Observation of anomalous tunneling in collective excitations via a cloud experiment platform for Bose-Einstein condensates

TL;DR

The paper investigates anomalous tunneling of Bogoliubov excitations in a Bose-Einstein condensate using a cloud-based Oqtant platform. It combines a quasi-one-dimensional Gross-Pitaevskii model with Bogoliubov analysis and cloud-based experiments in a double-well trap created by a central Gaussian barrier. The authors predict and observe that low-energy collective modes exhibit reduced sensitivity to barrier height, and that neighboring mode frequencies merge as the barrier increases, with the merging points linked to the anomalous tunneling effect. This work demonstrates the viability of cloud-based platforms for quantum-body physics and provides indirect experimental evidence for anomalous tunneling in collective excitations of BECs.

Abstract

Recent development of cloud-based experiment platforms has enabled physicists to examine theoretical concepts with unprecedented accessibility. Oqtant is a cloud-accessible platform for trapped Bose-Einstein Condensates (BECs) of neutral atomic gases, providing an invaluable experimental tool for studying the dynamics of BECs. An intriguing theoretical prediction of a characteristic phenomenon of BECs is anomalous tunneling, whereby low-energy phonon excitations of BECs easily transmit through a barrier potential. We utilize Oqtant to observe the effects of anomalous tunneling on collective excitations of BECs. For this purpose, we theoretically show that anomalous tunneling affects the frequencies of the collective excitations in the low-energy regime, and experimentally measure these frequencies using Oqtant. Our results reveal that low-energy collective modes are less affected by a potential barrier, which indicates the presence of anomalous tunneling. Our work would contribute to fundamental understandings of BECs, as well as highlight the potential of cloud-based experiments in quantum-body physics.

Figures (6)

• Figure 1: (a) Schematic picture of the tunneling problem. The solid and dashed curves mean the condensate density $|\psi_0|^2$ and the Gaussian barrier. (b) Calculated transmission coefficient $|\mathcal{T}|^2$ as functions of the energy of the incident wave $\varepsilon$ for some barrier heights $V_0$. We also show that the halfwidths $\Delta \varepsilon_{\rm L}$ and $\Delta \varepsilon_{\rm H}$ for $V_0 / \mu = 0.7$. (c) Schematic drawing of the situation in examining collective modes. The solid and dashed curves are the same as panel (a). The dash-dot line denotes a collective excitation.
• Figure 2: Calculated collective mode frequencies $\varepsilon$ as functions of the barrier height $V_0$. The solid and dashed lines are odd-parity mode and even-parity mode frequencies. The dash-dotted line shows the halfwidth due to anomalous tunneling $\Delta \varepsilon_{\rm L}(V_0)$. The dotted line is the halfwidth of high-energy excitations $\Delta \varepsilon_{\rm H}(V_0)$. We also put dots at $(V_{\rm m}, \varepsilon_{2i+1}(V_{\rm m}))$ to indicate characteristic barrier height $V_{\rm m}$ for the merging of two neighboring modes.
• Figure 3: Experimental protocol after BEC preparation. (a) Barrier schedule. We use three potentials: $V_{\rm canc}$, $V_{\rm load}$, and $V_{\rm pert}$. The horizontal axis represents elapsed time after BEC preparation. The vertical axis shows potential heights. (b) Potential shape. $V_{\rm canc}$ is used for the cancellation of unwanted initial motion. $V_{\rm load}$ is the barrier at the center of the trap and linearly grows to $V_0$ over 8ms. $V_{\rm pert}$ is used to excite collective motions. We actually use three types of perturbation potentials and here show only one of them; for more details, see Supplementary Note 2.
• Figure 4: (a) One example of observed atom cloud distribution at elapsed time 18 ms in the absence of a barrier. The color bar shows the optical depth corresponding to the atom density in an arbitrary unit. (b) Center of mass (CoM) and standard deviation (SD) of atom clouds along the $z$ direction. We also show these power spectra (PS) in panel (c). In the power spectra, we remove the offsets of the original signals. The squares with error bars show the estimated peaks of PS. The vertical dashed lines show the theoretical predictions for the lowest, second-lowest, and third-lowest collective mode frequencies in descending order of frequency.
• Figure 5: Estimated collective mode frequency. Circles, triangles, and squares denote the estimated lowest, second-lowest, and third-lowest frequencies, respectively. Unfilled (filled) symbols represent frequencies estimated from fit (Fourier) analysis, whose $x$-axis values are shifted by $-1(+1)$ for better readability. The data of the lowest mode from fitting at $V_0 / \hbar \omega_z \approx 70$ and those of the third-lowest mode from fitting at $V_0 / \hbar \omega_z \approx 60$ and $70$ are absent because we cannot determine them. Solid, dashed, and dash-dotted lines are the same as those in Fig. \ref{['fig_freqs_de']}. The cross and diamond show the collective mode frequency merging points for the lowest and second-third lowest modes determined from experimental data, respectively.