Electro-Optic Fourier Transform Chronometry of Pulsed Quantum Light

The power spectrum of an optical field can be acquired without a spectrally resolving detector by means of Fourier-transform spectrometry, based on measuring the temporal autocorrelation of the optical field. Analogously, we here perform temporal envelope measurements of ultrashort optical pulses without time resolved detection. We introduce the technique of Fourier transform chronometry, where the temporal envelope is acquired by measuring the frequency autocorrelation of the optical field in a linear interferometer. We apply our technique, which is the time-frequency conjugate measurement to Fourier-transform spectrometry, to experimentally measure the pulse envelope of classical and single-photon light pulses.

Figure 1

Schematic of the Fourier transform tunable electro-optic spectral shearing interferometry. BS, beam splitter; PD, photodiode.

Figure 2

Optical setup. SPDC: spontaneous parametric down conversion, PBS: polarising beam splitter, FM: flip mirror, HWP: half-wave plate, POL: polariser, EOPM: electro-optic phase modulator, AMP: amplifier, SBC: Soleil-Babinet compensator, PC: polarisation controller, $\tau$: delay between polarisation components, SPD: single photon detector, PD: photodiode, DET: detector (SPD in case of quantum measurement or PD in case of classical measurement), &: coincidence circuit.

Figure 3

(a) Measured interference signal as a function of spectral shift (red points) in which the positive side has been measured and the negative side is the mirror of the measured data. The blue line is used to guide the eye. (b) Energy envelope of the retrieved optical pulse in temporal domain. (c) Impact of input bandwidth change on temporal width of the classical (green points) and quantum (blue points) light pulse—experimental data along with linear fits as shown by green dash-dotted and blue dotted lines respectively. Red points: theoretical simulation. The temporal pulse width is calculated based on the RMS pulse width calculation. The red shaded area shows the variation of temporal pulse width for up to 10% error in the applied spectral shift. The direct measurement of the temporal duration of the classical pulses using the optical complex spectrum analyzer is shown by black points along with linear fit as indicated by the black dashed line. (d) Measured temporal width (red points) of the optical pulse versus dispersion (added PM fiber). The blue line is the theoretical calculation for the measured initial temporal width of the optical pulse before adding dispersion.

Figure 4

(a) Fringe pattern resulting from single-photon coincidences versus spectral shift where negative side is the mirror of positive side. The blue line is a guide to the eye. (b) Energy envelope of the measured single photon pulse in temporal domain.