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Nonlinear Optics

Nonlinear Optics and Quantum Temporal Imaging

Mikhail I. Kolobov, Giuseppe Patera, D. B. Horoshko

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Temporal imaging is a technique that enables manipulation of temporal optical signals in a manner similar to manipulation of optical images in spatial domain. The main building block of temporal imaging, the time lens, is based on nonlinear optical processes such as the sum- frequency generation or the four-wave mixing. While classical temporal imaging is nowadays a well-established domain, its quantum counterpart is still in its nascent period. In this talk we shall give and overview of the quantum temporal imaging and its application for manipulation of non-classical states of the light.

DOI
10.1364/nlo.2019.ntu1b.7

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Temporal imaging is a technique that enables manipulation of temporal optical signals in a manner similar to manipulation of optical images in spatial domain. The main building block of temporal imaging, the time lens, is based on nonlinear optical processes such as the sum- frequency generation or the four-wave mixing. While classical temporal imaging is nowadays a well-established domain, its quantum counterpart is still in its nascent period. In this talk we shall give and overview of the quantum temporal imaging and its application for manipulation of non-classical states of the light.
Temporal imaging is a technique enabling manipulation of temporal optical signals in a manner similar to manipulation of optical images in spatial domain. The quantum description of temporal imaging is relevant in the context of long range quantum communication. Indeed this technology relies on the efficiency of quantum repeaters for which the temporal mode matching between the quantum emitters, the communication network and the quantum memories is critical. In this work we address the problem of temporal imaging of a temporally broadband squeezed light generated by a traveling-wave optical parametric amplifier. We consider a single-lens temporal imaging system formed by two dispersive elements and a parametric temporal lens, based on a non- linear process such as sum-frequency generation or four-wave mixing. We derive a unitary transformation of the field operators performed by this kind of time lens and evaluate the squeezing spectrum at the output of the single-lens imaging system. When the efficiency factor of the temporal lens is smaller than unity, the vacuum fluctuations deteriorate squeezing at its output. For efficiency close to unity, when certain imaging conditions are satisfied, the squeezing spectrum at the output of the imaging system will be the same as that at the output of the OPA in terms of the scaled frequency ΩI = MΩ which corresponds to the scaled time tI = t/M . The magnification factor M gives the possibility of matching the coherence time of the broadband squeezed light to the response time of the photodetector.
Temporal imaging is a technique that enables manipulation of temporal optical signals in a manner similar to manipulation of optical images in spatial domain. It uses the notion of space-time duality with dispersion phenomena playing the role of diffraction and quadratic phase modulation in time acting as a time lens. In this work we address the problem of temporal imaging of a temporally broadband squeezed light generated by a traveling-wave optical parametric amplifier or a similar device. We consider a single-lens temporal imaging system formed by two dispersive elements and a parametric temporal lens, based on a sum-frequency generation process. We derive a unitary transformation of the field operators performed by this kind of time lens. We evaluate the squeezing spectrum at the output of the single-lens imaging system and find the conditions preserving squeezing in the output field. When the efficiency factor of the temporal lens is smaller than unity, the vacuum fluctuations deteriorate squeezing at its output. For efficiency close to unity, when certain imaging conditions are satisfied, the squeezing spectrum at the output of the imaging system will be the same as that at the output of the OPA. This scheme gives the possibility of matching the coherence time of the broadband squeezed light to the response time of the photodetector. We finally discuss a temporal imaging scheme which allows to partially compensating the frequency dispersion of the OPA.
The point-spread function of an optical system determines its optical resolution for both spatial and temporal imaging. For spatial imaging, it is given by a Fourier transform of the pupil function of the system. For temporal imaging based on nonlinear optical processes, such as sum-frequency generation or four-wave mixing, the point-spread function is related to the waveform of the pump wave by a nonlinear transformation. We compare the point-spread functions of three temporal imaging schemes: sum-frequency generation, co-propagating four-wave mixing, and counter-propagating four-wave mixing, and demonstrate that the last scheme provides the best temporal resolution. Our results are valid for both quantum and classical temporal imaging.
Optical temporal imaging is a technique of stretching or compressing an optical waveform in time, while fully preserving its temporal structure [1]. The key element of a temporal imaging system is a time lens, introducing a quadratic in time phase modulation into the signal field, which may be based, for example, on the sum-frequency generation (SFG). A quantum treatment of the time lens becomes important in some special cases, in particular when the information on some physical process is conveyed by single photons or by squeezed light [2,3].
We consider a simple quantum temporal imaging system on the basis of a time lens implemented by a parametric nonlinear optical process with a chirped pump. We review the main results of the modal theory of temporal imaging, developed recently by us. We illustrate this theory by a concrete example of type-I non-collinear sum-frequency generation process, where the phase matching is limited by the temporal walk-off of the signal and the idler waves. We have shown that the temporal modal functions of such an imaging system are chirped Hermite-Gauss functions.
A time-lens can image signals in time and map ultrafast signals from frequency to time. The concept of time-lens is based on the duality between the diffraction of light in space and the dispersion of pulses in time, which arises from the similarity between the equations describing these two phenomena. In this paper we explain how to use time-lenses in order to perform high-resolution temporal imaging on non-classical ultrafast signals. Such a scheme can be used e.g. for diagnosing quantum cryptography schemes on optical fiber networks or assessing the performance of photonic quantum computers and simulators.