Slow Polaritons in Atomic Bose-Einstein Condensates

Abstract

We consider the slowing down and storing of laser pulses in atomic Bose-Einstein condensates (BEC). The theory is based on the concept of slow polaritons for describing the propagation of laser pulses in an electromagnetically induced transparency (EIT) medium. A general treatment shows the possibility to revert the stopped polaritons. In contrast to the previous analysis of EIT polaritons, the slow polaritons need not necessarily be at the exact EIT resonance, in which case they acquire a finite radiative lifetime. It is shown that the slow polariton can be moved out of the EIT resonance by reversing the control beam; the effect is most significant for counter-propagating control and probe lasers. 32.70.Jz, 42.50.Fx, Recently, electromagnetically induced transparency (EIT) [1][2][3][4] was shown to slow down dramatically [5], or even to stop completely [6,7], laser pulses in atomic gases. The experiments [5-7] involve media of three-level atoms interacting with two lasers-a control beam and a probe pulse. The atoms have two hyperfine ground states, |g and |q , and an electronically excited state |e , as illustrated in Fig. 1(a). The level g is populated initially (before applying the probe pulse to couple the states |g and |e ). The role of the control beam is to introduce a transparency window for the probe pulse which then propagates slowly in the medium. Such behavior can be understood in terms of a branch of slow polaritons appearing between two close atomic resonances, as shown in Fig. 2 (see also Fig. 2b in Ref. [8]). In fact, the control laser couples dynamically the states |q and |e , bringing the level |q into resonance with the excited state |e . Consequently, the excited level splits into the doublet [ Fig. 1(b)] required for the formation of a branch of slow polaritons as shown in Fig. 2. Polaritons are the normal modes of a combined system of the radiation field and matter. Over the last decade the polariton concept has been applied widely to describe the quantized radiation field in dielectric media [8][9][10][11][12][13][14]. Most of these studies, however, have been designed for media composed of two-level atoms, and hence do not accommodate the slow EIT polaritons. Slow polaritons appear in the analysis beyond the two-level model [8,13,14]. Yet the existing theoretical work [8,13,14] does not deal specifically with EIT. More recently, EIT (dark state) polaritons were considered by Fleischhauer and Lukin [15,16] who predicted the storage of a probe pulse (stopping of the polariton) by switching off the control laser.Here we present a general treatment of slow polaritons in EIT media. Our analysis shows the possibility to revert the stopped polariton. The theory is designed for atomic Bose-Einstein condensates (BECs), yet the findings are relevant to ordinary atomic gases as well. In contrast to the previous analysis of EIT polaritons [15][16][17], the slow polariton is now not necessarily at the exact EIT resonance. (For instance, the slow polariton can be moved out of the EIT resonance by rever...

Polariton analysis of a four-level atom strongly coupled to a cavity mode

“…Polariton analysis has been used extensively of late to study the dynamics of EIT systems [17,18,19], but these analyses have concentrated on the semiclassical case of an atomic gas driven by laser light; in particular, on the dynamics of 'slow' light. Juzeliunas and Carmichael [20] have refined the analysis of the corresponding 'slow polaritons', and showed that it is possible to reverse a stopped polariton by reversing the control beam. However, none of the treatments so far have dealt with the coupled atom-cavity system.…”