Dear Anil,

Because a three level system such as the ATOM-CAVITY-RESERVOIR model offers great richness of quantum effects, yet it provides simplicity at the same time. For instance you can use this three level system to examine non-trivial non-Markovian dynamics between any two subsystems, and examine  non local effects between one of the two  subsystem and the third subsystem. It is good to get feedback from others as to why  there are other  more compelling reasons.

Hi,

The use of three-level quantum systems (qutrits) can enhance the performance of quantum communication protocols compared to qubit-based ones. See for example:

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.87.217901

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.89.197901

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.89.100402

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.93.053601

http://journals.aps.org/pra/abstract/10.1103/PhysRevA.77.050301

I hope it helps,

Assaf

They are very important in lasers operation, e.g. ,  in the He-Ne laser.

also the three level system is the simplest system to exhibit contextuality. don't know if that helps.

Line width narrower

 Three level ladder system can be modelled as a two level system with two photon resonance condition with the required detuning of the first excitation laser. This helps us to study the EIT etc which we cannot study using the two level system.. This is  one more advantage along with previous answers..

Light-atom interaction  induces coherence between atomic states that modifies the optical response of a medium. A two-level atomic system driven by a near-resonant light field leads to oscillatory population transfer between ground and excited states. This oscillatory behavior is known as Rabi flopping or Rabi oscillations. The generalization of this coherent situation to a three-level atomic system driven by two light fields leads to variety of physical phenomena for practical applications. Some of the important phenomena related to three-level system are Autler-Townes  splitting, electromagnetically induced transparency (EIT) , coherent population trapping  and lasing without inversion.

To extend the discussion on  three-level system, I will choose the phenomenon of EIT: The phenomenon of EIT is of great importance and it leads to the cancellation of absorption for the resonant probe field. EIT is a phenomenon in which absorbing medium for the weak probe field becomes nearly transparent (i.e., absorption eliminates at resonance) in the  presence of the strong control field. In addition, the dispersive behavior of the probe field also changes drastically under EIT conditions.

The effect of EIT is caused by the destructive interference between atomic coherences excited by electromagnetic fields. The EIT systems involve a three-level atom interacting with the two e.m. fields in such a way that both the fields connect a separate transition and the two transitions share a common energy level. The atomic dipole selection rules require that only two pairs of transitions are dipole allowed while the third transition is dipole forbidden. The three-level systems are commonly classified into three categories, i.e., lambda (Λ), cascade (Ξ) and Vee (V) systems. In these systems, EIT involves in specific case, in which  probe field is very weak and control field is allowed to have varying strengths.

The interference associated with EIT arises due to the presence of strong control field. The atomic coherence associated with the probe field transition include an additional term that depends upon the strength of the control field. The presence of this additional term leads to the cancellation of probe absorption . In the dressed state picture, the strong control field dresses the levels associated with it into their superposition. Under the weak probe condition, the ground states of probe field transition become a dark state. The dark state is one from which no excitation can occur. In this situation, the destructive interference between the probe absorption amplitudes due to the dressed states formation leads to EIT.

From a process, procedural standpoint, three level systems, provide an avenue for transitions instead of a truncated, two-level, start to finish, beginning to end. While three is more realistic, two may be more amendable to binary logic and hence computable approaches.

It gives a true handle to manipulate realistic system. We have a series of work on three-level system, its utility and implementation, you may check the arXiv for the papers.

Population difference is zero after some time, so we prefer three level laser.