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arXiv:2112.02172 · Physical Review A

Quantum control of two critically dressed spin-1/2 species in magnetic fluctuations

Raymond Tat, Christopher Swank

Published May 25, 2022• 1 citation
arXivHTMLPDF

Abstract

The neutron electric dipole moment experiment at the Spallation Neutron Source (nEDM@SNS experiment) proposes to measure the nEDM using the spin-dependent capture cross section of neutrons on $^{3}\mathrm{He}$. The critical dressing mode of this experiment uses an oscillating magnetic field to dress the gyromagnetic ratios of neutrons and $^{3}\mathrm{He}$ to the same value. While this technique grants increased sensitivity to the nEDM by improving the signal-to-noise ratio, this mode of measurement also introduces additional noise from the power supply used to drive the dressing field. This can lead to randomly fluctuating magnetic fields which cause the spins of neutrons and $^{3}\mathrm{He}$ to drift apart over time. Here we use second-order time-dependent perturbation theory to compute relaxation and frequency shifts due to fluctuations in the dressing field in terms of the magnetic field noise power spectrum and compare these calculations to numerical solutions obtained by integrating the Bloch equations. We then use these results to develop mitigation strategies for this type of noise. Furthermore, we report on spin dressing modulation techniques that significantly amplify coherence times for the critically dressed system, and attempt to quantify the achievable coherence time.

DOI
10.1103/physreva.105.053120

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Controlled modifications of the quantum magnetic response are produced in dressed systems by a high frequency, strong and not-resonant electromagnetic field. This quantum control is greatly enhanced and enriched by the harmonic, commensurable and orthogonally oriented dual dressing theoretically discussed here. The secondary field enables a fine tuning of the qubit response, with control parameters amplitude, harmonic content, spatial orientation and phase relation. Our analysis is based on a perturbative approach and includes few numerical solutions. The long-time dynamics is described in terms of an anisotropic effective static magnetic field representing the handle for the system full engineering. Through a low-order harmonic mixing the bichromatic driving generates a rectified static field acting on the spin. The Zeeman response becomes anisotropic in a triaxial geometry and includes a quadratic contribution. Our dressing increases the two-level energy splitting, improving the spin detection sensitivity. On the low field direction it compensates the static fields applied in different geometries. A resonant spin exchange between two species having very different magnetic response as electron and nucleus is allowed by the dressing. The spin temporal evolution includes a micromotion at harmonics of the driving frequency whose role in the spin detection is examined and can be exploited in quantum information. The results presented here lay a foundation for additional applications to be harnessed in quantum simulations.
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Cold atom experiments usually need a controllable and low-noise bias magnetic field to provide a quantization axis. Most labs need home-made stabilization of the field according to the actual setup, as commercially available power supply cannot directly satisfy their requirements. Here, by measuring the field fluctuations and active feedback modulating current supply of the applied magnetic field, we successfully demonstrate a field of 10.58 G with a stability to the level of 2.8 × 10−7 in a duration of 5 min. The root mean square noise is reduced to 0.05 mG, compared to the noise of 1.3 mG without stabilization. The coherence time of the magnetic-field sensitive transition between the rubidium ground states F=1,mF=−1 and 1,0, as measured by Rabi oscillation, is extended to 19.2 ms from the unstabilized value of 1.3 ms. This result is long enough for most experiments on quantum simulation and precision measurement. As our system has no passive magnetic shielding and additional compensation coils, it is highly simple and compact to provide the stable magnetic field and would be adapted to various applications with cold atoms.