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arXiv:2111.14700 · Physical Review A

Quantum nondemolition measurements of photon number in monolithic microcavities

Stepan N. Balybin, Andrey B. Matsko, Farid Ya Khalili, Dmitry Strekalov, Vladimir S. Ilchenko, Anatoliy A. Savchenkov, N. M. Lebedev, Igor A. Bilenko

Published Jul 28, 2022• 10 citations

Abstract

We revisit the idea of quantum nondemolition measurement (QND) of optical quanta via a resonantly enhanced Kerr nonlinearity taking into account quantum backaction. We show that the monolithic microcavities enable QND measurement of the number of quanta in a weak signal field using a classical probe field spatially overlapping with the signal. The phase of the probe field acquires information about the signal number of quanta without altering it due to the cross-phase modulation effect. We find the exact solution to the Heisenberg equations of motion of this system and calculate the measurement error, accounting for the optical losses in the measurement path. We identify a realistic approximation to obtain the explicit form of the final conditional quantum state of the signal field, accounting for the undesirable self-phase modulation effect and designing the optimal homodyne measurement of the probe beam to evade this effect. We show that the best modern monolithic microcavities allow achieving the measurement imprecision several times better than the standard quantum limit.

DOI: 10.1103/physreva.106.013720

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We revisit the idea of quantum nondemolition measurement (QND) of optical quanta via a resonantly enhanced Kerr nonlinearity taking into account quantum backaction. We show that the monolithic microcavities enable QND measurement of the number of quanta in a weak signal field using a classical probe field spatially overlapping with the signal. The phase of the probe field acquires information about the signal number of quanta without altering it due to the cross-phase modulation effect. We find the exact solution to the Heisenberg equations of motion of this system and calculate the measurement error, accounting for the optical losses in the measurement path. We identify a realistic approximation to obtain the explicit form of the final conditional quantum state of the signal field, accounting for the undesirable self-phase modulation effect and designing the optimal homodyne measurement of the probe beam to evade this effect. We show that the best modern monolithic microcavities allow achieving the measurement imprecision several times better than the standard quantum limit.

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

\frac{1}{2}

as the latter increases from

\frac{2}{3}

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.

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.

We report the quantum-nondemolition measurement of the photon number of an optical soliton. Taking advantage of the conservation properties of quantum solitons, we were able to read out the photon number of a ``signal'' soliton via the phase of a ``probe'' soliton after a soliton collision in a single-mode low-loss optical fiber. Subsequent noise measurements showed the photon number fluctuations of the signal soliton at the shot-noise limit to be correlated to the phase fluctuations of the probe soliton, signifying a backaction-evading measurement of the photon number.

In the work by Balybin et al. [Phys. Rev. A 108, 053708 (2023)], the scheme of quantum nondemolition measurement of optical quanta that uses a resonantly enhanced Kerr nonlinearity in the optical microresonator, presqueezing 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 nonlinear 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 sensitivity for the intracavity photon number approaching the single-photon one can be achieved. Therefore, this scheme could be of interest for optical quantum information processing tasks.

The collision of two optical solitons, one a probe and the other a signal, writes out the energy of the signal soliton as a phase shift of the probe soliton. Consequently, a readout of the probe phase shift gives the photon number of the signal soliton. If the collision takes place in a low-loss optical fiber with the usual Kerr nonlinearity, the photon number of the signal soliton is preserved, and the measurement can be a quantum nondemolitional (QND) measurement. We describe experimental progress towards soliton collision QND measurements. We have collided two solitons at 1.460 nm (probe) and 1.463 nm (signal) and with the help of a delayed reference soliton (identical to the probe) in a homodyne detector system, we have measured the resulting probe soliton phase shifts. Toward a QND measurement, we correlate the shot noise fluctuations of the signal soliton with the corresponding phase noise fluctuations written on the probe. We present our current results.