Dissipation Driven Coherent Dynamics Observed in Bose-Einstein Condensates

Abstract

We report the first experimental observation of dissipation-driven coherent quantum many-body oscillation, and this oscillation is manifested as the coherent exchange of atoms between the thermal and the condensate components in a three-dimensional partially condensed Bose gas. Firstly, we observe that the dissipation leads to two different atom loss rates between the thermal and the condensate components, such that the thermal fraction increases as dissipation time increases. Therefore, this dissipation process serves as a tool to uniformly ramp up the system's temperature without introducing extra density excitation. Subsequently, a coherent pair exchange of atoms between the thermal and the condensate components occurs, resulting in coherent oscillation of atom numbers in both components. This oscillation, permanently embedded in the atom loss process, is revealed clearly when we inset a duration of dissipation-free evolution into the entire dynamics, manifested as an oscillation of total atom number at the end. Finally, we also present a theoretical calculation to support this physical mechanism, which simultaneously includes dissipation, interaction, finite temperature, and harmonic trap effects. Our work introduces a highly controllable dissipation as a new tool to control quantum many-body dynamics.

Figures (4)

• Figure 1: Illustration of the experimental setup and sequence. (a) $^{87}$Rb atoms are loaded into a crossed dipole trap and evaporated to a partially condensed phase. Then, a $96$ MHz blue-detuned dissipation light beams from six directions are applied to the atoms. An absorption imaging is applied along the $x$ axis. (b) Typical time-of-flight (ToF) image of the atoms (left) and their integrated optical density along $z$ axis (right), with which a bimodal fitting yields both condensate and thermal components. (c) Physical mechanism of the dissipation process. Atoms are initially prepared in $\ket{F=1,m_F=1}$ state, and they will leave the trap if they are pumped out of $\ket{F=1,m_F=1}$ and $\ket{F=2,m_F=-1}$ states by dissipation light. (d) Experimental sequence. For the first protocol denoted as "$5+x+y$", the dissipation light is first turned on for $5$ ms and then turned off, letting atoms evolve for $x$ ms without dissipation, then turned on again for $y$ ms before ToF measurement. For the second protocol, denoted as "$5+x$", the dissipation light is turned on for $5$ ms and then turned off, and the ToF measurement is performed right after the dissipation-free evolution of $x$ ms.
• Figure 2: Experimental observation of the dissipation driven coherent dynamics. We start with a partial condensate with the condensate-to-thermal ratio $\sim 2:1$. After the experimental sequence "$5+x+y$" shown in Fig. \ref{['setup']}(d), the total number of the remaining atoms oscillates as a function of the waiting duration $x$. (a) shows two data sets with the same experimental sequences but different harmonic trapping frequencies along $\hat{z}$, $\omega_z=2\pi \times 61.3\pm 0.4$ Hz for blue circles and $\omega_z=2\pi\times 72.1\pm 0.9$ Hz for red triangles. Here $y=3$ ms. The fitted frequencies are $2\pi \times 105\pm 6$ Hz for blue circles and $2\pi \times 129\pm 6$ Hz for red triangles. (b) shows two data sets with the same trapping frequency $\omega_z=2\pi \times 61.3\pm 0.4$ Hz but different duration $y$ of the second dissipation process. The fitted frequencies are $2\pi \times 105\pm 6$ Hz and $2\pi \times 108\pm 16$ Hz for blue circles (5+x+3) and red triangles (5+x+5), respectively. All data points are averaged over nine repeated experiments.
• Figure 3: (a) Decay of atom number from condensate (blue circles) and thermal component (red triangles) for initially prepared pure condensate or pure thermal gas. The inset shows the increase of the thermal-to-condensate ratio as a function of dissipation time for an initially partially condensed sample. (b-c) Before turning on the second dissipation period, oscillations between the number of condensate atoms and thermal atoms are observed as a function of waiting duration $x$. The blue circles and the red triangles are condensate and thermal atoms, respectively. The green diamonds denote the total number of atoms. $\omega_z=2\pi \times 61.3\pm0.4$ Hz for (b) and $2\pi \times72.1\pm0.9$ Hz for (c). The solid lines are fitting to single-frequency oscillation. (d) The oscillation frequency $f$ (blue circles) and relative amplitude $A$ (red triangles) for different trap frequencies. The dashed line denotes $2\omega_z/2\pi$. All data points are averaged over nine repeated experiments.
• Figure 4: (a-b) Oscillation of the condensate (blue line) and the thermal atoms (orange line) as a function of free evolution time $x$ for $"5+x"$ protocol. Here we choose the trapping frequency $\omega_z=2\pi\times 60$ Hz for (a) and $\omega_z=2\pi\times 80$ Hz for (b). The initial total atom number is $N_0=1033$ for $\omega_z=2\pi\times 60$ Hz and $N_0=765$ for $\omega_z=2\pi\times 80$ Hz and the condensate fraction is approximately $75\%$ for all cases. The first dissipation strength is taken as $2\omega_z$ for condensate and $\omega_z$ for thermal components, respectively. The interaction strength is chosen as $0.025~\hbar\omega_za_0$ where $a_0=\sqrt{\hbar/m\omega_z}$ is the harmonic length. The first dissipation period is $0.37/\omega_z$. (c) The total number of atoms as a function of $x$ after the $"5+x+y"$ protocol, with $y$ fixed at $0.37/\omega_z$. (d) The oscillation frequency $f$ (blue circles) and relative amplitude $A$ (red triangles) for different trap frequencies. The dashed line denotes $f=2\omega_z/2\pi$.