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Soviet Journal of Low Temperature Physics

Nonlinear response of superfluid 3He fermions to a longitudinal rf magnetic field

Andrei A. Zvyagin

Published May 1, 1988• 0 citations
Publisher

Abstract

The excitation of the A and A1 phases of superfluid 3He by a variable field parallel to a constant field is studied. It is shown that the longitudinal varying magnetic field does not cause a parametric instability in the system since the excitations in 3He are fermions. For small values of time, the magnetization of the system oscillates with the pumping frequency, as well as with a low resonance frequency whose value in the resonance is determined by the amplitude of the varying field. Introduction of the collision relaxation leads to a damping of the low-frequency oscillations. As the amplitude of the pumping field increases, the power absorbed by the system becomes limited.

DOI
10.1063/10.0031931

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The excitation of the A and A1 phases of superfluid 3He by a variable field parallel to a constant field is studied. It is shown that the longitudinal varying magnetic field does not cause a parametric instability in the system since the excitations in 3He are fermions. For small values of time, the magnetization of the system oscillates with the pumping frequency, as well as with a low resonance frequency whose value in the resonance is determined by the amplitude of the varying field. Introduction of the collision relaxation leads to a damping of the low-frequency oscillations. As the amplitude of the pumping field increases, the power absorbed by the system becomes limited.
We investigate the dynamic response of a highly degenerate ultracold Fermi gas to varying magnetic fields near the Feshbach resonance. Following the experimental practice, we calculate the dynamics of the excitation gap in response to the oscillating and linearly ramped magnetic fields, respectively. For oscillating magnetic fields, depending on the frequencies and the amplitudes of the oscillations, the response of the system shows either linear or rich nonlinear behavior. In addition, both the spectral studies through the linear-response theory and the time-domain simulations suggest the existence of a resonant frequency corresponding to the dissociation threshold of the fermion atom pairs. For linearly ramped magnetic fields, the response of the excitation gap shows damped oscillations, with the final value dependent on the rate of the field sweep. This work may find its applications in exploring the dynamics of the ultracold atom superfluidity near the BCS--Bose-Einstein-condensation crossover region.
The time dependence of the response of the quantum spin liquid with fermionic excitations to parametric pumping has been calculated exactly for the special case of periodic pumping, the steplike periodic field, without using the resonance approximation, and for any value of the pumping magnitude. In the closed regime each mode (related to each eigenstate of the system) oscillates with time. The oscillations persist about the steady-state values, which are determined by the parameters of the pumping. The magnitude of the oscillations is finite for any value of the magnitude of the pumping. Those features drastically differ from the well-known resonance parametric pumping of magnons in magnetically ordered system, where the number of resonance magnons grows exponentially in time. The interference of infinitely many modes generically yields only decaying-in-time modulated oscillations of the total number of quasiparticles per mode even in the closed regime. For the fermionic system only one mode is in resonance, while others are out of resonance. It is totally different from the bosonic behavior of magnons under parametric pumping, where all modes can exist in resonance. The inclusion of the linear relaxation in the open regime for that quantum spin liquid produces the decay of oscillations to the initial state.
Nonlinear spin precession has been observed in ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}B$ in large counterflow of the normal and superfluid fractions. The new precessing state is stabilized at a high rf excitation level and displays frequency-locked precession over a large range of frequency shifts, with the magnitude of magnetization at its equilibrium value. Comparison to analytical and numerical calculation indicates that in this state the orbital angular momentum L\mathbf{L}L of the Cooper pairs is oriented transverse to the external magnetic field in a ``non-Leggett'' configuration with broken spin-orbit coupling. The resonance shift depends on the tipping angle $\ensuremath{\theta}$ of the magnetization as $\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{L}=({\ensuremath{\Omega}}_{B}^{2}/2{\ensuremath{\omega}}_{L})(\mathrm{cos}\ensuremath{\theta}\ensuremath{-}1/5).$ The phase diagram of the precessing modes with arbitrary orientation of L\mathbf{L}L is constructed.
With the help of the exact solution of the Kitaev model the parametric pumping of the two-dimensional quantum spin liquid under the action of the ac magnetic field is studied. In the dynamical regime the field produces oscillations of the magnetization with the field's frequency, modulated by the Rabi-like oscillations. In the steady-state regime, the Rabi-like oscillations are damped. The absorption of the ac field by the Kitaev spin model is finite and manifests resonance features. Such a behavior is generic for quantum spin liquids with fermionic excitations, and it is different from the linear spin-wave response of magnetically ordered systems to such a parametric pumping.
We have investigated the behaviour of a large vibrating wire resonator in the B-phase of superfluid 3 He at zero pressure and at temperatures below 200 μK. The vibrating wire has a low resonant frequency of around 60 Hz. At low velocities the motion of the wire is impeded by its intrinsic (vacuum) damping and by the scattering of thermal quasiparticle excitations. At higher velocities we would normally expect the motion to be further damped by the creation of quasiparticles from pair-breaking. However, for a range of temperatures, as we increase the driving force we observe a sudden decrease in the damping of the wire. This results from a reduction in the thermal damping arising from the presence of quantum vortex lines generated by the wire. These vortex lines Andreev-reflect low energy excitations and thus partially shield the wire from incident thermal quasiparticles.