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Quantum Optics Journal of the European Optical Society Part B

Compensation of self-phase modulation in a QND measurement of photon number based on the optical Kerr effect

Hans Martens, Willem M. de Muynck

Published Oct 1, 1992• 3 citations
Publisher

Abstract

The authors study a quantum non-demolition (QND) set-up for the measurement of photon number, employing the optical Kerr effect. A method for the compensation of the negative effects of self-phase modulation is discussed. Losses are taken into account. It is seen that the performance of the device is limited in the first place by losses, rather than by self-phase modulation.

DOI
10.1088/0954-8998/4/5/006

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The authors study a quantum non-demolition (QND) set-up for the measurement of photon number, employing the optical Kerr effect. A method for the compensation of the negative effects of self-phase modulation is discussed. Losses are taken into account. It is seen that the performance of the device is limited in the first place by losses, rather than by self-phase modulation.
Quantum non-demolition (QND) measurements are of great interest in recent years as a method to increase the information capacity of communication systems. Common implementations of QND measurements in optical fiber are based on the Kerr effect: a probe beam acquires phase modulation which mimics the amplitude modulation of a signal beam. This phase is typically small and needs to be measured at high frequencies for practical fiber-optic communication systems. Here we present a self reflexive interferometer scheme adequate for this kind of measurements and describe its performance. Using this system we achieved fairly open eye-diagrams at 140 Mbit/sec.
A photon-number quantum nondemolition (QND) measurement theory that takes dissipative losses into account is presented. A QND measurement criterion is developed to determine the feasibility of QND measurements in a lossy optical medium. Using an analysis based on loss-error characteristics, we examine a lossy Kerr medium. We obtain restrictions on the losses and requirements for the nonlinearity and signal and probe powers necessary to observe the QND effect. We calculate the expected results for an experimental system meeting such requirements. We conclude that QND measurements are possible in existing media.
We analyze schemes for performing quantum nondemolition (QND) measurements in optical cavities. We consider three schemes: (1) measurement of a quadrature phase amplitude using a parametric process, (2) measurement of a quadrature phase amplitude using the optical Kerr effect in a nonlinear fiber, and (3) measurement of the photon number also using the Kerr effect in a fiber. We show that in the second scheme an enhancement of the QND effect may be obtained by making the cavity finesse for the signal larger than that for the probe.
When atoms are illuminated by an off-resonant field, the AC Stark effect will lead to phase shifts in atomic states. The phase shifts are proportional to the photon number of the off-resonant illuminating field. By measuring the atomic phase with newly developed atom-light hybrid interferometers, we can achieve quantum non-demolition measurement of the photon number of the optical field. In this paper, we analyze theoretically the performance of this QND measurement scheme by using the QND measurement criteria established by Holland et al [Phys. Rev. A 42, 2995 (1990)]. We find the quality of the QND measurement depends on the phase resolution of the atom-light hybrid interferometers. We apply this QND measurement scheme to a twin-photon state from parametric amplifier to verify the photon correlation in the twin beams. Furthermore, a sequential QND measurement procedure is analyzed for verifying the projection property of quantum measurement and for the quantum information tapping. Finally, we discuss the possibility for single-photon-number-resolving detection via QND measurement.
In Ref. [Phys. Rev. A 108, 053708], the scheme of quantum non-demolition measurement of optical quanta that uses a resonantly enhanced Kerr nonlinearity in the optical microresonator, pre-squeezing of the probe beam, and its parametric amplification before the detection, was analyzed theoretically. It was shown that the main factor that limits the sensitivity of the considered scheme is the interplay of optical losses and the non-linear self-phase modulation (SPM) effect. Here we show that using the intracavity squeezing of the probe beam in this scheme, it is possible to cancel out the SPM effect. In this case, the sensitivity will be limited only by the available power in the pump beam and by the input/output losses in the signal beam. Our estimates show, that using the best optical microresonators currently available, the single-photon sensitivity for the intracavity photon number can be achieved. Therefore, this scheme could be of interest for optical quantum information processing tasks.
Kerr effect cross-phase-modulation between signal and probe beams has been proposed and demonstrated as a means for quantum nondemolition (QND) measurement of the signal beam's photon number by homodyne detection of the probe beam. Recently, such QND measurements have been suggested as providing a new route to photonic quantum computation. For a signal-beam qubit, whose computational basis is the vacuum and one-photon states, the QND detector's error probability is shown to be determined by the qubit fidelity after the cross-phase-modulation interaction, with the former increasing from 0 to 12\frac{1}{2}21​ as the latter increases from 23\frac{2}{3}32​ to 1. This relationship is shown to hold regardless of the probe beam's input state. It also applies, without modification, when the cross-phase-modulation interaction is replaced with a more general unitary transformation.