Modulation and measurement of time-energy entangled photons

We describe a proof-of-principle experiment demonstrating a Fourier technique for measuring the shape of biphoton wave packets. The technique is based on the use of synchronously driven fast modulators and slow (integrating) detectors.

Figure 1

(Color online) Measurement of biphoton wave functions. Amplitude modulators in the signal and idler paths are driven synchronously. The coincidence count rate versus frequency is measured by slow detectors.

Figure 2

(Color online) (a) Schematic of experiment. Long biphotons are generated in the cold-atom Rb cell. Using an optical fiber, the anti-Stokes photon is delayed by 175 ns and the photons are modulated by synchronously driven sinusoidal modulators. (b) Energy-level diagram for paired photon generation in Rb.

Figure 3

(Color online) Modulation of the biphoton correlation function. (a) $m_1\left(t\right)=1$ and $m_2\left(t\right)=\text{cos}\left(\omega t+\phi \right)$. The inset in (a) shows the correlation functions with both modulators open. (b) $m_1\left(t\right)=m_2\left(t\right)=\text{cos}\left(\omega t+\phi \right)$. Here $\omega =2\pi \times 35\times {10}^6{\text{s}}^{-1}$.

Figure 4

Fourier transform measurement technique at an optical depth of 15. (a) Frequency domain data, (b) Fourier cosine transform (gray), and temporal correlation (black). The term modulation frequency on the $x$ axis of (a) refers to the applied frequency. The observed modulation frequency [Eq. (4)] is a factor of 2 higher.

Figure 5

Fourier transform measurement technique at an optical depth of 35. (a) Frequency domain data, (b) Fourier cosine transform (gray), and temporal correlation (black).