Fermi-pressure-assisted cavity superradiance in a mesoscopic Fermi gas

Abstract

We study the superradiant phase transition of a mesoscopic Fermi gas comprising between a few tens and a few thousand $^6$Li atoms in a high-finesse cavity across a wide range of densities. We observe a non-monotonic variation of the superradiant threshold as a function of density, with a minimum reached when the Fermi and recoil wavevectors are comparable. The minimum corresponds to a crossover between Fermi pressure-assisted ordering and Pauli blocking of photon scattering, in good agreement with theory. This interpretation is confirmed by a study of the atom-number dependence of the ordering threshold and photon number scaling. Lastly, we demonstrate the operation of our mesoscopic system in a regime where light-induced forces are opposite for the two spin components, leading to an ordered phase with a spin-density-wave character. Our system opens the perspective of studying few-fermion systems with strong and coherent light-matter coupling.

Figures (7)

• Figure 1: Concept of the experiment. (a) Recoil processes involved in the scattering from a pump laser into a cavity and vice versa at wavevectors $\pm\mathbf{k}_{\pm}$ (), compared with the radius $\mathrm{k}_{\mathrm{F}}$ of the Fermi surface, at low (a), intermediate (b), and high density (c). () shows an example process at $\mathbf{k_+}$ favored by the existence of the Fermi sea, and () and example of Pauli-blocked $\mathbf{k_+}$ process. In (c), these processes correspond to the overlap between the Fermi sea (blue) and the Fermi sea displaced by $\pm\mathbf{k}_{\pm}$ (orange). (d) Cavity-microscope system comprising two mirrors contacted to aspherical lenses allowing to focus a tweezer trap (orange) onto an atomic cloud at the center of the cavity. The cavity mode with wavevector $\mathbf{k_c}$ (red) shares the same optical axis as the tweezer trap beam. A retro-reflected transverse pump beam with wavevector $\mathbf{k}_{\mathrm{p}} \bot \mathbf{k}_{\mathrm{c}}$ (red) drives the atoms. Photons leaking through one of the cavity mirrors are detected on a single-photon counter. (e-g) Absorption images of atoms in state $\ket{\downarrow}$ after evaporation in the cavity-dipole trap alone (purple, not shown in panel (d)), (e), in the cavity-dipole trap superimposed with the tweezer trap (f), and after releasing the cavity dipole trap, yielding about $\mathrm{N}= 4000$ atoms in the tweezer (g).
• Figure 2: Superradiant phase transition varying atomic density. (a) The two spin components $\ket{\downarrow},\ket{\uparrow}$ interact with the cavity with resonance frequency $\omega_{\mathrm{c}}$ and are driven by the pump field at frequency $\omega_{\mathrm{p}}$. (b) Photon number $\mathrm{N_{ph}}$ detected within 30µs following a quench of the pump laser power to $\mathrm{V}_0$, with varying trap frequency. Unless otherwise stated, all uncertainties on atom number represent $68\%$ confidence interval on the mean, estimated using a resampling method supp. Black points indicate the extracted thresholds. Error bars represent the standard deviation obtained by varying the critical photon number by $\pm30\%$supp. Solid and dashed lines show theoretical predictions using the local density approximation () and exact harmonic-oscillator eigenstates (). Each datapoint is averaged $9$ times. (c) Normalized susceptibility extracted from the threshold as a function of the reduced wavevector $\mathrm{k}_{\pm}/\mathrm{k}_{\mathrm{F}}$, showing a local maximum near $\mathrm{k}_{\pm}/\mathrm{k}_{\mathrm{F}} \sim 1.7$. The experimental data are compared to theory with zero-temperature LDA () and exact eigenstates (), as well as finite-temperature LDA theory for $\mathrm{T}/\mathrm{T}_{\mathrm{F}}=0.3$ () and $0.5$ () and with the predictions for a Bose-Einstein condensate (). The shaded area represents the effect of atom-number uncertainties on the zero-temperature LDA. (d) Susceptibility normalized by Fermi energy, compared with the same susceptibility predictions of panel (c).
• Figure 3: Superradiant phase transition varying atom number. (a) Photon number with varying atom number within $70\leq\mathrm{N}<2100$ for $\Delta_{\uparrow}/2\pi=$400MHz, $\tilde{\Delta}_{\mathrm{p}}/2\pi=$1.3MHz. For each atom number the trap depth was adapted, with a value depicted using the grey scale. We overlap the measurement with the theory predictions () based on LDA simulation at zero temperature. The data is averaged between 2 and 10 times, depending on the signal-to-noise ratio. (b) Normalized susceptibility per atom extracted from the thresholds, compared with LDA predictions (), demonstrating the universality of the behavior shown in Figure \ref{['fig:fig2']}c. (c) Number of collected photons as a function of atom number for $\mathrm{V_0} = 6.2\,\mathrm{E_r}$ (horizontal cut in panel (a)), for which the threshold is exceeded for all atom numbers. Error bars on the photon number represent the standard deviation of the mean, calculated from different experimental repetitions. The dashed line is a guide to the eye showing the expected superradiant scaling $\mathrm{N_{ph}}\propto \mathrm{N^2}$.
• Figure 4: Magnetic superradiance (a) Cavity transmission spectrum showing two avoided crossings corresponding to the cavity being on resonance with states $\ket{\uparrow}$ () and $\ket{\downarrow}$ () respectively. $\Delta_{\mathrm{pc}}$ refers to the detuning between the cavity probe and the cavity resonance and $\Delta_{\mathrm{ac}}$ is the detuning between the atomic resonances and the cavity resonance. Each vertical line is averaged 15 times. To study magnetic superradiance, we fix the cavity resonance in between the two states () as shown in (b). (c) Sketch of the light intensity produced by the combined pump and cavity fields in the superradiant phase along the cavity direction, repulsive for $\ket{\uparrow}$ and attractive for $\ket{\downarrow}$, trapping atoms at node and antinodes respectively. (d) Photon numbers detected as a function of $\Delta_{\mathrm{p}}$ and $\mathrm{V_0}$ showing superradiance in the magnetic regime for $\mathrm{N}= 520\pm 40$ atoms and the LDA prediction for the threshold (). Each data point is averaged between 2 and 4 times.
• Figure S1: (a-c) Photon number recorded within 30µs following a quench as a function of both $\mathrm{V_0}$ and $\Delta_{\mathrm{p}}$ plane for (a) $\mathrm{N}=1120\pm 120$, (b) $\mathrm{N}=320\pm 48$ and (c) $\mathrm{N} = 108\pm 60$. The dashed line () represents the LDA predictions for the thresholds. Measurements are taken at $\Delta_{\uparrow}/2\pi=$414MHz. Each data is averaged $2$ times. Both measurements are taken at the same tweezer trap depth of 11µK, resulting in $\mathrm{k/k_F}=(0.63,0.75,0.9)$ for the three atom numbers.