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arXiv:1108.2979 · Laser Physics

Spectral analysis of a four mode cluster state

S. L. W. Midgley, M. K. Olsen

Published Jun 12, 2012• 1 citation
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Abstract

We theoretically evaluate the squeezed joint operators produced in a single optical parametric oscillator which generates quadripartite entangled outputs, as demonstrated experimentally by Pysher et al. [1]. Using a linearized fluctuation analysis we calculate the squeezing of the joint quadrature operators below threshold for a range of local oscillator phases and frequencies. These results add to the existing theoretical understanding of this potentially important system.

DOI
10.1134/s1054660x12070092

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We theoretically evaluate the squeezed joint operators produced in a single optical parametric oscillator which generates quadripartite entangled outputs, as demonstrated experimentally by Pysher et al. [1]. Using a linearized fluctuation analysis we calculate the squeezing of the joint quadrature operators below threshold for a range of local oscillator phases and frequencies. These results add to the existing theoretical understanding of this potentially important system.
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The optical parametric oscillator is one of the most well-characterized devices in nonlinear optics, with many useful applications, especially as a frequency converter and as a wide-band amplifier. Novel discoveries made with these devices in the quantum domain include demonstrations of large amounts of both single-mode and two-mode squeezing, and, in the two-mode case, significant quantum intensity correlations between the two modes and quadrature correlations, which provided the first experimental demonstration of the original Einstein–Podolsky–Rosen (EPR) paradox. In this chapter, a systematic theory is developed of quantum fluctuations in the degenerate parametric oscillator. The quantum statistical effects produced by the degenerate parametric amplifier and oscillator have been intensely studied. As we have seen, the amount of transient squeezing produced in an ideal lossless parametric amplifier was calculated using asymptotic methods by Crouch and Braunstein. It was found to scale inversely with the square root of the initial pump photon number. When the system is put into a cavity, and driving and dissipation are introduced, we find that the steady state of a driven degenerate parametric oscillator bifurcates. There is a single steady state at low driving strengths, but, as the driving field increases, a threshold value is reached and the single state splits and forms two stable states. Below the threshold, a linearized analysis of squeezing in the quantum quadratures is possible; while above this threshold, or critical point, the tunneling time between the two states due to quantum fluctuations can be calculated.
We study theoretically and experimentally the quantum properties of a type-II frequency-degenerate optical parametric oscillator below threshold with a quarter-wave plate inserted inside the cavity which induces a linear coupling between the orthogonally polarized signal and idler fields. This original device provides a good insight into general properties of two-mode Gaussian states, illustrated in terms of the covariance matrix. We report on the experimental generation of a two-mode squeezed vacuum on nonorthogonal quadratures depending on the plate angle. After a simple operation, the entanglement is maximized and put into standard form, i.e., quantum correlations and anticorrelations on orthogonal quadratures. A half sum of squeezed variances as low as $0.33\ifmmode\pm\else\textpm\fi{}0.02$, well below the unit limit for inseparability, is obtained and the entanglement measured by the entropy of formation.
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This thesis demonstrates the presence of two-mode squeezing within a broadband squeezed light field generated by an OPO pumped just below threshold. Past experiments have confirmed the existence of this phenomenon, but we have demonstrated the technique over an approximately 1 MHz frequency range, with a highly tunable measurement technique. Through the use of a two-frequency local oscillator generated by a double sideband modulation of an EOM, we are able to measure many two-mode squeezed fields within the spectrum of one OPO output mode. Such a technique has great potential for observing larger, more densely packed optical cluster states, which could be used to construct a quantum computer.