Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime

Christ, Andreas; Brecht, Benjamin; Mauerer, Wolfgang; Silberhorn, Christine

doi:10.1088/1367-2630/15/5/053038

Cited by 141 publications

(171 citation statements)

References 59 publications

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“…In PDC, this approximation is shown to work well beyond the single-photon regime (See Fig. 4 in the (Christ et al, 2013), where only minor deviations occur at a mean photon number larger than one). The propagator U PDC depends on the effective Hamiltonian…”

Section: Entangled Photons Generation By Parametric Down Conversionmentioning

confidence: 91%

Nonlinear optical signals and spectroscopy with quantum light

2016

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Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. We present an intuitive diagrammatic approach for calculating ultrafast spectroscopy signals induced by quantum light, focusing on applications involving entangled photons with nonclassical bandwidth properties -known as "time-energy entanglement". Nonlinear optical signals induced by quantized light fields are expressed using time ordered multipoint correlation functions of superoperators in the joint field plus matter phase space. These are distinct from Glauber's photon counting formalism which use normally ordered products of ordinary operators in the field space. One notable advantage for spectroscopy applications is that entangled photon pairs are not subjected to the classical Fourier limitations on the joint temporal and spectral resolution. After a brief survey of properties of entangled photon pairs relevant to their spectroscopic applications, different optical signals, and photon counting setups are discussed and illustrated for simple multi-level model systems.

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Section: Entangled Photons Generation By Parametric Down Conversionmentioning

confidence: 91%

Nonlinear optical signals and spectroscopy with quantum light

2016

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“…The quantum state contains not only two-photon terms but also higher-order Fock components, and its calculation in the Schrödinger picture is difficult. Many recent theoretical investigations of such strong pumping regime are based on the concept of collective input/output modes introduced mostly to describe the spectral properties in the frequency domain [9][10][11][12][13]. In a high-gain regime it is convenient to calculate the observables in the Heisenberg picture.…”

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confidence: 99%

Schmidt modes in the angular spectrum of bright squeezed vacuum

et al. 2015

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We study the spatial properties of high-gain parametric down-conversion (PDC). From the Hamiltonian we find the Schmidt modes, apply the Bloch-Messiah reduction, and calculate analytically the measurable quantities, such as the angular distributions of photon numbers and photon-number correlations. Our approach shows that the Schmidt modes of PDC radiation can be considered the same as for the low-gain (biphoton) case while the Schmidt eigenvalues strongly depend on the parametric gain. Its validity is confirmed by comparison with several experimental results, obtained by us and by other groups.PACS numbers: 42.65. Lm, 42.65.Yj, 42.50.Lc Introduction. Currently, much interest is attracted to bright squeezed vacuum (BSV), a macroscopic nonclassical state of light that can be obtained via high-gain parametric down conversion (PDC). This is because BSV contains huge photon numbers and at the same time is strongly nonclassical, manifesting entanglement [1] and noise reduction below the standard quantum limit [2]. These features make it interesting for applications such as quantum imaging [3,4] and metrology [5], quantum optomechanics [6] and nonlinear optics with quantum light [7]. Besides, large photon-number correlations arising in BSV are richer than entanglement in two-photon light emitted via low-gain PDC [8].At the same time, theoretical description of BSV presents certain difficulties. In contrast to low-gain PDC, BSV generation cannot be described in the framework of the perturbation theory. The quantum state contains not only two-photon terms but also higher-order Fock components, and its calculation in the Schrödinger picture is difficult. Many recent theoretical investigations of such strong pumping regime are based on the concept of collective input/output modes introduced mostly to describe the spectral properties in the frequency domain [9][10][11][12][13]. In a high-gain regime it is convenient to calculate the observables in the Heisenberg picture. In this case the Schmidt-mode formalism used in the Schroedinger picture for the description of multimode two-photon light [14] is replaced by a similar procedure, called Bloch-Messiah reduction [15]. However beyond the perturbation approach the solution for the field operators was up to now obtained only numerically, usually through a set of integro-differential equations [12,13,[16][17][18].Here we present a fully analytical description of the angular properties of BSV. Our approach is based on the Bloch-Messiah reduction and allows one to obtain the evolution of the photon creation (annihilation) operators both for the Schmidt modes and for the plane-wave modes. After obtaining the evolution of these, we calculate analytically the angular distributions of the inten-

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“…We assume in the following that time-ordering corrections [42] can be neglected, which is a good approximation in the low-gain regime [43], and expand the exponential in a simple Taylor series by keeping all terms where two or fewer signal or idler photons are created or equivalently to first order in the nonlinear phase shift φ NL = γ P p L. Suppressing the integral limits for convenience, with the understanding that space integrals are from 0 to L and time integrals over all time, this gives the expansion…”

Section: Theorymentioning

confidence: 99%

“…Doing this, we assume that time-ordering corrections can be neglected [42], which is only valid in the low-gain regime [43]. Thus, Eq.…”

Section: Appendix A: Hamiltoniansmentioning

confidence: 99%

Effects of noninstantaneous nonlinear processes on photon-pair generation by spontaneous four-wave mixing

2017

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We present a general model, based on a Hamiltonian approach, for the joint quantum state of photon pairs generated through pulsed spontaneous four-wave mixing, including nonlinear phase modulation and a finite material response time. For the case of a silica fiber, it is found that the pair-production rate depends weakly on the waveguide temperature, due to higher-order Raman scattering events, and more strongly on pump-pair frequency detuning. From the analytical model, a numerical scheme is derived, based on the well-known split-step method. This scheme allows computation of joint states where nontrivial effects are included, such as groupvelocity dispersion and Raman scattering. In this work, the numerical model is used to study the impact of the noninstantaneous response on the prefiltering purity of heralded single photons. We find that for pump pulses shorter than 1 ps, a significant detuning-dependent change in quantum-mechanical purity may be observed in silica. This shows that Raman scattering not only introduces noise, but can also drastically change the spectral correlations in photon pairs when pumped with short pulses.

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Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime

Cited by 141 publications

References 59 publications

Nonlinear optical signals and spectroscopy with quantum light

Nonlinear optical signals and spectroscopy with quantum light

Schmidt modes in the angular spectrum of bright squeezed vacuum

Effects of noninstantaneous nonlinear processes on photon-pair generation by spontaneous four-wave mixing

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