Effect of Number-State Filtration on Atomic Population Inversion

Introduction:

The interaction of a two-level atom with an electromagnetic field inside a cavity is described by the Jaynes–Cummings model. It predicts an interesting feature, namely, the collapse and revival of atomic population inversion especially when an atom interacts with the coherent state |α>.

Methods:

In this study, we consider the Jaynes–Cummings Hamiltonian H=ω₀σ_z/2 + ω_ca⁺a + g(σ_{_}a⁺ + σ₊a). The atomic population inversion is defined as W(t)=<Ψ(t)|σ_z|Ψ(t)>, where |Ψ(t)> is the time-evolved state calculated through |Ψ(t)>= e^-iHt |Ψ(0)>. The initial state is defined as follows: the atom is in its excited state and the field is in a number-state filtered coherent state (NSFCS). NSFCS is obtained by filtering out a number state (for example, |m> from a coherent state).

Results and Discussion:

We observed the following: (i) The atomic population inversion no longer exhibits the collapse feature; instead, it displays micro-Rabi oscillations with small amplitudes, indicating a washout of perfect destructive interference. (ii) The amplitude can be tuned by filtering an appropriate number state. (iii) The amplitude is maximum when m is |α|². (iv) The number of oscillations present in the collapse region is
given by k=√m+1 gΔt_c/ Π, where g is the atom–cavity coupling strength.

Conclusion: We studied the effect of number-state filtration from an initial coherent state on the temporal dynamics of atomic population inversion. We observed the emergence of micro-oscillations in the collapse region due to washout of destructive
interference.