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 Ω<sup>I</sup> = MΩ which corresponds to the scaled time t<sup>I</sup> = 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.
Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous “Schroedinger cat” state. The recent progress shows an increase in the number of components and the number of modes involved. Our work gives a theoretical treatment of multicomponent two-mode Schroedinger cat states. We consider a class of single-mode states, which are superpositions of N coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RICS). A two-mode extension of this basis is created by splitting a single-mode RICS on a balanced beam-splitter. After performing a symmetric (Loewdin) orthogonalization of the sets of coherent states in both modes we obtain the Schmidt decomposition of the two-mode state, and therefore an analytic expression for its entanglement. We show that the states obtained by splitting a RICS are generalizations of Bell states of two qubits to the case of N -level systems encoded into superpositions of coherent states on the circle, and we propose for them the name of generalized quasi-Bell states. We show that an exact probabilistic teleportation of arbitrary superposition of coherent states on the circle is possible with such a state used as shared resource.
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.
Proc. SPIE. 8518, Quantum Communications and Quantum Imaging X
KEYWORDS: Signal to noise ratio, Optical imaging, Diffraction, Super resolution, Imaging systems, Fourier transforms, Signal processing, Quantum physics, Reconstruction algorithms, Diode pumped solid state lasers
Sparsity constraint is a priori knowledge of the signal, which means that in some properly chosen basis only a small percentage of the signal components is nonzero. Sparsity constraint has been used in signal and image processing for a long time. Recent publications have shown that by taking advantage of the Sparsity constraint of the object, super-resolution beyond the diffraction limit could be realized. In this paper we present the quantum limits of super-resolution for the sparse objects. The key idea of our paper is to use the discrete prolate spheroidal sequences (DPSS) as the sensing basis. We demonstrate both analytically and numerically that this sensing basis gives superior performance over the Fourier basis conventionally used for sensing of sparse signals. The explanation of this phenomenon is in the fact that the DPSS are the eigenfunctions of the optical imaging system while the Fourier basis are not. We investigate the role of the quantum fluctuations of the light illuminating the object, in the performance of reconstruction algorithm. This analysis allows us to formulate the criteria for stable reconstruction of sparse objects with super-resolution.
We calculate the Schmidt number for a two-dimensional model of the nonfactorable spatiotemporal wave-function
of biphotons produced in type-I spontaneous parametric down-conversion with degenerate and collinear phase-
matching taking into consideration a major part of the broad spectral and angular bandwidth of the down-
converted light. We derive an analytical expression for the Schmidt number as a function of the filter bandwidth
in the limit of spectrally narrow pump.
The teleportation of entangled optical images is for the first time considered. The scheme offered is based on
process of four-partite state generation in coupled parametric interactions realizing in an aperiodic nonlinear
photonic crystal. The coupled nonlinear optical process consists of one parametric down-conversion process
which is followed by two up-conversion ones. We study nonclassical properties of the generated fields by
analyzing the EPR correlations for different pairs of modes and carry out the comparison of the EPR correlations
of the input and images output images and also calculate fidelity of the teleportation exploiting the covariance
matrices of the images. We take into account the difference of spatial frequency bandwidths of the entangled
images and fields generated in the coupled process. It has been established that under certain parameters of the
scheme one can be obtain rather high fidelity of the teleportation and good preservation of the quantum
correlations of the input images for all details of the images.
Quantum multipartite entanglement is a striking phenomenon predicted by quantum mechanics when several
parts of a physical system share the same quantum state that cannot be factorized into the states of individual
subsystems. The Gaussian quantum states are usually characterized by the covariance matrix of the quadrature
components. A powerful formalism for treating the Gaussian states is that of the symplectic eigenvalues. In
particular, a quantitative measure of multipartite entanglement is the so-called logarithmic negativity, related
to the symplectic eigenvalues of the partially transposed covariance matrix.
Considering only global variances of the field quadratures one completely neglects the spatiotemporal properties
of the electromagnetic field. We propose, following the spirit of quantum imaging, to generalize the theory
of multipartite entanglement for the continuous variable Gaussian states by considering the local correlation
matrix at two different spatiotemporal points [see manuscript for characters] and [see manuscript for characters] with [see manuscript for characters] being the transverse coordinate. For
stationary and homogeneous systems one can also introduce the spatiotemporal Fourier components of the correlation
matrix. The formalism of the global symplectic eigenvalues can be straightforwardly generalized to
the frequency-dependent symplectic eigenvalues. This generalized theory allows, in particular, to introduce the
characteristic spatial area and time of the multipartite entanglement, which in general depend on the number of
"parties" in the system.
As an example we consider multipartite entanglement in spontaneous parametric down-conversion with
spatially-structured pump. We investigate spatial properties of such entanglement and calculate its characteristic
spatial length.
Proc. SPIE. 6256, ICONO 2005: Ultrafast Phenomena and Physics of Superintense Laser Fields; Quantum and Atom Optics; Engineering of Quantum Information
We give a definition of asyimnetric universal entangling machine, entangling a system in an unknown state to
a specially prepared ancilla. We describe explicitly such a machine for a d-level quantmn system and prove its
optimality.
We investigate amplification of optical images by means of a traveling-wave optical parametric amplifier. As shown recently by Kolobov and Lugiato [Phys. Rev. A 52, 4930 (1995)] for a cavity-based geometry, such a scheme can amplify images, without deteriorating their sign-to-noise ratio, thus working as a noiseless amplifier. Here we consider a configuration without cavity, which is more realistic for a possible experimental realization. We investigate in detail the quantum fluctuations of the amplifier and formulate criteria for its noiseless performance. The spatial resolution power, which guarantees noiseless amplification is estimated. We demonstrate how the optimum phase matching of a phase-sensitive wavefront of the image can improve the noise performance of the amplifier and bring it to the ultimate value achievable under given physical conditions. We discuss the effect of improvement of the signal-to-noise ratio in the case of observation of both the input and the amplified image, with an ideal photodetector of small area (i.e., much less than the coherence area of the amplifier). This improvement is due to the fact that the signal-to-noise ratio in the input is deteriorated by the observation with the photodetector of small area.