In quantum mechanics, a coherent state refers to a particular type of quantum state that exhibits wave-like behavior and possesses some characteristics of classical waves. Specifically, a coherent state is a quantum state that closely resembles a classical wave in terms of its properties such as its average energy and phase.
When we say that the atoms of a macroscopic object are prepared in a coherent state, it means that the quantum mechanical description of these atoms resembles a classical wave with well-defined properties. In this state, the atoms are in a superposition of different quantum states, but the superposition is such that the average properties of the atoms, such as their position or momentum, are well-defined and exhibit a wave-like behavior.
In the case of macroscopic objects, such as a collection of atoms or a macroscopic quantum system, the preparation of coherent states can be achieved through various methods, such as cooling techniques or the use of external fields to manipulate the quantum states of the atoms. These methods allow for the creation of a large number of atoms that collectively exhibit coherent behavior.
Coherent states have some distinctive features. For instance, they exhibit minimal uncertainty in certain observables, such as position and momentum, which means that these properties can be simultaneously known with high precision. Coherent states also tend to spread out over time due to the quantum mechanical phenomenon known as wavefunction spreading.
The concept of coherent states is particularly relevant in the field of quantum optics, where it describes the states of light in laser beams. In this context, a coherent state represents a well-defined and predictable electromagnetic field that can be used for various applications, such as interferometry or quantum information processing.
In summary, when the atoms of a macroscopic object are prepared in a coherent state, it means that their quantum mechanical behavior resembles that of a classical wave, with well-defined average properties and minimal uncertainty in certain observables.