6

Spontaneous emission: From irreversible decay to Rabi oscillations1

Humpty Dumpty sat on a wall,

Humpty Dumpty had a great fall.

All the king's horses,

And all the king's men,

Couldn't put Humpty together again!

—Old nursery rhyme2

This chapter is divided into two sections. In the first section we use the formalism developed in Chapter 5 to discuss spontaneous emission in free space. We address the problem of atomic stability when the coupling with the dynamic electromagnetic field is included and the atom is allowed to radiate. We examine the roles of vacuum fluctuations and radiation reaction in the spontaneous emission process and the stability of the ground state of the atom [3, 129, 131, 449, 450, 453, 456, 557]. Then we show that spontaneous emission in free space leads to an exponential decay of the atomic energy until it reaches the ground state.

In the second section we address the problem of spontaneous emission in a cavity. We examine two limits: the weak and strong coupling regimes. We show that in the weak-coupling regime, there is still an exponential decay, but the rate is changed by the cavity. In the strong-coupling regime, however, spontaneous emission becomes reversible with the atom performing Rabi oscillations. We also discuss what happens for long interaction times compared to the Rabi frequency, and we show that the oscillation collapses to revive only several periods later. We give an interpretation for these collapses and revivals where we find that ...

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