Interferences in Parametric Interactions Driven by Quantized Fields

Abstract

We report interferences in the quantum fluctuations of the output of a parametric amplifier when the cavity is driven by a quantized field at the signal frequency. The interferences depend on the phase fluctuations of the input quantized field and result in splitting of the spectrum of the output, and thus the recent observation [H. Ma et al., Phys. Rev. Lett. 95, 233601 (2005)] of interferences in the classical domain have a very interesting counterpart in the quantum domain. The interferences can be manipulated, for example, by changing the amount of squeezing in the input field. DOI: 10.1103/PhysRevLett.97.023601 PACS numbers: 42.50.Lc, 42.50.St, 42.65.Lm In recent times quantum interferences have been central to many new applications of few level quantum systems driven by the coherent fields. In particular, the electromagnetically induced transparency (EIT) has led to the possibilities of enhanced nonlinear optical phenomena [1], ultraslow light [2], storage and stopping of light [3], an efficient method of laser cooling [4], and control of chiral anisotropies [5]. The EIT has also been demonstrated for quantized fields [6]. In this Letter we report the possibility of quantum interferences in totally different class of systems which are nonresonant and which are being extensively used in the context of quantum imaging and quantum information science [7,8]. We use parametric interactions driven by quantized fields at the signal or the idler frequency. The generated quantum fields in parametric interactions exhibit a variety of interferences depending on the phase fluctuations in the input quantized field [8]. We note that optical parametric interactions have been studied extensively since the classical work of Armstrong et al. [9]. These classical interactions are known to possess unusual properties. Kaplan [10] discovered that under certain conditions on the pump and signal amplitudes, there is no exchange of energy between the pump and signal. There is yet another very interesting situation where by a suitable choice of the phases of the input amplitudes can lead to either purely growing solutions or decaying solutions. To see this consider the classical Hamiltonian for the parametric processwhich in the limit of undepleted pump b leads to a t 1 2 e 2jgjbt a ÿ igb jgbj a y 1 2 e ÿ2jgjbt a igb jgbj a y :Thus by choosing a=a y igb=jgbj one can suppress the growing solution. Yet another very interesting aspect of classical parametric interactions was discovered in a recent letter by Ma et al. [11]. They have studied a variety of interference effects in parametric interactions in a cavity when the cavity is also driven by a field at the signal frequency, i.e., a Þ 0. The interferences arise from the nonzero signal field at the input and the signal field produced by the pump field. Ma et al. in particular reported mode splitting in transmission spectra. All the above remarkable developments refer to the behavior of parametric interactions when all the fields are treated classically. Clearly it is important t...

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