Controllable manipulation and detection of local densities and bipartite entanglement in a quantum gas by a dissipative defect

We study the complex dynamics of a one-dimensional Bose gas subjected to a dissipative local defect which induces one-body atom losses. In experiments these atom losses occur, for example, when a focused electron or light beam or a single trapped ion is brought into contact with a quantum gas. We discuss how within such setups one can measure or manipulate densities locally and specify the excitations that are induced by the defect. In certain situations the defect can be used to generate entanglement in a controlled way despite its dissipative nature. The careful examination of the interplay between hole excitations and the collapse of the wave function due to nondetection of loss is crucial for the understanding of the dynamics we observe.

Figure 1

Weak dissipative coupling $\Gamma /J=0.25$, $L=105$ and 53 or 105 particles. In (a) and (b) we show density profiles at different times. Densities are rescaled by their initial values and size-dependent features in the vicinity of the edges of the systems are discarded. We depict the “light cone” of waves moving with the sound velocity [20] by vertical lines. Star and cross symbols represent $|{\psi }_{\mathrm{nd}}\left(t\right)\rangle$, $|{\psi }_{\mathrm{hole}}\left(t\right)\rangle$, respectively. In the lower panels we plot the total atom loss (c) and the central density (d), both rescaled by the initial density $n_{\mathrm{in}}$. In (c) four curves almost lie on top of each other. Boundary effects are eliminated by interrupting simulations before reaching the recurrence times. Statistical errors are either marked by bars or are smaller than the line width or symbol sizes.

Figure 2

(a) ${\overline{n}}_0$ in the weakly dissipative regime. Error bars indicate systematic fluctuations and statistical errors. (b) Long-time loss rate for the strongly dissipative case. (c) Loss rate from weak to strong dissipation. Lines are guides to the eye.

Figure 3

Numerical results for strongly dissipative coupling $\Gamma /J=8$. For an explanation of (a)–(c), see Fig. 1. (d) shows the evolution of the von Neumann entropy between the subsystems separated by the defect.