Realization of fractional Fermi seas

Abstract

The Pauli exclusion principle is a cornerstone of quantum physics: it governs the structure of matter. Extensions of this principle, such as Haldane's generalized exclusion statistics, predict the existence of exotic quantum states characterized by fractional Fermi seas (FFS), i.e. momentum distributions with uniform but fractional occupancies. Here, we report the experimental realization of fractional Fermi seas in an excited one-dimensional Bose gas prepared through ramping cycles in the interaction strength. The resulting excited yet stable Bose-gas states exhibit Friedel oscillations, smoking-gun signatures of the underlying FFS. The stabilization of these states offers an opportunity to deepen our understanding of quantum thermodynamics in the presence of exotic statistics and paves the way for applications in quantum information and sensing.

Figures (4)

• Figure 1: Emergence of FFS from holonomy cycles.--- (A): Holonomy cycles are realized by slowly changing the contact interaction from repulsive $g_{\text{1D}}\!>\!0$ to attractive $g_{\text{1D}}\!<\!0$, passing through the $g_{\text{1D}}\!=\!\pm \infty$ point, before again reaching finite repulsive interactions after crossing the non-interacting point $g_{\text{1D}}\!=\!0$. The special points on the cycles are indexed by the charge parameter $\ell$Marciniak2025ThHolo. (B) Momentum-space representation of the FFS for an idealized homogeneous 1D Bose gas. The FFS are realized at the non-interacting points. (C) Experimental platform: Array of vertically oriented 1D tubes (red) generated by a 2D optical lattice (gray shading) filled with Cs atoms.
• Figure 2: The implementation of interaction cycles--- We plot $a_{\text{3D}}$ and $g_{\text{1D}}$ as a function of magnetic field strength $B$. One cycle consists of one $B$-field ramp, one jump, another $B$-field ramp, and one quench between the field values labeled as A to D. The green arrows indicate slow ramps from point A to B and point C to D. The jump from point B to C and the quench from point D to A close out the cycle. The $B$-field values of these points are $B_\text{A}\!=\!40.85$ G, $B_\text{B}\!=\!47.20$ G, $B_\text{C}\!=\!47.64$ G and $B_\text{D}\!=\!49.01$ G. The vertical dashed line indicates the CIR's pole. The inset shows an atom-loss measurement for the sTG state at point C that gives a $1/e$-lifetime of $5.4$ s.
• Figure 3: Evidence for FFS.--- (A) Momentum distributions $n(k)$ of the ideal Bose gas for $\ell=\!=\!0, 2,$ and $4$, produced by integrating the ToF absorption images (inset) over the transversal $y$ direction, comparing the experimental data (solid points) to the GHD simulation data (solid lines) and the analytical prediction using Thomas-Fermi approximation for $\ell\!=\!2$ and $\ell\!=\!4$ (dashed lines). The shaded regions show the effect of thermal fluctuations on the GHD simulation, by changing the fitted 1D temperature $T_\text{1D}=\!=\!5\text{ nK}$ by $\pm5\%$. First-order correlation function $G^{(1)}(x)$, in linear scale (B) and for its absolute value in log scale in (C). The inset in (B) is a zoom-in around the zero crossing. All experimental data is the average of 10 repetitions, with error bars reflecting the standard error of the mean. When not visible, the error bars are smaller than the symbols.
• Figure 4: Irreversibility of the interaction cycles.--- (A) Measurement of atomic losses in forward and backward ramping. The remaining atom number is measured on each step of the forward and reverse cycles. Red shading indicates attractive interaction and blue shading indicates repulsive interaction. The size of the marker is proportional to the fractional atom loss from the previous step of the ramp. (B) Energy evolution during the cycles, calculated from the GHD simulation. The solid line indicates the total energy of the system versus $g_{\text{1D}}$ in the forward ramp of the interaction cycles. The dashed lines give the energy evolution when ramped in reverse from the repulsive excited states. The overall energy decreases sharply due to the negative binding energy.