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Journal of Physics Conference Series

Symmetries of the squeezed Kerr oscillator

FRANCESCO IACHELLO

Published Nov 1, 2024• 0 citations
Publisher

Abstract

Abstract The algebraic structure of the squeezed Kerr oscillator sp(2,R)~su(1,1) is described. It is shown that the Kerr oscillator has a novel and hitherto unknown symmetry su(2) which occurs for integer values of the ratio η=Δ/K of detuning Δ to the Kerr coefficient K. The effect of quadratic, cubic and quartic squeezing of the Kerr oscillator is discussed. The results are of importance for the generation and stabilization of states useful for quantum computing.

DOI
10.1088/1742-6596/2883/1/012007

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Abstract The algebraic structure of the squeezed Kerr oscillator sp(2,R)~su(1,1) is described. It is shown that the Kerr oscillator has a novel and hitherto unknown symmetry su(2) which occurs for integer values of the ratio η=Δ/K of detuning Δ to the Kerr coefficient K. The effect of quadratic, cubic and quartic squeezing of the Kerr oscillator is discussed. The results are of importance for the generation and stabilization of states useful for quantum computing.
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Three basic properties (eigenstate, orbit and intelligence) of the canonical squeezed states (SS) are extended to the case of n arbitrary observables. The SS for n observables X i can be constructed as eigenstates of their linear complex combinations or as states which minimize the Robertson uncertainty relation. When X i close a Lie algebra L the generalized SS could also be introduced as orbit of Aut ( L C ). It is shown that for the nilpotent algebra h N the three generalizations are equivalent. For the simple su (1, 1) the family of eigenstates of uK - + vK + ( K ± being lowering and raising operators) is a family of ideal K 1 – K 2 SS, but it cannot be represented as an Aut ( su C (1, 1) orbit although the SU (1, 1) group related coherent states (CS) with symmetry are contained in it. Eigenstates | z, u, v, w ; k ⟩ of general combination of uK - + vK + + wK 3 the three generators K j of SU (1, 1) in the representations with Bargman index k = 1/2, 1, ... , and k = 1/4, 3/4 are constructed and discussed in greater detail. These are ideal SS for K 1,2,3 . In the case of the one mode realization of su (1, 1) the nonclassical properties (sub-Poissonian statistics, quadrature squeezing) of the generalized even CS | z, u, v ; + ⟩ are demonstrated. The states | z, u, v, w ; k = 1/4, 3/4 ⟩ can exhibit strong both linear and quadratic squeezing.