Spectral Density Matrix of a Single Photon Measured

We propose and demonstrate a method for measuring the spectral density matrix of a single photon pulse. The method is based on registering Hong-Ou-Mandel interference between a photon to be measured and a pair of attenuated and suitably delayed laser pulses described by a known spectral amplitude. The density matrix is retrieved from a two-dimensional interferogram of coincidence counts. The method has been implemented for a type-I down-conversion source, pumped by ultrashort laser pulses. The experimental results agree well with a theoretical model which takes into account the temporal as well as spatial effects in the source.

Figure 1

Scheme of the experiment. A weak laser pulses described by a spectral amplitude $A(\omega )$ are split in a Michelson interferometer, comprising mirrors M1 and M2 and a $50/50$ beam splitter BS1, to form the local oscillator ${\varphi }_{\mathrm{LO}}(\omega )$. Then they interfere with an unknown photon described by the density operator $\widehat{\rho }$ on a $50/50$ beam splitter BS2 and may give rise to a coincidence click of the detectors D1 and D2.

Figure 2

(a) A typical coincidence interferogram as a function of delays $t_1$ and $t_2$ and (b) its Fourier transform. The black parallelogram in (a) defines the scan range, which with suitable sampling density yields the region of interest in the frequency domain, outlined in (b).

Figure 3

The experimental setup. BS: beam splitter; FL: focusing lens; XSH: BBO crystal for generation of the second harmonic; IL: imaging lens; DM: dichroic mirrors; BG: blue glass filter; $X$: down-conversion crystal; IF: interference filter; FC: fiber coupling stage, HWP: half wave plate; P: polarizer; ND: neutral density filter; FPC: fiber polarization controller; D1 and D2: single photon counting modules.

Figure 4

Spectral intensity $|A(\omega ){|}^2$ (solid line) and phase $\arg A(\omega )$ (dashed line) of the master laser pulse retrieved using FROG.

Figure 5

Contour plot of the absolute value of the measured spectral density matrix $|\rho (\omega ,{\omega }^{\prime })|$ as a function of wavelengths $\lambda =2\pi c/\omega$ (solid lines) and a theoretical prediction for this quantity (dashed red lines). The contours were drawn at 0.75, 0.5, and 0.25 of the maximum values, the outermost encircles $7\times 5$ experimental data points.