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Journal of Modern Optics

Superposition Phases and Squeezing

Hai-Woong Lee

Published Jun 1, 1993• 3 citations
Publisher

Abstract

Quadrature variances of a radiation field depend not only on the photon number distribution in the field but also on the relative phases of the photon number probability amplitudes. Two fields with the same photon number distribution can show different degrees of squeezing if photon number states are superposed with different relative phases. It is thus possible, for example, for a radiation field with Poissonian photon statistics to exhibit squeezed quadrature fluctuations. Since different relative superposition phases in general yield different maximum and minimum values of the quadrature variances, measurement of the variances can yield information concerning the relative phases between different number states.

DOI
10.1080/09500349314551151

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Quadrature variances of a radiation field depend not only on the photon number distribution in the field but also on the relative phases of the photon number probability amplitudes. Two fields with the same photon number distribution can show different degrees of squeezing if photon number states are superposed with different relative phases. It is thus possible, for example, for a radiation field with Poissonian photon statistics to exhibit squeezed quadrature fluctuations. Since different relative superposition phases in general yield different maximum and minimum values of the quadrature variances, measurement of the variances can yield information concerning the relative phases between different number states.
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An arbitrary radiation field has limits on its quadrature variances and cross-correlations given by the positivity of the density matrix. These limits are derived and related to the optimisation of the squeezing measurements. The results are designed to deal with typical multimode squeezing experiments. In particular, the bounds indicate the necessity of achieving equal photon number intensities for optimal squeezing. A photon number imbalance can be compensated to some extent by using unequal gains. The optimal relative gain is obtained here.
We analyze the phase and squeezing properties of the cotangent states of the electromagnetic field. We calculate the phase distribution, phase variance, and number-phase uncertainty product for these states. Under appropriate conditions, the phase distribution develops oscillations resulting from the formation of states, reminiscent of macroscopic superpositions. In other cases the cotangent states are nearly minimum number-phase uncertainty states, emulating the coherent states. We also study the quadrature squeezing properties of the cotangent states and find that under a wide range of conditions they are highly squeezed.
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