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International Journal of Modern Physics B

NON-DEMOLITIVE PHOTON NUMBER MEASUREMENT VIA χ(2) NONLINEARITY

Stefania Castelletto, Ivo Pietro Degiovanni, Maria Luisa Rastello

Published Nov 10, 1999• 1 citation
Publisher

Abstract

The aim of this paper is to present a possible experiment for measuring photon number by a non-demolitive scheme. We show that, in principle, it is possible to deduce the number of photons of an intense pump coherent field by measuring the phase-shift on two frequency conjugated beams due to the interaction with the pump in a nonlinear crystal, which exhibits χ(2) nonlinearity. We perform a theoretical evaluation of the relative uncertainty associated to the photon number measurement, obtaining high accuracy results when high pump power levels, low coupling between pump and crystal and squeezing generators are used. The accuracy obtained are compared with results obtainable with a beam splitter setup.

DOI
10.1142/s0217979299003088

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The aim of this paper is to present a possible experiment for measuring photon number by a non-demolitive scheme. We show that, in principle, it is possible to deduce the number of photons of an intense pump coherent field by measuring the phase-shift on two frequency conjugated beams due to the interaction with the pump in a nonlinear crystal, which exhibits χ(2) nonlinearity. We perform a theoretical evaluation of the relative uncertainty associated to the photon number measurement, obtaining high accuracy results when high pump power levels, low coupling between pump and crystal and squeezing generators are used. The accuracy obtained are compared with results obtainable with a beam splitter setup.
This paper proposes a realistically feasible experiment, within the realm of existing technology and proved techniques, to measure the mean photon number of a coherent source by means of a quantum non-demolition scheme, exploiting the parametric amplification of correlated photons in χ (2) media. We deduce the number of photons of an input source interacting with a high-intensity pump field in a nonlinear crystal, using as the probe the shift in the quadrature amplitude of the pump beam induced by the source under measurement. We perform a theoretical evaluation of the noise level associated with this measurement and compare it with the quantum limit. We explore the possible implications of this method for radiometry.
Abstract We discuss the generation of entangled photons using a nonlinear photonic crystal and beam splitter. In our method, the photonic crystal is assumed to be composed of a material with a large second-order nonlinear optical susceptibility χ ( 2 ) . Our proposal relies on two facts: (1) A nonlinear photonic crystal changes coherent incident light into squeezed light. (2) A beam splitter transforms the squeezed light into entangled light beams flying in two different directions. We estimate the yield efficiency of pairs of entangled photons per pulse of the very weak coherent light for our method at 0.0783 for a specific concrete example. Our method is more effective because the conversion efficiency (entangled biphotons per incident pump photons) in the spontaneous parametric downconversion is of the order of 4 × 10 − 6 . The only drawback is that it requires very fine tuning of the frequency of signal photons fed into the photonic crystal; for example, an adjustment is given by Δ ν = 3.11 × 10 8 Hz for the signal light of ν = 3.23 × 10 14 Hz. We investigate the application of entangled photons produced by our method to the BB84 quantum key distribution protocol, and we explore how to detect an eavesdropper. We suggest that our method is promising for decoy-state quantum key distribution using weak coherent light.
Measurements have been made of the rate at which signal photons are produced in a nonlinear crystal in the process of parametric downconversion, when a coherent light beam from a He:Ne laser is injected into the crystal in the direction of the conjugate-idler photons. The latter provides a stimulating field for the downconversion. When the phase matching condition inside the nonlinear medium is satisfied, the rate of downconversion is enhanced by the presence of the He–Ne laser beam by a factor of the form 1 + βIi, where li is the intensity of the He:Ne laser beam. The effect of defocusing either the pump beam or the He–Ne idler beam is investigated. Possible use of this phenomenon to study the photon amplifier with single-photon input will be discussed.
A proposed experiment is analyzed theoretically. In the proposed experiment two coherent pump waves fall on two identical nonlinear crystals, down-converted signal and idler beams from the two crystals are mixed by two beam splitters, and the coincidence counting rate for photons leaving the beam splitters is measured. We show that this counting rate depends on the phase difference between the two coherent pump waves, and results from the interference of the vacuum with the down-converted photons. The experiment could be used to look for locality violations along the lines recently proposed by Grangier, Potasek, and Yurke [Phys. Rev. A 38, 3132 (1988)], but without the need for a coherent reference beam for homodyning.
Realization of a room-temperature ultrafast photon-number-resolving quantum nondemolition (QND) measurement would have significant implications for photonic quantum information processing, enabling, for example, deterministic quantum computation in discrete-variable architectures, but the requirement for strong coupling has hampered the development of scalable implementations.In this work, we propose and analyze a nonlinear-optical route to photon-number-resolving QND using quadratic (i.e., χ (2) ) nonlinear interactions.We show that the coherent pump field driving a frequency-detuned optical parametric amplifier (OPA) experiences displacements conditioned on the number of signal Bogoliubov excitations.A measurement of the pump displacement thus provides a QND measurement of the signal Bogoliubov excitations, projecting the signal mode to a squeezed photon-number state.We then show how our nonlinear OPA dynamics can be utilized to deterministically generate Gottesman-Kitaev-Preskill states with only additional Gaussian resources, offering an all-optical route for fault-tolerant quantum information processing in continuous-variable systems.Finally, we place these QND schemes into a more traditional context by highlighting analogies between the frequency-detuned optical parametric oscillator and multilevel atom-cavity quantum electrodynamics systems by showing how continuous monitoring of the outcoupled pump quadrature induces conditional localization of the intracavity signal mode onto squeezed photon-number states.Our analysis suggests that our proposal may be viable in near-term χ (2) nonlinear nanophotonics, highlighting the rich potential of the OPA as a universal tool for ultrafast non-Gaussian quantum state engineering and quantum computation.
We re-examine the properties of the states produced by nondegenerate coherently stimulated parametric down-conversion wherein the signal and idler modes are seeded with coherent states of light and where the nonlinear crystal is driven by a strong classical field as described by the parametric approximation. The states produced are the two-mode squeezed coherent states defined with a specific ordering of operators, namely, the displacement operators of the two modes acting on the double vacuum state followed by the action of the two-mode squeeze operator representing the down-conversion process. Though mathematically equivalent to the reverse ordering of operators, but with different displacement parameters, the ordering we consider is closely related to what could most easily be implemented in the laboratory. The statistical properties of the state are studied with an emphasis on how they, and its average photon number, are affected by the various controllable phases, namely, those of the classical pump field of the two input coherent states. We then consider the multiphoton interference effects that arise if the two beams are overlapped on a 50:50 beam splitter, investigating the role of the phases in controlling the statistical properties of the output states. Finally, we study the prospects for the application of the states to quantum-optical interferometry to obtain sensitivities in phase-shift measurements beyond the standard quantum limit.