Observation of a Lee-Huang-Yang Fluid

We observe monopole oscillations in a mixture of Bose-Einstein condensates, where the usually dominant mean-field interactions are canceled. In this case, the system is governed by the next-order Lee-Huang-Yang (LHY) correction to the ground state energy, which describes the effect of quantum fluctuations. Experimentally such a LHY fluid is realized by controlling the atom numbers and interaction strengths in a ${}^{39}\mathrm{K}$ spin mixture confined in a spherical trap potential. We measure the monopole oscillation frequency as a function of the LHY interaction strength as proposed recently by Jrgensen et al. [Phys. Rev. Lett. 121, 173403 (2018)] and find excellent agreement with simulations of the complete experiment including the excitation procedure and inelastic losses. This confirms that the system and its collective behavior are initially dominated by LHY interactions. Moreover, the monopole oscillation frequency is found to be stable against variations of the involved scattering lengths in a broad region around the ideal values, confirming the stabilizing effect of the LHY interaction. These results pave the way for using the nonlinearity provided by the LHY term in quantum simulation experiments and for investigations beyond the LHY regime.

Figure 1

(a) Schematic representation of the experiment showing a LHY fluid undergoing monopole oscillations in a spherical potential composed of three red-detuned laser beams. (b) Typical absorption image after time of flight (TOF) during which atoms in states $|1⟩$ and $|2⟩$ are separated by a magnetic field gradient. (c),(d) Extracted BEC radii of atoms in states $|1⟩$ (c) and $|2⟩$ (d) after 28 ms TOF as a function of evolution time. The radii along the $y$ and $z$ directions are shown as blue dots and red triangles, respectively, and the gray lines are fits of Eq. (1) to the mean radius. The data were recorded for ${\omega }_0=2\pi \times 113.1(6)\mathrm{Hz}$ and $N=2.3(3)\times {10}^4$ corresponding to $U=0.5(1)$.

Figure 2

Results of the dynamical two-component simulations. (a),(b) Simulated radii and atom numbers for a LHY fluid including inelastic losses for ${\omega }_0=2\pi \times 113.6\mathrm{Hz}$ and $N=4\times 10^4$ corresponding to $U=1.2$. Results for atoms in states $|1⟩$ and $|2⟩$ are shown as solid orange and dashed purple lines, respectively. (c) Extracted oscillation frequencies of atoms in the $|1⟩$ state as a function of LHY interaction strength. Results with and without inelastic losses are shown as blue circles and green squares, respectively. The low-amplitude limit is shown as a red line and the noninteracting limit is shown as a dashed black line.

Figure 3

Observed monopole oscillation frequency depending on interaction strength of the LHY fluid for spherical traps with ${\omega }_0=2\pi \times 113.1(6)\mathrm{Hz}$ (circles), 113.7(1) Hz (squares), 115.3(4) Hz (diamonds), 111.1(3) Hz (pentagons), and 110.9(5) Hz (triangles). Simulated results calculated for ${\omega }_0=2\pi \times 113.6\mathrm{Hz}$ including inelastic losses are shown as a blue line. The dash-dotted and dotted lines correspond to simulations without losses and a doubled loss coefficient for the channel involving three atoms in the $|2⟩$ state, respectively. The red line shows the monopole frequency of an ideal LHY fluid in the low-amplitude limit and the dashed black line shows the noninteracting limit.

Figure 4

Monopole frequency of the spin mixture depending on magnetic field and $\delta a$. Experimental results for ${\omega }_0=2\pi \times 110.9(5)\mathrm{Hz}$ and $N=9.4(6)\times {10}^4$ corresponding to $U=4.1(4)$ are shown as gray points. Simulated results using the same parameters with and without including the LHY correction are shown as blue circles and orange diamonds, respectively. The shaded region indicates the magnetic field regime where $\delta a=0$ within $1\sigma$. The horizontal errors on the experimental results are smaller than the markers.