Bose-Einstein condensates (BECs) are unique states of matter that occur at extremely low temperatures, where a large number of bosonic particles occupy the same quantum state. In a BEC, the individual particles lose their individual identities and behave collectively as a single macroscopic quantum object. However, this does not mean that the BEC can be considered as a single particle.
The concept of quantum entanglement involves the correlation of the quantum states of two or more particles, where the state of one particle is dependent on the state of the other(s). Quantum entanglement typically refers to the entanglement between distinct particles, rather than a single particle with itself.
In the case of a BEC, all the particles are in the same quantum state, so they are not distinct entities that can be individually entangled with each other. The macroscopic behavior of a BEC arises from the collective behavior of the particles, but they are still fundamentally separate particles with their own quantum properties.
However, it is possible to create entanglement between different BECs or between a BEC and other particles. For example, if two separate BECs are allowed to interact with each other, their collective behavior can become entangled. Additionally, if a BEC interacts with another quantum system, such as an individual atom or a photon, entanglement can be generated between the BEC and that system.
So, while a single BEC cannot be split and become quantum-entangled with itself, entanglement can occur between different BECs or between a BEC and other quantum systems.