sensitivity of the resulting state surpasses the standard quantum limit, reaching the Heisenberg limit under symmetric coupling strength conditions. We also explore asymmetric coupling strengths, identifying specific preparation windows in time for optimal sensitivity. Our findings introduce a novel method for generating large-scale, non-classical, entangled states, enabling quantum-enhanced metrology within current experimental capabilities.
We propose a Ramsey interferometry experiment using an entangled state of N atoms to reach the Heisenberg limit for the estimation of an atomic phase shift if the atom number parity is perfectly determined. In a more realistic situation, due to statistical fluctuations of the atom source and the finite detection efficiency, the parity is unknown. We then achieve about half the Heisenberg limit. The scheme involves an ensemble of circular Rydberg atoms which dispersively interact successively with two initially empty microwave cavities. The scheme does not require very high-Q cavities. An experimental realization with about ten entangled Rydberg atoms is achievable with state of art apparatuses. 1
We propose a novel type of composite light–matter magnetometer based on a transversely driven multi-component Bose–Einstein condensate coupled to two distinct electromagnetic modes of a linear cavity. Above the critical pump strength, the change of the population imbalance of the condensate caused by an external magnetic field entails the change of relative photon number of the two cavity modes. Monitoring the cavity output fields thus allows for nondestructive measurement of the magnetic field in real time and we show that the sensitivity of the proposed magnetometer exhibits Heisenberg-like scaling with respect to the atom number. For state-of-the-art experimental parameters, we calculate the lower bound on the sensitivity of such a system to be of the order of [See the attached file] for a condensate of 10⁴ atoms with coherence times on the order of several ms.
We show that the ground state of a spin-1 atomic condensate with antiferromagnetic interactions constitutes a useful resource for quantum metrology upon approaching the Heisenberg limit. Unlike a ferromagnetic condensate state where individual atomic spins are aligned in the same direction, the antiferromagnetic ground-state condensate is a condensate of spin-singlet atom pairs. The inherent correlation between paired atoms allows for parameter estimation at precisions beyond the standard quantum limit (SQL) for uncorrelated atoms. The degree of improvement over the SQL is measured by the scaled quantum Fisher information (QFI), whose dependence on the ratio of linear Zeeman shift ppp to spin-dependent atomic interaction ccc is studied. At a typical value of p=0.4cp=0.4cp=0.4c, which corresponds to a magnetic field of $28.6\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{G}$ for c=50hc=50\mathrm{h}c=50h Hz (for 23Na^{23}\mathrm{Na}23Na atom condensate in the F=1F=1F=1 state at a typical density of $\ensuremath{\sim}{10}^{14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$), the scaled QFI can reach $\ensuremath{\sim}0.48N$, which approaches the limit of 0.5N0.5N0.5N for the twin-Fock state ${|N/2\ensuremath{\rangle}}_{+}{|N/2\ensuremath{\rangle}}_{\ensuremath{-}}$. Our work encourages experimental efforts to reach the ground state of an antiferromagnetic condensate at a extremely low magnetic field.
Abstract We propose a novel type of composite light–matter magnetometer based on a transversely driven multi-component Bose–Einstein condensate coupled to two distinct electromagnetic modes of a linear cavity. Above the critical pump strength, the change of the population imbalance of the condensate caused by an external magnetic field entails the change of relative photon number of the two cavity modes. Monitoring the cavity output fields thus allows for nondestructive measurement of the magnetic field in real time and we show that the sensitivity of the proposed magnetometer exhibits Heisenberg-like scaling with respect to the atom number. For state-of-the-art experimental parameters, we calculate the lower bound on the sensitivity of such a system to be of the order of fT ( H z ) − 1 –pT ( H z ) − 1 for a condensate of 104 atoms with coherence times on the order of several ms.