A quantum pulse gate based on spectrally engineered sum frequency generation

Eckstein, Andreas; Brecht, Benjamin; Silberhorn, Christine

doi:10.1364/oe.19.013770

Cited by 234 publications

(265 citation statements)

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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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Schmidt modes in the angular spectrum of bright squeezed vacuum

et al. 2015

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“…Current researches also demonstrate simultaneous wavelength translation and amplitude modulation of single photons from a quantum dot by pulsed frequency upconversion [29]. Additionally, the concept of a quantum pulse gate is presented and an implementation is proposed based on spectrally engineered frequency upconversion [30].…”

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confidence: 99%

Ultrashort Laser Pulses for Frequency Upconversion

Huang¹,

Wu²,

Gu³

et al. 2012

Laser Pulses - Theory, Technology, and Applications

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“…One very interesting case of the last equation is when the JCA is separableJ 1 (ω a , ω b ) = εr 0 k 0 (ω a )l * 0 (ω b ) and thus has only one nonzero Schmidt number in Eq. (6). Then one can selectively upconvert only Schmidt function 0 and leave the rest unchanged; this is precisely the ideal operation of a quantum pulse gate (QPG) as introduced by Eckstein et al [6].…”

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“…(6). Then one can selectively upconvert only Schmidt function 0 and leave the rest unchanged; this is precisely the ideal operation of a quantum pulse gate (QPG) as introduced by Eckstein et al [6]. However, theÛ 1 in Eq.…”

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High efficiency in mode-selective frequency conversion

Quesada

Sipe

2016

Opt. Lett.

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Frequency conversion (FC) is an enabling process in many quantum information protocols. Recently, it has been observed that upconversion efficiencies in single-photon, mode-selective FC are limited to around 80%. In this letter we argue that these limits can be understood as time-ordering corrections (TOCs) that modify the joint conversion amplitude of the process. Furthermore we show, using a simple scaling argument, that recently proposed cascaded FC protocols that overcome the aforementioned limitations act as "attenuators" of the TOCs. This observation allows us to argue that very similar cascaded architectures can be used to attenuate TOCs in photon generation via spontaneous parametric down-conversion. Finally, by using the Magnus expansion, we argue that the TOCs, which are usually considered detrimental for FC efficiency, can also be used to increase the efficiency of conversion in partially mode selective FC.Nonlinear photonic materials provide some of the most advanced platforms for manipulating the frequency and spectral profile of photons. This manipulation is typically achieved using a process known as frequency conversion (FC) [1,2]. In the version of FC we consider, two photons (one of them typically coming from a bright classical field) are fused into another photon with a higher energy by the process of sum frequency generation. FC has several important applications, including photon detection [3], and the establishment of compatibility between sources and quantum memories [4]. FC can also be used to modify in a controlled manner the properties of weak signals or single photons, a useful component of several quantum information processing protocols that harness the infinite dimensional Hilbert space structure of the frequency degree of freedom of photons [5][6][7][8]. A set of orthogonal frequency amplitude functions for the photon(s) (henceforth referred as "modes") provides a natural basis in which to encode information in this Hilbert space [5], and FC provides a natural way to do controlled operations in this Hilbert space [6]. For all applications of FC it is important to have conversion efficiency near unity, and for controlled operations it is also important to have mode selectivity. In the limit of very short crystals, or equivalently very long pulses (effectively CW fields) it has been shown that 100% FC is achievable [4,9]. Nevertheless in these limits most mode selectivity is lost. In this letter, we examine limitations to highly efficient mode selective FC. We show below that these limitations are due to time-ordering corrections (TOCs) that appear because the interaction picture Hamiltonian that describes the χ 2 (or χ 3 ) interaction between the different fields does not commute with itself at different times. Our study allows us to separate very cleanly the "ideal" operation of an FC device from the "undesirable" effects of time ordering. Thus, we can explicitly write the operation of an FC gate, in a language very close to the one used in quantum information, as a unitary operati...

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A quantum pulse gate based on spectrally engineered sum frequency generation

Cited by 234 publications

References 34 publications

Schmidt modes in the angular spectrum of bright squeezed vacuum

Schmidt modes in the angular spectrum of bright squeezed vacuum

Ultrashort Laser Pulses for Frequency Upconversion

High efficiency in mode-selective frequency conversion

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