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Photon Pair Production from a Hot Atomic Ensemble in the Diamond Configuration

R. T. Willis

Published Jan 1, 2009• 2 citations
OpenAlex

Abstract

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.

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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.
Generation of nonclassical light is an essential tool for quantum optics research and applications in quantum information technology. We present realization of the source of nonclassically correlated photon pairs based on the process of spontaneous four-wave-mixing in warm atomic vapor. Atoms are excited only by a single laser beam in retro-reflected configuration and narrowband frequency filtering is employed for selection of correlated photon pairs. Nonclassicality of generated light fields is proved by analysis of their statistical properties. Measured parameters of the presented source promise further applicability for efficient interaction with atomic ensembles.
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.
We present our recently-built experimental setup designed to generate near-infrared and narrow-band correlated photon pairs by inducingfour-wave mixing in a cold gas of 87Rb atoms confined in a magneto-optical trap. The experimental setup and its automation and control approach are described in detail. A characterization of the optical density of the atomic ensemble as well as the basic statistical measurements of the generated light are reported. The non-classical nature of the photons pairs is confirmed by observing a violation of Cauchy-Schwarz inequality by a factor of 5.6 × 10 5 in a Hanbury Brown – Twiss interferometer. A 1/e coherence time for the heralded, idler photons of 4.4 ± 0.1 ns is estimated from our observations. We are able to achieve a value of 104 s−1pair-detection-rate, which results in a spectral brightness of 280 (MHz s)−1. The combination of high brightness and narrow-band spectrum makes this photon-pair source a viable tool in fundamental studies of quantum states and opens the door to use them in quantum technologies.
We present measurements of the polarization correlation and photon statistics of photon pairs that emerge from a laser-pumped warm rubidium vapor cell. The photon pairs occur at 780 nm and 1367 nm and are polarization entangled. We measure the autocorrelation of each of the generated fields as well as the cross-correlation function, and observe a strong violation of the two-beam Cauchy-Schwartz inequality. We evaluate the performance of the system as source of heralded single photons at a telecommunication wavelength. We measure the heralded autocorrelation and see that coincidences are suppressed by a factor of ≈ 20 from a Poissonian source at a generation rate of 1500 s(-1), a heralding efficiency of 10%, and a narrow spectral width.
The limits of the well-established single-atom model for describing photon-pair generation via four-wave mixing in a diamond configuration in atomic ensembles are experimentally tested. Using a cold-atom source, biphotons are generated and detected through polarization analyzers that resolve the emitted light into horizontal and vertical components in the laboratory frame. The pump lasers driving the first and second excitation transitions are horizontally and vertically polarized, respectively. To predict single-photon counts and coincidence rates in all polarization channels, the first- and second-order correlation functions are calculated directly using a comprehensive model that accounts for all Zeeman sublevels of the relevant hyperfine states. Furthermore, the population dynamics with and without the re-pump laser of the magneto-optical trap are compared, revealing substantial differences in the populations of the Zeeman sublevels. This motivates the inclusion of two additional hyperfine levels and their corresponding Zeeman sublevels in the final model. The resulting density matrix is used to calculate expectation values of the far-field electric-field operators and compare them with experimental measurements over a range of pump-laser powers. Excellent agreement with the measured photon counts is obtained over most of this range. For the coincidence measurements, good agreement is found when the polarization of the photon generated by the first (second) decay is parallel to that of the first (second) pump beam. In contrast, the model consistently underestimates the experimental coincidence rates for the opposite polarization configuration. These findings indicate that effects beyond the internal level dynamics of individual atoms, most notably collective phenomena, are required to fully account for photon coincidences generated by four-wave mixing in atomic ensembles.