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arXiv:2401.10197 · AVS Quantum Science

Perfect pulsed inline twin-beam squeezers

Martin Houde, Nicolás Quesada

Published Jun 1, 2024• 7 citations
arXivHTMLPDF

Abstract

Perfect inline squeezers are both spectrally pure and have identical input and output temporal modes, allowing one to squeeze an arbitrary input quantum state in the sole input mode on which the device acts, while the quantum states of any other modes are unaffected. We study theoretically how to obtain a perfect pulsed inline squeezer in twin-beam systems by considering three commonly used configurations: unpoled single pass, poled single pass, and poled double pass. By obtaining analytical relations between the input and output temporal modes from the Bloch–Messiah decomposition of the discretized Heisenberg-picture propagator, we find that a double-pass structure produces a perfect pulsed inline squeezer when operated in a frequency degenerate, symmetric group-velocity matched type-II configuration.

DOI
10.1116/5.0203013

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Perfect inline squeezers are both spectrally pure and have identical input and output temporal modes, allowing one to squeeze an arbitrary input quantum state in the sole input mode on which the device acts, while the quantum states of any other modes are unaffected. We study theoretically how to obtain a perfect pulsed inline squeezer in twin-beam systems by considering three commonly used configurations: unpoled single pass, poled single pass, and poled double pass. By obtaining analytical relations between the input and output temporal modes from the Bloch–Messiah decomposition of the discretized Heisenberg-picture propagator, we find that a double-pass structure produces a perfect pulsed inline squeezer when operated in a frequency degenerate, symmetric group-velocity matched type-II configuration.
Methods to decompose nonlinear optical transformation vary from setting to setting, leading to apparent differences in the treatments used to model photon pair sources, compared to those used to model degenerate down-conversion processes. The Bloch-Messiah reduction of Gaussian processes to single-mode squeezers and passive (linear) unitaries appears juxtaposed against the practicalities of the Schmidt-decomposition for photon pair sources into two-mode squeezers and passive unitaries. Here, we present a general framework which unifies these forms as well as elucidating more general structure in multimode Gaussian transformations. The decomposition is achieved by introducing additional constraints into the Bloch-Messiah reduction used to diagonalise Gaussian processes, these constraints motivated by physical constraints following from the inequivalence of different physical degrees of freedom in a system, ie. the temporal-spectral degrees of freedom vs different spatial modes in a transformation. The result is the emergence of the two-mode squeezing picture from the reduction, as well as the potential to generalise these constraints to accommodate spectral imperfections in a source generating 3-mode continuous variable GHZ-like states. Furthermore, we consider the practical scenario in which a transformation aims to generate a multiphoton entangled state, whereby spatial modes provide desirable degrees of freedom, whilst undesired spectral mode structure contributes noise, and show that this spectral impurity can be efficiently modeled by finding an optimal low dimensional bases for its simulation.
We study the Bloch-Messiah reduction of parametric down-conversion of light in the pulsed regime with a nondegenerate phase matching providing generation of twin beams. We find that in this case every squeezing eigenvalue has multiplicity at least two. We discuss the problem of ambiguity in the definition of the squeezing eigenmodes in this case and develop two approaches to unique determination of the latter. First, we show that the modal functions of the squeezing eigenmodes can be tailored from the Schmidt modes of the signal and idler beams. Alternatively, they can be found as a solution of an eigenvalue problem for an associated Hermitian squeezing matrix. We illustrate the developed theory by an example of frequency nondegenerate collinear twin beams generated in beta barium borate crystal. In this example we demonstrate how the squeezing eigenmodes can be approximated analytically on the basis of the Mehler's formula, extended to complex kernels. We show how the multiplicity of the eigenvalues and the structure of the eigenmodes are changed when the phase matching approaches the degeneracy in frequency.
It has been known for a while that coherent high-intensity photon number eigenstate fields can be generated through nonlinear optical parametric processes,1 the same ones that give rise to quadrature squeezing.2,3 In contrast to quadrature squeezing which is essentially a single-mode phenomenon, although it is widely misunderstood that it is a two-mode phenomenon, the generation of single-mode number states through three- or four-wave mixing depends on two separate signal and idler modes that are perfectly correlated in photon numbers, in other words a twin beam. The nature of such twin beams is elucidated in both the Schrodinger and the Heisenberg pictures. In particular, it is shown that strong photon number correlation in a twin beam can still be obtained in an amplifier rather than an oscillator configuration, another widely missed point.
We report the realization of a bright ultrafast type II parametric down-conversion source of twin beams free of any spatiotemporal correlations in a periodically poled KTiOPO4 (PP-KTP) waveguide. From a robust, single-pass setup it emits pulsed two-mode squeezed vacuum states: photon-number entangled pairs of single-mode pulses or, in terms of continuous variables quantum optics, pulsed Einstein-Podolsky-Rosen states in the telecom wavelength regime. We verify the single-mode character of our source by measuring Glauber correlation functions g(2) and demonstrate with a pump energy as low as 75 pJ per pump pulse a mean photon number of 2.5.
Nowadays, the realization of quantum computations and communications based on continuous variables has attracted a significant attention due to a substantial expansion of the system dimensionality. The main progress in this area is attributed to the implementation of multimode systems based on squeezed states of light. One of the simplest ways to generate such states relies upon their producing in a single-pass optical parametric amplifier (OPA) using ultrafast pumping. However, for homodyne detection of such multimode states, the profile of the local oscillator (LO) must perfectly match the profile of the measured mode. Usually, this is not the case; therefore a proper treatment of multimode squeezing is required. In this work, we study both theoretically and experimentally the multimode squeezed light generated in type-0 and type-II OPA. We characterize such sources and investigate the degree of squeezing in dependence on the LO spectral profile, employing a pulse shaping technique. The theoretical analysis is performed using the Schmidt-mode theory. This work might have a significant impact on the realization of multimode quantum protocols