We propose an efficient scheme to manipulate spontaneous emission spectra using optical vortices carrying orbital angular momentum (OAM) in a coherently driven cold five-level atomic system assisted by a radio frequency (RF) or microwave field. Using experimentally achievable parameters, we find that the spontaneous emission is strongly influenced by quantum destructive interference. And we show that the structured light profile of the probe field can be transferred to the spontaneous emission spectrum via spontaneously generated coherence (SGC). With the aid of SGC, the intensities and detunings of the control and RF fields can be used to tailor the vortex-induced spontaneous emission spectra. When the control and RF fields are configured as vortex beams, it is demonstrated that the spontaneous emission can be coherently controlled through quantum interference by adjusting their topological charges (TCs). Furthermore, we explore intriguing optical properties of the vortex-induced spontaneous emission by varying the TCs of the probe and control fields. This coherently driven atomic system features three closely spaced levels, giving rise to multiple vortex-induced SGC pathways. Our scheme opens avenues for applications in structured light, ranging from optical storage to optical communication.
The interaction between the electromagnetic field and a number of identical atomic systems, individually characterized by an electric dipole moment and two energy levels, is analyzed for the case where the atomic systems are inside a lossy cavity and exposed to a coherent driving field, resonance being assumed between atomic system, cavity, and driving field.The problem of introducing loss into a quantum-mechanical formalism is treated first. Formal operator expressions are obtained for the field variables which include the absorption and the fluctuation (both thermal and quantum-mechanical) effects of the loss mechanism. Expectation values are then obtained for the field strength and the field energy which are valid for times short compared to the lifetime of the excited state. It is shown that the spontaneous-emission energy in the field increases initially as the square of the time and approaches a steady-state value after a transient period which is of the order of the cavity relaxation time. The induced emission contains two parts: incoherent emission induced by the thermal field, and coherent emission induced by the driving field. The incoherent induced-emission energy has the same time dependence as the spontaneous-emission energy, and the ratio of the former to the latter is the number of photons in the thermal (inducing) field. The coherent induced-emission energy does not approach a steady-state value, but, after a transient period, increases linearly with the time. The ratio of the coherent induced-emission energy to the spontaneous-emission energy is equal, initially, to the number of photons in the driving-field energy, but becomes $\ensuremath{\beta}t$ times as large after the transient period, where $\ensuremath{\beta}$ is the reciprocal of the cavity relaxation time.The expectation value of the rate of energy emission by the atomic systems is also obtained. It is shown that the ratio of the downward to the upward transition probabilities has the well-known value of
n(n+1), where
n is the field energy in units of the photon energy, only in the absence of a coherent field.
The theory of the previous articles of this series is extended to allow analysis of the spectral distribution of induced and spontaneous emission in a cavity and to study the steady-state condition when a molecular beam traverses the cavity.It is shown that the induced emission energy, when averaged over a reasonable time, depends only on the energy spectrum of the driving field. Expressions are obtained for the spectral distribution of induced, spontaneous, and thermally induced emission. These results are then applied to a molecular beam analysis and conditions for a steady state in the cavity are obtained.The amplification by the molecular beam of the driving field (signal) and of the thermal and spontaneous emission energies (noise) is studied. Signal and noise energies are compared and the dependence of the results on both the bandwidth of the signal and the bandwidth of detection is examined.