Variable electro-optic shearing interferometry for ultrafast single-photon-level pulse characterization

Abstract

Despite the multitude of available methods, the characterization of ultrafast pulses remains a challenging endeavor, especially at the single-photon level. We introduce a pulse characterization scheme that maps the magnitude of its short-time Fourier transform. Contrary to many well-known solutions it does not require nonlinear effects and is therefore suitable for single-photon-level measurements. Our method is based on introducing a series of controlled time and frequency shifts, where the latter is performed via an electro-optic modulator allowing a fully-electronic experimental control. We characterized the full spectral and temporal width of a classical and single-photon-level pulse and successfully tested the applicability of the reconstruction algorithm of the spectral phase and amplitude. The method can be extended by implementing a phase-sensitive measurement and is naturally well-suited to partially-incoherent light.

Teleportation-based error correction protocol of time-frequency qubits states

“…In [1], we also argue that frequency noise arises from frequency broadening caused by the generation of photon pairs itself, and we describe one method to correct such a noise. There are numerous processes that can distort the spectral distribution of single photons, such as distortions caused by frequency shifts induced by electro-optic modulators [49,50], or the presence of a filter during single photon heralding. σ is the half-width of the Gaussian peak, and ∆ is the spectral separation between the two logical states (b) Time-frequency GKP state.…”

“…The receiver sends to spatial port c which detectors have measured coincidences, and then a product of Pauli matrix gates must be applied to recover the initial state of interest. Pauli matrices for the time-frequency cat states are frequency and temporal shifts operations [1], which can be implemented by either a electro-optical modulator [49,50] and a delay line respectively. The full optical scheme of the teleportation-based error correction protocol is represented in Fig.…”

Quantum optics with time-frequency degrees of freedom of single photons

“…An alternative method was performed experimentally in Ref. 13 Note that also, frequency displacement operation can be achieved using linear optics, which can be efficiently applied to single photon states Ref 14 . By using electro-optic phase modulation synchronized with the pulses, a spectral shift µ is achieved.…”

“…By using electro-optic phase modulation synchronized with the pulses, a spectral shift µ is achieved. Besides, such a frequency shift was used to perform the full spectral tomography of classical fields at the single photon level (see Ref 14 ), or for measuring the spectral envelope Ref 15 .…”

Experimental implementation of the optical fractional Fourier transform in the time-frequency domain

“…Operations beyond the Fourier transform have been proposed but scarcely implemented. They range from trivial but useful frequencytranslation operators [27] to complex modulations that could allow largely arbitrary modal operations [28]. Those more complex operations could allow for super-resolved sensing of system parameters [29][30][31] or enhanced data rate for communication in the photon-starved regime [32].…”