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Quantum Optics Journal of the European Optical Society Part B

Multiatom quasi-intelligent and squeezed states

M.‐A. Dupertuis, Alexey N. Kireev

Published Apr 1, 1990• 5 citations
Publisher

Abstract

Multiatom quasi-intelligent and squeezed states with more than two atoms are constructed. A new general criterion for the squeezing of quasi-intelligent states and a method adapted to find maximally squeezed states are proposed. Multiatom quasi-intelligent states related to the collective dipole moment of an arbitrary number of non-identical two-level atoms are constructed. Squeezed states of the system of identical two-level atoms are investigated on the basis of symmetric multiatom states. The authors show in particular that there are no stationary squeezed states for which the expectation value of the collective dipole rising and lowering operators vanish for an odd number of atoms, whilst arbitrary large squeezing is realisable with an even number of atoms. A constructive procedure to generate squeezed light from the ground state by a squeezed multiatom system is proposed. These properties do not depend on whether the multiatom system consists of identical or non-identical atoms.

DOI
10.1088/0954-8998/2/2/004

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Multiatom quasi-intelligent and squeezed states with more than two atoms are constructed. A new general criterion for the squeezing of quasi-intelligent states and a method adapted to find maximally squeezed states are proposed. Multiatom quasi-intelligent states related to the collective dipole moment of an arbitrary number of non-identical two-level atoms are constructed. Squeezed states of the system of identical two-level atoms are investigated on the basis of symmetric multiatom states. The authors show in particular that there are no stationary squeezed states for which the expectation value of the collective dipole rising and lowering operators vanish for an odd number of atoms, whilst arbitrary large squeezing is realisable with an even number of atoms. A constructive procedure to generate squeezed light from the ground state by a squeezed multiatom system is proposed. These properties do not depend on whether the multiatom system consists of identical or non-identical atoms.
Abstract Collective spin operators for symmetric multi-quDit (namely identical D -level atom) systems generate a U( D ) symmetry. We explore generalizations to arbitrary D of SU(2)-spin coherent states and their adaptation to parity (multi-component Schrödinger cats), together with multi-mode extensions of NOON states. We write level, one- and two-quDit reduced density matrices of symmetric N -quDit states, expressed in the last two cases in terms of collective U( D )-spin operator expectation values. Then, we evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies of the corresponding reduced density matrices. In particular, we analyze the numerical and variational ground state of Lipkin–Meshkov–Glick models of 3-level identical atoms. We also propose an extension of the concept of SU(2)-spin squeezing to SU( D ) and relate it to pairwise D -level atom entanglement. Squeezing parameters and entanglement entropies are good markers that characterize the different quantum phases, and their corresponding critical points, that take place in these interacting D -level atom models.
Recent years have witnessed revolutionary improvement in the production, manipulation, characterization and quantification of multiatom (multiqubit) states - because of their promising applications in high precision atomic clocks, atomic interferrometry, quantum metrology and quantum information protocols. In the characterization and quantification of non-classical atomic correlations, two concepts namely, spin squeezing and quantum entanglement emerge. While spin squeezing originates from the uncertainty relation between atomic collective angular momentum operators, entanglement is a peculiar phenomena arising due to superpositions in the multiparticle Hilbert space. Here, we outline different quantitative measures of spin squeezing and discuss the intrinsic relation of spin squeezing with quantum entanglement in multiqubit systems.
I show that, in the case of both one- and two-photon resonances, a many-cascade two-photon correlated-spontaneous-emission laser can generate light exhibiting phase and photon-number squeezings. Optimizing the mean photon number in the cavity with respect to a phase factor sin[1/2(n-1)\ensuremath{\theta}]/sin(1/2\ensuremath{\theta}), we find that the maximized mean photon number and its squeezing increase with increasing the top populations ${\mathrm{\ensuremath{\rho}}}_{\mathit{n}\mathit{n}}^{\mathit{a}}$ of the active atoms. However, the photon-number squeezing may decrease, increase, or not change when increasing the number n-1 of lower, almost degenerate atomic levels, depending on the relative phase \ensuremath{\theta} of lower atomic states determined by the optimization conditions. The phase squeezing has a maximum value with increasing n-1 and ${\mathrm{\ensuremath{\rho}}}_{\mathit{n}\mathit{n}}^{\mathit{a}}$.
The Robertson–Schrödinger uncertainty relation for two observables A and B is shown to be minimized in the eigenstates of the operator λA+iB, λ being a complex number. Such states, called generalized intelligent states (GIS), can exhibit arbitrarily strong squeezing of A or B. The time evolution of GIS is stable for Hamiltonians which admit linear in A and B invariants. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the spin CS are a subset of SU(2) GIS. CS for an arbitrary semisimple Lie group can be considered as a GIS for the quadratures of the Weyl generators.