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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Quantum Temporal Imaging with Finite Time Aperture

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

Published Jun 1, 2019• 0 citations
Publisher

Abstract

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].

DOI
10.1109/cleoe-eqec.2019.8873147

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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].
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.
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.
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.
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.
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
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.