** Coherently precessing spin structure in **^{3}He-B – high resolution quantum amplifier

The HPD is a dynamical spin structure. When it is created, the volume of the ^{3}He-B is divided into two parts, from a viewpoint of spin orientation. In one part, the spins are deflected to Leggett angle (∼104°) and are precessing coherently, while in the other part they are stationary. Actually, two domains are created - HPD and so-called stationary domain (SD), separated from each other by a domain wall situated at a position fulfilling a Larmor resonance condition. From a viewpoint of energy, the HPD-SD state corresponds to the state of minimum total energy, i.e. to state of minimum Zeeman, dipole and gradient energies. As a consequence, the phase of the spin precession in HPD (i.e. the phase of spin part of the order parameter) is very sensitive to any perturbation. Any disturbances or external forces applied to HPD-SD structure will deviate it from the dynamical equilibrium state creating thus a gradient of the phase of spin precession.
The gradient excites spin currents - a powerful feedback mechanism restoring back the dynamical equilibrium state. This results in generation of oscillations of the spin distribution around the equilibrium state. A typical absorption and dispersion
signals of a surface oscillation mode is presented in Fig.1, where one can see nearly ideal resonance line.

**Figure 1:***Typical measured absorption and dispersion
signals of HPD low frequency oscillation mode.*

In some sense the surface oscillation mode is a double resonance: it is a low
frequency resonance of the HPD-SD structure, which is excited by a high frequency continuous NMR technique. Due to the state of homogeneous spin precession, the whole
spin system of the HPD-SD structure will coherently respond to any perturbation, amplifying, thus, this perturbation, i.e. the surface oscillations of HPD-SD structure is working like the low frequency quantum resonance amplifier tuned by magnetic
field gradient. The inset of Fig. 2. shows the response of the HPD as a function of the amplitude of the perturbation field for constant magnetic field gradient. The response is linear in the range of small fields from 1 nT up to around 100 nT. Measuring such dependence for various gradients (resonance frequencies) one can get a gain versus
frequency characteristic of the HPD response. However, it is worth to point out that the characteristic presented in Fig.2. has been normalized to constant displacement,
i.e. constant deviation of the position of Larmor resonance condition.
Hence, it is a value of voltage induced only by HPD when a perturbation magnetic field slightly shifts the position of domain wall.

**Figure 2:** *Gain vs. frequency response of the HPD measured at temperature of 0.7 **T*_{c} and pressure of 11bar. The inset shows linear response of the
HPD to magnetic field perturbation.

With an existing experiment we can detect changes of magnetic field with sensitivity of 1 nT on the background of about 10 mT NMR field. This leads us to speculate, whether
the HPD-SD structure might be of interest as a possible detector to measure magnetic field anomalies, changes in the Earth's magnetic field etc.

*E. Gažo, M. Kupka, M. Medeová, P. Skyba*