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arXiv:1303.2100 · Physical Review A

Aberration-corrected quantum temporal imaging system

Yunhui Zhu, Jungsang Kim, Daniel J. Gauthier

Published Apr 8, 2013• 24 citations
arXivHTMLPDF

Abstract

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 $D$ is constrained by the available bandwidth $\ensuremath{\Delta}\ensuremath{\nu}$ by $D>t/\ensuremath{\Delta}\ensuremath{\nu}$, where $t$ is the temporal width of the wave form associated with the dispersion $D$. 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.

DOI
10.1103/physreva.87.043808

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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 \ensuremathΔ\ensuremathν\ensuremath{\Delta}\ensuremath{\nu}\ensuremathΔ\ensuremathν by D>t/\ensuremathΔ\ensuremathνD>t/\ensuremath{\Delta}\ensuremath{\nu}D>t/\ensuremathΔ\ensuremathν, 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≫\ensuremathπt2/8D\ensuremath{\gg}\ensuremath{\pi}{t}^{2}/8D\ensuremath≫\ensuremathπt2/8 required to satisfy the Fraunhofer condition in the far-field approach.
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.
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.
Techniques to control the spectro-temporal properties of quantum states of light at ultrafast time scales are crucial for numerous applications in quantum information science. In this work, we report an all-optical time lens for quantum signals based on Bragg-scattering four-wave mixing with picosecond resolution. Our system achieves a temporal magnification factor of 158 with single-photon level inputs, which is sufficient to overcome the intrinsic timing jitter of superconducting nanowire single-photon detectors. We demonstrate discrimination of two terahertz-bandwidth, single-photon-level pulses with 2.1 ps resolution (electronic jitter corrected resolution of 1.25 ps). We draw on elegant tools from Fourier optics to further show that the time-lens framework can be extended to perform complex unitary spectro-temporal transformations by imparting optimized temporal and spectral phase profiles to the input waveforms. Using numerical optimization techniques, we show that a four-stage transformation can realize an efficient temporal mode sorter that demultiplexes 10 Hermite–Gaussian (HG) modes. Our time-lens-based framework represents a new toolkit for arbitrary spectro-temporal processing of single photons, with applications in temporal mode quantum processing, high-dimensional quantum key distribution, temporal mode matching for quantum networks, and quantum-enhanced sensing with time-frequency entangled states.
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.
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.