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Journal of Physics A Mathematical and General

Two photon absorption with coherent and partially coherent driving fields

S. Chaturvedi, P. D. Drummond, Daniel F. Walls

Published Nov 1, 1977• 66 citations
Publisher

Abstract

A model of two photon absorption in a cavity with an external driving field is presented. Phase and amplitude fluctuations in the driving field are taken into account to model a partially coherent multimode source. The photon statistics of the light in the cavity are investigated through a calculation of the second-order correlation function of the light field in the steady state. For a coherent driving field the field inside the cavity will exhibit photon antibunching for low intensities. As the fluctuations in the driving field are increased the photon antibunching is lost. For a particular coherent field, g (2) (0) is reduced with increasing laser intensity. This reduction with laser intensity is slower with increasing laser amplitude fluctuations. This could provide a possible explanation for the recent experimental observations of Kransinski and Dinev (1976).

DOI
10.1088/0305-4470/10/11/003

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A model of two photon absorption in a cavity with an external driving field is presented. Phase and amplitude fluctuations in the driving field are taken into account to model a partially coherent multimode source. The photon statistics of the light in the cavity are investigated through a calculation of the second-order correlation function of the light field in the steady state. For a coherent driving field the field inside the cavity will exhibit photon antibunching for low intensities. As the fluctuations in the driving field are increased the photon antibunching is lost. For a particular coherent field, g (2) (0) is reduced with increasing laser intensity. This reduction with laser intensity is slower with increasing laser amplitude fluctuations. This could provide a possible explanation for the recent experimental observations of Kransinski and Dinev (1976).
We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.
We present analytic results for the photon statistics of a weakly driven optical cavity containing N two-level atoms. The second-order intensity correlation function g(2)() is calculated in the weak field limit for arbitrary atomic and cavity loss rates, and cavity and atomic detunings are included. The transmitted light field may exhibit photon antibunching, sub-Poissonian photon statistics, and other novel nonclassical effects.1,2 The size of these effects depends principally on the single-atom coupling constant C1 = g2/κγ, so these effects persist with many atoms in the cavity. Our results can be interpreted via the collapse of the wave function and quantum interference of probability amplitudes. These phenomena can also be understood in terms of the self-homodyning of the driving field with squeezed polarization fluctuations.2
The photon statistics of the transmitted light from a driven cavity containing a single resonant two-level atom are studied in the bad-cavity limit. For weak driving fields, the second-order intensity correlation function shows novel nonclassical behavior due to the interference of the driving field and forward reradiation from the atom. This behavior is related to squeezing in the cavity transmission. A physical interpretation is given in terms of the reduced quantum state of the coupled atom-field system following photodetection.>
By solving the master equation in the steady-state limit and calculating the zero-delay-time second-order correlation function, a strong photon antibunching is found in two coupled cavities with weak nonlinearity χ(2). An optimal antibunching condition is derived that is complementary to the result in a recent publication [Phys. Rev. A89, 031803(R) (2014)]. Numerical simulations confirm the optimal condition. These results are extended from the case with a single drive to the case with two drives. We find that the parameter added to the system due to the second drive can lift the restriction on the detuning for the antibunching to occur. This may open a new door towards the application of the antibunching into single photon sources.
We report measurements of the absorption spectrum for two-photon absorption from a variety of randomly amplitude-modulated laser fields. The fields are generated by modulating the output of a stabilized tunable ring dye laser external to the laser cavity. As such, the field statistical properties are controllable and well characterized. The fields which we have used in this investigation include the real Gaussian field, the complex Gaussian field, and the real Gaussian field with a coherent component. For the last field, an interesting correlation effect is seen when the coherent component is in phase or 90\ifmmode^\circ\else\textdegree\fi{} out of phase with the stochastic component. We have also investigated the effect of partial correlation of the two counterpropagating fields used in the measurements. In all cases we find excellent agreement between the measured absorption spectra and those calculated from the known fourth-order field-correlation functions.
We theoretically investigate the photon statistics in a cavity quantum electrodynamics system of a single quantum dot coupled to a bimodal nanocavity. It is shown in a recent work [A. Majumdar, M. Bajcsy, A. Rundquist, and J. Vu\ifmmode \check{c}\else \v{c}\fi{}kovi\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. Lett. 108, 183601 (2012)] that the system can generate strongly sub-Poissonian light when one of the cavity modes is driven coherently and resonantly. We study the two-mode coherent driving regime of the coupled system. The effect of additional cavity mode driving on statistical characteristics of photon emission is presented by evaluating the zero-delay second-order correlation function g2{g}^{2}g2(0). The antibunching character can be optimized by regulating the ratio between driving strengths of two cavity modes to achieve optimal combination of superbunched and coherent light. As a result g2{g}^{2}g2(0) can be reduced up to several orders of magnitude [g2{g}^{2}g2(0)$\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}101010{}^{\ensuremath{-}7}]withpropersystemparameters,comparedwiththeone−modedrivingsystem[] with proper system parameters, compared with the one-mode driving system []withpropersystemparameters,comparedwiththeone−modedrivingsystem[{g}^{2}(0)(0)(0)\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}$0.1].