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Physica Scripta

States of maximum polarization for a quantum light field and states of a maximum sensitivity in quantum interferometry

Vlasta Peřinová, A. Lukš

Published Jun 1, 2015• 0 citations
Publisher

Abstract

The SU(2) group is used in two different fields of quantum optics, the quantum polarization and quantum interferometry.Quantum degrees of polarization may be based on distances of a polarization state from the set of unpolarized states.The maximum polarization is achieved in the case where the state is pure and then the distribution of the photon-number sums is optimized.In quantum interferometry, the SU(2) intelligent states have also the property that the Fisher measure of information is equal to the inverse minimum detectable phase shift on the usual simplifying condition.Previously, the optimization of the Fisher information under a constraint was studied.Now, in the framework of constraint optimization, states similar to the SU(2) intelligent states are treated.

DOI
10.1088/0031-8949/90/7/074056

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The SU(2) group is used in two different fields of quantum optics, the quantum polarization and quantum interferometry.Quantum degrees of polarization may be based on distances of a polarization state from the set of unpolarized states.The maximum polarization is achieved in the case where the state is pure and then the distribution of the photon-number sums is optimized.In quantum interferometry, the SU(2) intelligent states have also the property that the Fisher measure of information is equal to the inverse minimum detectable phase shift on the usual simplifying condition.Previously, the optimization of the Fisher information under a constraint was studied.Now, in the framework of constraint optimization, states similar to the SU(2) intelligent states are treated.
The degree of polarization of a quantum field can be defined as its distance to an appropriate set of states. When we take unpolarized states as this reference set, the states optimizing this degree for a fixed average number of photons N‾\overline{N}N present a fairly symmetric, parabolic photon statistic, with a variance scaling as N‾2{\overline{N}}^{2}N2. Although no standard optical process yields such a statistic, we show that, to an excellent approximation, a highly squeezed vacuum can be taken as maximally polarized. We also consider the distance of a field to the set of its SU(2) transformed, finding that certain linear superpositions of SU(2) coherent states make this degree to be unity.
Quantum optics entails polarization properties that cannot be fully described by the classical Stokes parameters. In this work, we characterize the polarization of classical as well as quantum fields by means of a probability distribution on the Poincar\'e sphere. This serves to define the degree of polarization of a field state as the distance between the corresponding polarization distribution and the uniform distribution representing unpolarized light. We apply this definition to relevant quantum field states such as SU(2) coherent, squeezed, number, and phase states.
We study the phase sensitivity of SU(2) and SU(1,1) interferometers fed by two-mode field states which are intelligent states for Hermitian generators of the SU(2) and SU(1,1) groups, respectively. Intelligent states minimize uncertainty relations and this makes possible an essential reduction of the quantum noise in interferometers. Exact closed expressions for the minimum detectable phase shift are obtained in terms of the Jacobi polynomials. These expressions are compared with results for some conventional input states, and some known results for the squeezed input states are reviewed. It is shown that the phase sensitivity for an interferometer that employs squeezing-producing active devices (such as four-wave mixers) should be analyzed in two regimes: (i) fixed input state and variable interferometer, and (ii) fixed interferometer and variable input state. The behavior of the phase sensitivity is essentially different in these two regimes. The use of the SU(2) intelligent states allows us to achieve a phase sensitivity of order 1/N\ifmmode\bar\else\textasciimacron\fi{} (where N\ifmmode\bar\else\textasciimacron\fi{} is the total number of photons passing through the phase shifters of the interferometer) without adding four-wave mixers. This avoids the duality in the behavior of the phase sensitivity that occurs for the squeezed input. On the other hand, the SU(1,1) intelligent states have the property of achieving the phase sensitivity of order 1/N\ifmmode\bar\else\textasciimacron\fi{} in both regimes. \textcopyright{} 1996 The American Physical Society.
Abstract In this work we address the optimization of two important quantum states in terms of interferometric phase sensitivity, given a constraint on the total average number of input photons, N ¯ We use the quantum Fisher information (QFI) as our main tool. We employ both the single- and two-parameter QFI in order to address detection schemes having, and respectively, not having access to an external phase reference. The first quantum state we consider is the coherent plus squeezed vacuum input and find the optimum coherent fraction that maximizes both the single- and two-parameter QFI. We also discuss detection schemes able to perform almost optimally. Finally, we consider the double squeezed vacuum input and determine the squeezed fraction between the inputs that maximizes the QFI. Similar to the previous input state, we also provide detection schemes able to perform optimally.