Fermi Condensates for Dynamic Imaging of Electromagnetic Fields

Ultracold gases provide micrometer size samples whose sensitivity to external fields may be exploited in sensor applications. Bose-Einstein condensates of atomic gases have been demonstrated to perform excellently as magnetic field sensors in atom chips. Here we propose that condensates of fermions can be used for noninvasive sensing of time-dependent and static magnetic and electric fields, by utilizing the tunable energy gap in the excitation spectrum as a frequency filter. Perturbations by the field create collective excitations and quasiparticles. The latter requires the frequency of the perturbation to exceed the gap. The frequencies of the field may be selectively monitored from the amount of quasiparticles which is measurable, e.g., by rf spectroscopy. We analyze the method by calculating the density-density susceptibility and discuss its sensitivity and spatial resolution.

Figure 1

A Fermi condensate is trapped near the sample of interest. A gap opens around the Fermi level of the superfluid and sets the minimum energy of single particle excitations to the value of the order parameter, $\Delta$. Magnetic fields with certain frequency and location in the sample cause density perturbations in the condensate. Only if the frequency exceeds $2\Delta$, quasiparticles are created, which allows sensing perturbations of different frequencies by tuning the gap.

Figure 2

Dynamic structure factor $S$ as a function of frequency, with two momenta, $q=0.2k_F$ (solid line) and $q=0.4k_F$ (dashed line). The smaller momentum case shows the $AB$ phonon as a clear peak, and the quasiparticle continuum above $\omega =2\Delta \approx 0.13$, whereas when $q$ approaches $k_F$ the phonon merges with the quasiparticle continuum. Both curves are scaled to unity for readability.

Figure 3

Dynamic structure factor as a function of the pairing gap, summed for four frequencies, 0.03, 0.06, 0.09, and 0.12, with two different momenta, $0.4k_F$ (top) and $1k_F$ (bottom). This corresponds to the amount of quasiparticles caused by a perturbing field with these four frequencies. The solid line shows the data with the $AB$ phonon suppressed: for the momenta considered, the dynamic structure factor mainly corresponds to quasiparticle creation as the solid line closely follows the full result. The dashed line shows the result at a finite temperature, $T=0.01E_F$, which is of the order $0.5T_c$ for the $\Delta$ considered.

Figure 4

The dynamic structure factor for a single frequency $\omega =0.03$ and $q=1k_F$, averaged for a harmonic confinement using LDA, as a function of the gap at the center of the trap ${\Delta }_0$. Since the pairing gap is always small at the edges of the trap, there is a finite response already for ${\Delta }_0>{\omega }_0/2$. Decreasing ${\Delta }_0$ allows quasiparticle creation in larger areas in the trap, increasing the response, but once the quasiparticles can be formed also at the center of the trap, such growth stops. This leads to a maximum of the response at ${\Delta }_0={\omega }_0/2$, shown by the vertical dashed line.