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arXiv:2307.09493 · Optics Express

Erecting time telescope for photonic quantum networks

Shivang Srivastava, D. B. Horoshko, Mikhail I. Kolobov

Published Sep 15, 2023• 7 citations
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Abstract

A time lens allows one to stretch or compress optical waveforms in time, similar to the conventional lens in space. However, a single-time-lens imaging system always imparts a residual temporal chirp on the image, which may be detrimental for quantum networks, where the temporal image interacts with other fields. We show that a two-time-lens imaging system satisfying the telescopic condition, a time telescope, is necessary and sufficient for creating a chirpless image. We develop a general theory of a time telescope, find the conditions for loss minimization, and show how an erecting time telescope creating a real image of a temporal object can be constructed. We consider several applications of such a telescope to making indistinguishable the photons generated by spontaneous parametric downconversion or single emitters such as quantum dots.

DOI
10.1364/oe.501609

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A time lens allows one to stretch or compress optical waveforms in time, similar to the conventional lens in space. However, a single-time-lens imaging system always imparts a residual temporal chirp on the image, which may be detrimental for quantum networks, where the temporal image interacts with other fields. We show that a two-time-lens imaging system satisfying the telescopic condition, a time telescope, is necessary and sufficient for creating a chirpless image. We develop a general theory of a time telescope, find the conditions for loss minimization, and show how an erecting time telescope creating a real image of a temporal object can be constructed. We consider several applications of such a telescope to making indistinguishable the photons generated by spontaneous parametric downconversion or single emitters such as quantum dots.
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].
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 describe the design of a temporal imaging system that simultaneously reshapes the temporal profile and converts the frequency of a photonic wave packet, while preserving its quantum state. A field lens, which imparts a temporal quadratic phase modulation, is used to correct for the residual phase caused by field curvature in the image, thus enabling temporal imaging for phase-sensitive quantum applications. We show how this system can be used for temporal imaging of time-bin entangled photonic wave packets and compare the field lens correction technique to systems based on a temporal telescope and far-field imaging. The field-lens approach removes the residual phase using four dispersive elements. The group delay dispersion DDD is constrained by the available bandwidth $\ensuremath{\Delta}\ensuremath{\nu}$ by $D>t/\ensuremath{\Delta}\ensuremath{\nu}$, where ttt is the temporal width of the wave form associated with the dispersion DDD. This is compared to the much larger dispersion $D\ensuremath{\gg}\ensuremath{\pi}{t}^{2}/8$ required to satisfy the Fraunhofer condition in the far-field approach.
A time lens, which can be used to reshape the spectral and temporal properties of light, requires the ultrafast manipulation of optical signals and presents a significant challenge for single-photon application. In this work, we construct a time lens based on dispersion and sum-frequency generation to spectrally engineer single photons from an entangled pair. The strong frequency anticorrelations between photons produced from spontaneous parametric down-conversion are converted to positive correlations after the time lens, consistent with a negative-magnification system. The temporal imaging of single photons enables new techniques for time-frequency quantum state engineering.