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arXiv:1404.0160 · Physical Review A

Nonlinear photon subtraction from a multimode quantum field

Valentin Averchenko, Valérian Thiel, Nicolas Treps

Published Jun 12, 2014• 45 citations
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Abstract

We consider theoretically how to extract mode-dependent single photons from a time and frequency multimode nonclassical beam. To achieve this task, we calculate the properties of sum frequency generation with a pulse shaped pump, taking into account both temporal and spatial degrees of freedom. We show that using a noncollinear configuration it is possible to achieve a mode-dependent weakly reflective beam splitter, with Schmidt number compatible with photon extraction for continuous variable regime tasks. We make explicit the possible application to the degaussification of highly multimode squeezed frequency combs.

DOI
10.1103/physreva.89.063808

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We consider theoretically how to extract mode-dependent single photons from a time and frequency multimode nonclassical beam. To achieve this task, we calculate the properties of sum frequency generation with a pulse shaped pump, taking into account both temporal and spatial degrees of freedom. We show that using a noncollinear configuration it is possible to achieve a mode-dependent weakly reflective beam splitter, with Schmidt number compatible with photon extraction for continuous variable regime tasks. We make explicit the possible application to the degaussification of highly multimode squeezed frequency combs.
A theoretical approach has been developed in the Schmidt mode formalism and photon operators in these modes to describe the spectral properties of the light generated in the nonlinear process of sum-frequency generation. A special regime at which the frequency correlations of photons in the output beams are suppressed has been described in detail. The control of the mode composition and spectral properties of the nonclassical squeezed light used to illuminate the signal channel with the possibility of generating a squeezed vacuum at the sum-frequency mode has been demonstrated at this regime.
The nature of a quantum network, in particular in the continuous variable regime, is governed not only by the light quantum state but also by the measurement process. It can then be chosen after the light source has been generated. Multimode entanglement is not anymore an intrinsic property of the source but a complex interplay between source, measurement and eventually post processing. This new avenue paves the way for adaptive and scalable quantum information processing. However, to reach this ambitious goal, multimode degaussification has to be implemented. Single-photon subtraction and addition have proved to be such key operations, but are usually performed with linear optics elements on single-mode resources. We present a device able to perform mode dependant non Gaussian operation on a spectrally multimode squeezed vacuum states. Sum frequency generation between the state and a bright control beam whose spectrum has been engineered through ultrafast pulse-shaping is performed. The detection of a single converted photon heralds the success of the operation. The resulting multimode quantum state is analysed with standard homodyne detection whose local oscillator spectrum is independently engineered. The device can be characterized through quantum process tomography using weak multimode coherent states as inputs. Its single-mode character can be quantified and its inherent subtraction modes can be measured. The ability to simultaneously control the state engineering and its detection ensures both flexibility and scalability in the production of highly entangled non-Gaussian quantum states.
Single-photon subtraction plays important roles in optical quantum information processing as it provides a non-Gaussian characteristic in continuous-variable quantum information.While the conventional way of implementing single-photon subtraction based on a low-reflectance beam splitter works properly for a single-mode quantum state, it is unsuitable for a multimode quantum state because a single photon is subtracted from all multiple modes without maintaining their mode coherence.Here, we experimentally implement and characterize a mode-tunable coherent single-photon subtractor based on sum-frequency generation.It can subtract a single photon exclusively from one desired time-frequency mode of light or from a coherent superposition of multiple time-frequency modes.To experimentally characterize the time-frequency modes of the single-photon subtractor, we employ quantum process tomography based on coherent states.The mode-tunable coherent single-photon subtractor will be an essential element for realizing non-Gaussian quantum networks necessary to get a quantum advantage in information processing.
Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions for the produced fields. Based on the representation generated by the two-mode SU(2) coherent states, we introduce a model of entangled light beams leading to the subtraction of photons in one of the modes, conditioned to the detection of any photon in the other mode. We show that photon subtraction does not produce nonclassical fields from classical fields. It is also derived a compact expression for the output field from which the calculation of conditional probabilities is straightforward for any input state. Examples include the analysis of squeezed-vacuum and odd-squeezed states. We also show that injecting optical cats into a beam splitter gives rise to entangled states in the Bell representation.
Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables [1]. They can be generated either by mixing different squeezed light sources using linear optical operations [2], or directly in a multimode optical device [3, 4]. Synchronously Pumped Optical Parametric Oscillators (SPOPO) — which correspond to an OPO pumped by a train of ultrashort pulses that are synchronized with the cavity round-trip time — have been theoretically shown to be promising devices for the generation of multimode nonclassical frequency combs, since a SPOPO is a sole optical cavity acting as an assembly of independent squeezers in a particular basis called the supermodes basis [5]. The supermodes are optical frequency combs with specific spectrum and phase profiles that are determined by the length of the intracavity nonlinear crystal and the pulse shape of the pump.