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Chinese Optics Letters

Improving the resolution in quantum and classical temporal imaging

Junheng Shi, Giuseppe Patera, Youzhen Gui, Mikhail I. Kolobov, D. B. Horoshko, Shensheng Han

Published Jan 1, 2018• 6 citations
Publisher

Abstract

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.

DOI
10.3788/col201816.092701

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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.
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.
Using the space-time analogy, we compare the performance of quantum temporal imaging with its classical counterpart. We consider a temporal imaging scheme, based on the sum-frequency generation time lens, but our results can be applied to other temporal imaging schemes such as, for instance, four-wave mixing. Extending the theory presented in our previous publications, in this paper we take into account the finite time aperture of the imaging system, characterized by its pupil function. Using the quantum theory, we obtain a unitary transformation of the quantum field from the input to the output of the imaging scheme and identify the contribution of the vacuum fluctuations missing in the classical theory. This contribution plays a key role in the quantum temporal imaging of nonclassical temporal waveforms, characterized by nonclassical fluctuations of the electromagnetic field. As an example, we consider quantum temporal imaging of broadband squeezed light and formulate the criteria for conservation of its squeezing properties at the output of the system.
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.
Abstract We consider application of a temporal imaging system, based on the sum-frequency generation (SFG), to a nonclassical, squeezed optical temporal waveform. We analyze restrictions on the pump and the phase-matching condition in the summing crystal, which are necessary for preserving the quantum features of the initial waveform. We show that modification of the notion of the field of view (FOV) in the quantum case is necessary, and that the quantum FOV is much narrower than the classical one for the same temporal imaging system. These results are important for temporal stretching and compressing of squeezed fields, which are used in quantum-enhanced metrology and quantum communications.
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.
We study the problem of quantum temporal imaging in the case where the time lens is implemented by a sum frequency generation nonlinear process. We consider the general case where the time lens is characterized by a finite aperture and a not-perfect phase-matching in a regime close to 100% conversion efficiency. In particular we tackle this problem in term of the eigenmodes of the entire transformation of the field in the temporal imaging system. We show that in the case of modeling the phase-matching function by a double Gaussian the eigenmodes are given by chirped Gauss-Hermite functions. The effective number of involved eigenmodes is estimated as the ratio of the temporal aperture of the lens to the walk-off time of the signal and the idler waves in the nonlinear crystal. Our theoretical treatment allows us to identify the criteria for designing imaging schemes with close to unity efficiencies