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Reports on Mathematical Physics

Higher-order squeezing of both quadrature components in superposition of orthogonal even coherent state and vacuum state

Pankaj Kumar, Rakesh Kumar

Published Aug 1, 2024• 1 citation
Publisher
DOI
10.1016/s0034-4877(24)00056-9

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It is shown that a particular combination of so-called even coherent state dubbed the orthogonal-even coherent state, while exhibiting no ``ordinary'' or second-order squeezing, can furnish near-optimal simultaneous-quadrature fourth-order squeezing [where the latter term is defined in the sense of Hong and Mandel, Phys. Rev. Lett. 54, 323 (1985)]. The Wigner function of the particular quantum-mechanical superposition of states is calculated and various plots compared to the Wigner function of a simple statistical mixture of the same states. Rather uninteresting behavior is found in the latter case, which illustrates that the higher-order squeezing effect is due to nonclassical, quantum-mechanical ``interference in phase space.''
By utilizing the general theory of multimode squeezed states, the effects of generalized nonlinear unequal-power higher-power difference in the multimode Schrodinger-cat state entangled light field is studied, that is formed by the linear superposition of three macroscopical distinguishable quantum states named the multimode complex conjugate coherent state, multimode complex conjugate imaginary coherent state and multimode vacuum state. It is found that 1) the difference of the cat state entangled light field is independent of its vacuum state component; 2) in some cases, the two quadrature phase components of this cat state entangled light field present unequal-power higher-power difference properties respectively ; 3) under some other conditions, the difference effects of two quadrature phase components of the state mentioned above can exist at the same time. The two preceding results stated above are in conformity with the uncertainty principle, but the last is not. It is called two-sided difference squeezing phenomenon and could be very useful in the application of squeezed light on light quanta communication.
We study the Hong-Mandel 2n th-order squeezing of the Hermitian operator, X θ ≡ X1 cos θ + X2 sin θ and amplitude n th-power squeezing of the Hermitian operator,], of vacuum state and even coherent state defined by |α,, a is the annihilation operator, α, θ, r and ϕ are arbitrary and the only restriction on these is the normalization condition of the superposed state.We show that the Hong-Mandel 2n th-order squeezing and amplitude odd-power squeezing exhibited by even coherent state enhance in its superposition with vacuum state.Variations of these higher-orders squeezing with different parameters near its maxima have also been discussed.