Abs trac t.In this article we study the potential for coherently control spontaneous emission in a four-level scheme. Our control parameter is the relative phase of two laser ® elds having the same angular frequency. We investigate in detail the trapping conditions, the population dynamics and the behaviour of the (long time) spontaneous emission spectrum, which are now phase dependent. Inhibition of spontaneous emission and extreme spectral narrowing are shown as the relative phase is varied. Our results are interpreted using a dressed state analysis of the dynamics.
In trod u c tionT here are two basic methods that could be used in order to modify (or control) spontaneou s emission of a multi-level atom. T he ® rst one relies on passive control and it is achieved by placing the atoms within reservoirs whose density of modes is dramatically di erent from that of free space vacuum. Such control can be realized in cases where atoms interact with microcavities [1± 3] or photonic band gap materials [4± 7]. T he second method uses active control and it is realized by using the properties of coherent (optical, microwave or radio-frequency) [8± 19] or incoherent [20, 21] ® elds. For the speci® c case of coherent ® elds it was known that control could be achieved by either varying the frequency (which leads to changes of the detuning) or by varying the intensity (which leads to changes of the Rabi frequency). In addition to this, it has only been recently realized that spontaneou s emission can also be e ciently controlled using phase control techniques [22± 28], where the phase of the driving coherent ® eld(s) is appropriately exploited in order to modify the spontaneou s emission dynamics.In this article we continue our investigation of coherent`phase' control of spontaneou s emission [24± 26] and study the potential for coherent control of a four-level quantum system, using the relative phase between two lasers with equal frequencies ! aˆ!bˆ! , which couple the ground state with the two excited states (as displayed in ® gure 1). T hese laser ® elds may be distinguished by their di erent transition characteristics , where it is possible to have a three (multi)-photon transition for laser ! a and a single photon transition for laser ! b using the corresponding harmonic. T his approach is usually referred to as the two-colour