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Extensions of Perturbation Theory for Spin Dressed Neutrons and 3He Comagnetometers in Superfluid 4He

A. Lipman

Published Sep 5, 2024• 0 citations
Publisher

Abstract

The nEDM experiment at Oak Ridge’s Spallation Neutron Source will probe for an electric dipole moment of the neutron at an unprecedented level of sensitivity. Polarized 3He atoms dressed by a radio-frequency field are a crucial component. For field parameters comparable to the parameters being used in the nEDM experiment, numerical studies using a fourth-order Runge-Kutta solver reveal inadequacies in earlier analyses of 3He spin dynamics. It’s seen that neutron absorption is influenced by avoided level-crossings omitted previously. Also, the critical dressing condition, used to eliminate effects of the static magnetic field, requires modification. First-order perturbative corrections to eigenstates and third-order corrections to eigenenergies are needed to account for the impact of avoided level-crossings and the changes in the critical dressing condition, respectively.

DOI
10.20944/preprints202409.0474.v1

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The nEDM experiment at Oak Ridge’s Spallation Neutron Source will probe for an electric dipole moment of the neutron at an unprecedented level of sensitivity. Polarized 3He atoms dressed by a radio-frequency field are a crucial component. For field parameters comparable to the parameters being used in the nEDM experiment, numerical studies using a fourth-order Runge-Kutta solver reveal inadequacies in earlier analyses of 3He spin dynamics. It’s seen that neutron absorption is influenced by avoided level-crossings omitted previously. Also, the critical dressing condition, used to eliminate effects of the static magnetic field, requires modification. First-order perturbative corrections to eigenstates and third-order corrections to eigenenergies are needed to account for the impact of avoided level-crossings and the changes in the critical dressing condition, respectively.
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 3He^{3}\mathrm{He}3He. The critical dressing mode of this experiment uses an oscillating magnetic field to dress the gyromagnetic ratios of neutrons and 3He^{3}\mathrm{He}3He 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 3He^{3}\mathrm{He}3He 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.
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Since the 1950s, experiments searching for the neutron electric dipole moment have increased in sensitivity by six orders of magnitude. Yet, the current experimental sensitivity lies well above that predicted from standard model calculations. Corrections from physics beyond the standard model increase the predicted size of the nEDM, resulting in the nextgeneration of experiments hovering tantalisingly close to the detection sensitivity, to either verify or quash standard model extensions. One such experiment, n2EDM, currently in the commissioning stage at the Paul Scherrer Institute in Switzerland, hopes to measure the nEDM with a sensitivity improvement over its predecessor. This thesis details the design, measurement and analysis of hybrid 3He/alkali magnetometers for both accurate and precise magnetic field readings at low and zero fields, crucial for the development of ever-more sensitive fundamental physics searches. The work exploits the precise nature of alkali (87Rb and 133Cs) magnetometry techniques to measure the simultaneous Larmor precession of polarised 3He, avoiding light shifts commonly associated with optically pumped magnetometers. The first part of this work demonstrates the use of a hybrid 3He/87Rb magnetometer for the minimisation of remnant fields in a magnetically shielded environment, resulting in absolute low-field readings below 5 pT. Furthermore, the hybrid magnetometer was shown to be applicable for the reduction of gradient fields by optimising the effective 3He T2 time. This new technique represents a convenient and consistent way to achieve a near-zero magnetic field environment for precision experiments. Second, a new measurement technique was demonstrated using a hybrid 3He/133Cs magnetometer in a 1 µT field, placing experimental limits on the coupling of axion-like dark matter to nucleons. The measurement excluded axion coupling strength to 2:5 x 10-1 GeV-1 for axion masses between 10-20 to 10-17 eV at the 95% level. With the resulting exclusion region weaker than previous measurements, possible improvements to the apparatus should drive the development of a low-cost long-term axion interaction search.
We report a measurement of dressed spin effects of polarized 3He^{3}\mathrm{He}3He atoms from a cold atomic source traversing a region of a constant magnetic field B0{B}_{0}B0​ and a transverse oscillatory dressing field ${B}_{d}\mathrm{cos}{\ensuremath{\omega}}_{d}t$. The observed effects are compared with a numerical simulation using the Bloch equation as well as a calculation based on the dressed atom formalism. An application of the dressed spin of 3He^{3}\mathrm{He}3He for a proposed neutron electric dipole moment measurement is also discussed.
We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.
Abstract We propose a novel approach in a search for the neutron electric dipole moment (EDM) by taking advantage of signal amplification in a weak measurement, known as weak value amplification. Considering an analogy to the weak measurement that can measure the spin magnetic moment interaction, we examine an experimental setup with a polarized neutron beam through an external electric field with spatial gradient, where the signal is sensitive to the EDM interaction. In particular, a dedicated analysis of effects from impurities in pre- and post-selections is performed. We show that the weak value amplification occurs where the signal is enhanced by up to two orders of magnitude, and demonstrate a potential sensitivity of the proposed setup to the neutron EDM.