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Physical Review A

Temporally shaping biphoton wave packets with periodically modulated driving fields

Shengwang Du, Jianming Wen, Chinmay Belthangady

Published Apr 10, 2009• 24 citations
Publisher

Abstract

We describe a method for waveform shaping of narrowband biphotons generated in a double-$\ensuremath{\Lambda}$ atomic system via four-wave mixing by periodically modulating the input driving lasers. We show that the input field profile(s) can be revealed in the two-photon temporal waveform and its correlation measurement.

DOI
10.1103/physreva.79.043811

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We describe a method for waveform shaping of narrowband biphotons generated in a double-\ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ atomic system via four-wave mixing by periodically modulating the input driving lasers. We show that the input field profile(s) can be revealed in the two-photon temporal waveform and its correlation measurement.
We study narrow-band biphoton generation from spontaneous four-wave mixing with electromagnetically induced transparency in a laser cooled atomic ensemble. We compare two formalisms in the interaction and Heisenberg pictures, and find that they agree in the low gain regime but disagree in the high gain regime. We extend both formalisms accounting the non-uniformity in atomic density and the driving laser fields. We find that for a fixed optical depth and a weak and far-detuned pump laser beam, the two-photon waveform is independent of the atomic density distribution. However, the spatial profiles of the two driving laser beams have significant effects on the biphoton temporal waveform. We predict that waveform shaping in time domain can be achieved by controlling the spatial profiles of the driving laser fields.
We demonstrate the generation of narrowband biphotons with controllable temporal waveform by spontaneous four-wave mixing in cold atoms. In the group-delay regime, we study the dependence of the biphoton temporal waveform on the spatial profile of the pump laser beam. By using a spatial light modulator, we manipulate the spatial profile of the pump laser and map it onto the two-photon entangled temporal wave function. This parallel-to-series conversion (or spatial-to-temporal mapping) enables coding the parallel classical information of the pump spatial profile to the sequential temporal waveform of the biphoton quantum state.
We study narrowband biphoton generation from spontaneous four-wave mixing with electromagnetically induced transparency in a laser-cooled atomic ensemble. We compare two formalisms in the interaction and Heisenberg pictures and find that they agree in the low-gain regime but disagree in the high-gain regime. We extend both formalisms to account for the nonuniformity of the atomic density and the driving laser fields. We find that for a fixed optical depth and a weak and far-detuned pump laser beam, the two-photon waveform is independent of the atomic density distribution. However, the spatial profiles of the two driving laser beams have significant effects on the biphoton temporal waveform. We predict that waveform shaping in the time domain can be achieved by controlling the spatial profiles of the driving laser fields.
Biphotons are entangled photon pairs that cannot be described as a product state of two individual photons. In this talk we summarize our recent progress in generating narrowband biphotons from spontaneous four-wave mixing (SFWM) in cold atoms with electromagnetically induced transparency (EIT). Here we are particularly interested in the group delay regime, where the biphoton time-frequency entanglement and joint wave function can be manipulated by controlling the group-delay-induced phase matching condition of the paired photons. The biphoton coherence time, thus its bandwidth of the joint spectrum, is determined by the relative group delay between the paired photons. The longest biphoton coherence time on record is more than 3 µs. We find that for a fixed optical depth, the twophoton waveform is independent of the atomic density distribution. However, the spatial profiles of the two driving laser beams have significant effects on the biphoton temporal wavefunction. We demonstrate a technique of shaping the biphoton temporal wavefunction by directly mapping the spatial profile of the pump laser beam onto the biphoton temporal waveform. This spatial-to-temporal mapping, or series-toparallel conversion, allows for coding the spatial information of the pump spatial profile to the sequential temporal modes of the biphtoon quantum state. Using a computer-controlled spatial light modulator, we produced biphotons with temporal waveforms of Gaussian, exponential, and double-peak shapes. As compared to temporally modulating the driving laser fields that reduces the frequency entanglement, this spatial-to-temporal biphoton shaping does not scarify the time-frequency entanglement and can be used to produce heralded narrowband single photons with controllable waveforms.