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Physical Review A

Exact transient photon correlation with arbitrary laser pulses

C. H. Raymond Ooi

Published Nov 21, 2011• 2 citations
Publisher

Abstract

We present a full quantum theory to study the transient evolution of photon pairs. We introduce a method which gives exact time-dependent solutions of the coupled quantum Langevin equations for a multilevel quantum particle driven by arbitrary time-dependent laser fields. The analytical solutions are used to develop a numerical code for computing exact time evolution of the two-photon correlation function. We analyze the effects of laser pulses sequence, pulse duration, chirping, and initial internal quantum states on the nonclassicality of the photon correlation through the violation of the Cauchy-Schwarz inequality. The results provide a promising possibility of controlling the generation of highly correlated photon pairs using tailored short laser pulses.

DOI
10.1103/physreva.84.053842

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We present a full quantum theory to study the transient evolution of photon pairs. We introduce a method which gives exact time-dependent solutions of the coupled quantum Langevin equations for a multilevel quantum particle driven by arbitrary time-dependent laser fields. The analytical solutions are used to develop a numerical code for computing exact time evolution of the two-photon correlation function. We analyze the effects of laser pulses sequence, pulse duration, chirping, and initial internal quantum states on the nonclassicality of the photon correlation through the violation of the Cauchy-Schwarz inequality. The results provide a promising possibility of controlling the generation of highly correlated photon pairs using tailored short laser pulses.
We study the effects of arbitrary laser pulse excitations on quantum correlation, entanglement, and the role of quantum noise. The transient quantities are computed exactly using a method that provides exact solutions of the Langevin field operators for photon pairs produced by a double Raman atom driven by laser pulses. Short pulses with appropriate chirping, delay, and/or detuning can generate broadband photon pairs and yield results that provide insights on how to generate very large nonclassical correlation. We find that short pulses are not favorable for entanglement. Photon correlation and entanglement are favored by exclusively two different initial conditions. We find rapid variations of entanglement with pulse width and strength. Explanation is given based on the pulse area concept and the phase-sensitive nature of entanglement. Analysis of results reinforces our understanding of the two nonclassical concepts and the nature of quantum noise.
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The time dependence of nonclassical correlations is investigated for two fields (1,2)(1,2)(1,2) generated by an ensemble of cold cesium atoms via the protocol of Duan et al. [Nature (London) 414, 413 (2001)]. The correlation function R(t1,t2)R({t}_{1},{t}_{2})R(t1​,t2​) for the ratio of cross to autocorrelations for the (1,2)(1,2)(1,2) fields at times (t1,t2)({t}_{1},{t}_{2})(t1​,t2​) is found to have a maximum value ${R}^{\mathrm{max}}=292\ifmmode\pm\else\textpm\fi{}57$, which significantly violates the Cauchy-Schwarz inequality $R\ensuremath{\le}1$ for classical fields. Decoherence of quantum correlations is observed over ${\ensuremath{\tau}}_{d}\ensuremath{\simeq}175\text{ }\text{ }\mathrm{n}\mathrm{s}$, and is described by our model, as is a new scheme to mitigate this effect.
We study the quantum correlation of photon pairs from a double Raman particle driven by laser fields in a modified photon density of states such as a cavity or a defect in a photonic crystal. We obtain an exact semianalytical expression for the photon correlation, which is characterized by two complex decay functions associated with the levels splitting (effective Rabi frequencies) that depend on the control laser field. The position and width of the cavity density of state with respect to the anti-Stokes transition determine the features in the two-photon correlation profile.