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Physical Review A

Four-wave mixing in the diamond configuration in an atomic vapor

R. T. Willis, F. E. Becerra, Luis A. Orozco, S. L. Rolston

Published Mar 12, 2009• 77 citations
Publisher

Abstract

We present measurements of the resonance structure for nondegenerate four-wave mixing (4WM) in the diamond configuration in a warm atomic vapor of rubidium. We show that a narrow sub-Doppler feature exists and can be understood as a result of velocity-class selection. We measure the efficiency of the 4WM process and show it to be on the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. Our observations are consistent with the results of a theoretical treatment based on the semiclassical Maxwell-Bloch equations for the system with the appropriate coupling values derived from the experimental values in Rb.

DOI
10.1103/physreva.79.033814

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We present measurements of the resonance structure for nondegenerate four-wave mixing (4WM) in the diamond configuration in a warm atomic vapor of rubidium. We show that a narrow sub-Doppler feature exists and can be understood as a result of velocity-class selection. We measure the efficiency of the 4WM process and show it to be on the order of 1\ifmmode×\else\texttimes\fi10\ensuremath−41\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}1\ifmmode×\else\texttimes\fi10\ensuremath−4. Our observations are consistent with the results of a theoretical treatment based on the semiclassical Maxwell-Bloch equations for the system with the appropriate coupling values derived from the experimental values in Rb.
We investigate experimentally and theoretically nondegenerate four-wave mixing in rubidium vapor using a diamond configuration (5S1/25{S}_{1/2}5S1/2​, 5P1/25{P}_{1/2}5P1/2​, 5P3/25{P}_{3/2}5P3/2​, and 6S1/26{S}_{1/2}6S1/2​ levels). We model this process of three classical fields interacting with a four-level atomic system with the Schr\"odinger equation. The experimental results are in good agreement with theoretical predictions for the generated light as a function of detuning.
This thesis discusses four-wave mixing (4WM) in a warm ensemble of rubidium using the diamond configuration level structure. Both classical 4WM and non- classical photon-pair production are investigated. Quantum information science has spawned a great amount of experimental work on the interaction of light with collective modes of excitation in atomic ensem- bles. Plans to build quantum networks and quantum repeaters with atom ensembles take advantage of nonlinear interactions to produce and store non-classical states of light. These technologies will require photon sources that not only generate non- classical light, but also resonant, narrow band light. Here we investigate a system which could be used as such a source. We take advantage of the 4WM interaction in a warm ensemble of Rubidium atoms. Our scheme utilizes the diamond energy level configuration which, in ru- bidium, allows for correlated pairs at telecommunications wavelengths. We start by examining the properties of classical 4WM in the system. We measure the reso- nance structure and see that it can be understood in terms of velocity class selective resonant enhancement and power splitting effects. The efficiency of the process is low and limited by linear absorption of the pumps. Our observations agree with a semi-classical Maxwell-Bloch theoretical treatment. Next we observe pair generation by spontaneous 4WM from the warm ensem- ble. The temporal profile of the cross-correlation function (CCF) for the photons depends on pump-laser power and detuning. This allows us to produce biphotons with controllable spectra. A simple quantum optical theoretical treatment based on linear filtering gives qualitative agreement with the data. We show that the photon pairs are polarization entangled, clearly violating Bell's Inequality. A perturbative quantum optical treatment predicts the polariza- tion state of the pairs and agrees with our measurements. We analyze the photon statistics of the source and find the largest violation of the two beam Cauchy-Schwarz inequality from a warm atomic source yet. We cast the system as a heralded sin- gle photon source at telecommunications wavelengths and see that it is competitive with other systems in terms of spectral brightness.
We present an experimental study of seeded four-wave mixing (4WM) using a diamond excitation scheme (with states from the 5S1/2,5P1/2,5P3/2 and 5D3/2 terms) in a thermal vapour of 87Rb atoms. We investigate the 4WM spectra under the application of a strong magnetic field (0.6 T). The Zeeman interaction is strong enough to realize the hyperfine Paschen–Back regime, which has the effect of separating the optical transitions by more than the Doppler width, thereby significantly simplifying the spectral features. We show that this facilitates a quantitative comparison, even in the regime of strong dressing, between experimental data and a simple theoretical model based only on four-level optical Bloch equations.
We present an experimental study of seeded four-wave mixing (4WM) using a diamond excitation scheme (with states from the 5S1/2_{1/2}1/2​, 5P1/2_{1/2}1/2​, 5P3/2_{3/2}3/2​ and 5D1/2_{1/2}1/2​ terms) in a thermal vapour of 87^{87}87Rb atoms. We investigate the 4WM spectra under the application of a strong magnetic field (0.6 T). The Zeeman interaction is strong enough to realise the hyperfine Paschen-Back regime, which has the effect of separating the optical transitions by more than the Doppler width, thereby significantly simplifying the spectral features. We show that this facilitates a quantitative comparison, even in the regime of strong dressing, between experimental data and a simple theoretical model based only on four-level optical Bloch equations.
We report on observations of four-wave mixing in rubidium vapor via two-photon resonant excitation with nd and (n+2)s states, for n=14–20. The intensity of the generated beam is studied in a collinear configuration, and the results are consistent with the predictions of a theoretical model based on the semiclassical Maxwell–Bloch equations, considering interference effects associated with multiple excitation pathways and with internally generated fields. We have also observed spectral broadening of the two-photon resonant lines, which is well described by a linear dependence on atomic density, in accordance with collision-induced broadening.