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Annual Meeting Optical Society of America

Quantum nondemolition measurements in the nondegenerate optical parametric oscillator

Silvania F. Pereira, H. J. Kimble, Paul M. Alsing, Daniel F. Walls

Published Jan 1, 1987• 0 citations
Publisher

Abstract

We consider a scheme for quantum nondemoliton (QND) measurements involving a cavity containing a Faraday rotator and a nonlinear crystal for (frequency degenerate) parametric downconversion into orthogonal polarizations. For the case of nondepletion of the pump field we analyze the coupled equations for the quadrature amplitudes of the fields using both semiclassical and quantum mechanical approaches. We show that when the magnitudes of the coupling coefficients κ of the crystal and σ of the Faraday rotator are appropriately chosen, the Hamiltonian of the system is of an ideal QND form for the intracavity field in the absence of dissipation. With the inclusion of cavity damping in the form of a single mirror of finite transmissivity, we demonstrate that information in the quadrature amplitude X1 of one polarization of the incident field can be measured (in a QND sense) by monitoring the quadrature amplitude Y2 of the orthogonal polarization.

DOI
10.1364/oam.1987.me9

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We consider a scheme for quantum nondemoliton (QND) measurements involving a cavity containing a Faraday rotator and a nonlinear crystal for (frequency degenerate) parametric downconversion into orthogonal polarizations. For the case of nondepletion of the pump field we analyze the coupled equations for the quadrature amplitudes of the fields using both semiclassical and quantum mechanical approaches. We show that when the magnitudes of the coupling coefficients κ of the crystal and σ of the Faraday rotator are appropriately chosen, the Hamiltonian of the system is of an ideal QND form for the intracavity field in the absence of dissipation. With the inclusion of cavity damping in the form of a single mirror of finite transmissivity, we demonstrate that information in the quadrature amplitude X1 of one polarization of the incident field can be measured (in a QND sense) by monitoring the quadrature amplitude Y2 of the orthogonal polarization.
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.
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.
A possibility of formation of nonclassical polarization states of light in the case of interaction of two orthogonally polarized modes in a spatio-inhomogeneous nonlinear medium is considered. A procedure of the quantum nondemolition (QND) measurement both of the Stokes parameters and the phase difference of two orthogonally polarized modes of optical field is presented and analyzed for the first time. We also introduce a new nonlinear parameter to describe the light polarization (depolarization) in quantum optics. The general approach to the measurement procedure under study allows to propose the new scheme for the QND-measurement of the angular momentum of atomic system as well.
We have constructed a mode-locked optical parametric oscillator (OPO), synchronously pumped by the second harmonic of a continuously mode-locked Nd:YAG laser and based on type II phase matching in a KTP crystal. The two subharmonics (signal and idler waves) are nearly degenerate in frequency but are distinct orthogonal polarization states, and the oscillator is thus a nondegenerate OPO. Above threshold, the intensities of the signal and idler output beams should be highly correlated, as recently demonstrated for a similar single-frequency OPO.1 Ideally, the quantum noise on the corresponding photocurrent difference signal is completely suppressed for frequencies that are small compared to the OPO cavity bandwidth. Since this configuration produces intense light beams with potentially very good noise suppression, it is an important prototype for possible applications, e.g., to spectroscopy. Initial results with our OPO show an excess uncorrelated polarization noise, possibly due to depolarized light scattering in the KTP crystal. When the OPO cavity is stabilized with the signal and idler degenerate in frequency, they can be mixed to form a superposition by manipulating their polarization. When the oscillator is pumped below threshold, a pulsed squeezed vacuum state is produced in two such mixtures.2 When the polarizations are mixed inside the OPO cavity by a Faraday rotator, the backaction evasion necessary for a quantum nondemolition (QND) measurement of one of the field quadratures of an externally injected beam is obtained.3 The pulsed local oscillator used in observing the squeezing or QND effects is derived from the fundamental output of the pump laser. Progress in implementing these experiments with our mode-locked OPO is described as well as possible applications to time-domain measurements with noise below the shot-noise limit.
Classical and quantum fluctuations are analyzed in the system of type-II harmonic generation where two frequency-degenerate subharmonic fields with orthogonal polarizations are required for the generation of a harmonic field. The two subharmonic fields as well as the harmonic fields are on resonance in a cavity. It is found that there is no self-pulsing behavior as predicted for the type-I case where the intensities of both the subharmonic and the harmonic fields undergo fast oscillation. Instead there exists a threshold that is identified as the onset of an optical parametric oscillator (OPO) formed by a subharmonic mode with its polarization orthogonal to the input polarization (not the original modes). When the loss for the harmonic field is small, most of the input power is converted to the output power of the OPO. Under this circumstance, quantum-nondemolition measurements of the input can be performed at certain frequencies. The spectra of squeezing are calculated for the two subharmonic modes and it is found that both modes are squeezed for a certain range of frequency. The output of the OPO is found to exhibit phase squeezing.
In this paper, we present a theoretical investigation into the quantum-nondemolition (QND) properties of a system which utilizes intracavity harmonic generation. It is found that a nearly ideal QND measurement of the amplitude of a signal can be performed using second-harmonic generation, while subharmonic generation can be utilized to give a nearly ideal QND measurement of a phase. The results show a significant improvement over the QND properties of other systems studied previously and should be accessible to experiment.