Optimal squeezing, pure states, and amplification of squeezing in resonance fluorescence

Both theoretical and experimental studies have shown that the resonance fluorescence of a driven atom can serve as a source of nonclassical light. For example, Carmichael and Walls, and Kimble and Mandel [1] predicted that the resonance fluorescence from a single two-level atom driven by a coherent laser field of low intensity would exhibit photon antibunching. The prediction has been confirmed in many laboratories [2–4]. The sub-Poissonian statistics of the fluorescent photons emitted in a short time interval by a single atom was also investigated experimentally [5]. There have been many theoretical investigations of squeezing in resonance fluorescence, both in terms of the total variances and in terms of the fluctuation spectra of the phase quadratures. Walls and Zoller, and Loudon [6] showed that the total quantum fluctuations in the phase quadratures of the resonance fluorescence of a driven two-level atom can be squeezed below the shot-noise limit. Single-mode [7], or frequency-tunable two-mode [8] squeezing with a finite bandwidth may be obtained, depending on the Rabi frequency and detuning. This internally produced squeezing results in line narrowing in the resonance fluorescence spectra [9,10]. Phase-quadrature squeezing has also been studied in the presence of an applied squeezed vacuum [10–12]. Experimental observation of squeezing in the fluorescence field has proved a great challenge, one problem being that atomic motion produces phase shifts which destroy squeezing [13]. This difficulty was surmounted in the recent experimental advances in homodyne detection schemes of the fluorescent radiation of a single trapped ion reported by Hoffges et al. [3]. Within the last couple of years, experiments carried out by Zhao et al. [14] have found some evidence of squeezing by measuring the phase-dependent fluorescence spectra of a coherently driven two-level atom with a long lifetime, stimulating the further exploration of squeezing in resonance fluorescence. Very recently, squeezing in the quadrature with phase π/4 relative to the driving laser was observed for the first time in the resonance fluorescence of a single two-level atom [15]. Also very recently, we have found that squeezing in resonance fluorescence can be greatly enhanced in a frequencytunable cavity [16], or in a squeezed vacuum [11,12]. The latter works mainly in the regime over which anomalous spectra such as hole-burning and dispersive profiles [17] occur, i.e., ∆ = 0 and Φ = 0, where squeezing occurs in the out-phase quadrature of the fluorescent field. In this paper we extend the study to the general case, and show that large squeezing occurs in different phase quadratures of the fluorescent field, depending upon the values of the parameters. The large squeezing is associated with an atomic pure state (a completely polarized state), and thereby with a large atomic coherence. Perfect fluorescent squeezing may only take place for the particular squeezing number N = 1/8. There is previous evidence that the value N = 1/8 is special. It has been shown that large squeezing in resonance fluorescence was produced for this input squeezed field [12], and that also for this value of N, the sidebands in the resonance fluorescence spectrum have the same linewidth as in the N = 0 case [18].