Quantum temporal imaging with squeezed light

Temporal imaging is a technique enabling manipulation of temporal opticalsignals in a manner similar to manipulation of optical images in spatialdomain. The concept of temporal imaging uses the notion of space-timeduality [1]... [ view full abstract ]

Temporal imaging is a technique enabling manipulation of temporal optical
signals in a manner similar to manipulation of optical images in spatial
domain. The concept of temporal imaging uses the notion of space-time
duality [1] with dispersion phenomena playing the role of diffraction and
quadratic phase modulation in time acting as a time lens.
Spatial quantum imaging investigates ultimate quantum limits of imaging
techniques in regimes where quantum fluctuations cannot be neglected [2].
On one hand it would be desirable to bring the experience from spatial
quantum imaging into temporal imaging and to establish its ultimate limits
imposed by the quantum nature of the light. On the other hand 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 non-linear
processes such as sum-frequency generation [3,4] and four-wave mixing [5].
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
Ω’=MΩ which corresponds to the scaled time t’=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.

[1] B. H. Kolner,  IEEE J. Quantum Electron. 30, 1951 (1994).
[2] M. I. Kolobov, “Quantum Imaging” (Spinger, 2006).
[3] G. Patera and M. I. Kolobov, Opt. Lett. 40, 1125 (2015).
[4] G. Patera, J. Shi, D. B. Horoshko, and M. I. Kolobov, J. Opt. 19, 054001 (2017)
[5] J. Shi, G. Patera, M. I. Kolobov, and S. Han, Opt. Lett. 42, 3121 (2017)