The double-slit experiment can indeed be performed with molecules, and it is possible to introduce a "which-slit" measurement that is weak enough to not completely destroy the interference pattern but still provide some information about which slit the molecule went through. However, it's important to note that the specific details and challenges of implementing such a measurement can vary depending on the nature of the molecules involved and the experimental setup.
In the traditional double-slit experiment with light or electrons, introducing a "which-slit" measurement typically involves placing detectors near the slits to determine through which slit each particle passes. However, the act of measurement can disturb the particle's wave-like behavior and destroy the interference pattern. This is known as the quantum measurement problem.
In the case of molecules, performing a "which-slit" measurement becomes more challenging due to their complex nature and sensitivity to interactions with the environment. Molecules can easily undergo decoherence, where their quantum states become entangled with the surrounding environment, leading to the loss of interference effects.
To mitigate this issue, researchers have developed techniques to perform weak measurements that extract partial information about the molecule's path while minimizing the disruption of interference. These techniques often involve minimizing the interaction between the molecule and the measuring apparatus, for example, by using a carefully designed setup or ultrafast measurement schemes.
One approach is to use a weak measurement technique known as quantum eraser, where the information about the molecule's path can be "erased" by post-selection on the measurement outcomes, restoring the interference pattern. This involves entangling the molecule with another quantum system and performing a measurement that is only weakly correlated with the molecule's path information.
Overall, implementing a "which-slit" measurement in the double-slit experiment with molecules involves careful design and control to balance between obtaining partial path information and preserving the interference pattern. The specifics can vary depending on the experimental setup and the characteristics of the molecules involved. Ongoing research in this field continues to explore different techniques and approaches to address these challenges.