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Physical Review A

Superposition of two squeezed vacuum states and interference effects

Barry C. Sanders

Published Apr 1, 1989• 73 citations
Publisher

Abstract

The superposition of two squeezed vacuum states is analyzed by studying the photon-number probability distribution and the quadrature-phase-eigenstate marginal distributions. Interference fringes in the distributions are observed for some superposition states. The nonlinear oscillator generates a particular superposition of two squeezed vacuum states and the properties of this superposition state are discussed and contrasted with the other superposition states.

DOI
10.1103/physreva.39.4284

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The superposition of two squeezed vacuum states is analyzed by studying the photon-number probability distribution and the quadrature-phase-eigenstate marginal distributions. Interference fringes in the distributions are observed for some superposition states. The nonlinear oscillator generates a particular superposition of two squeezed vacuum states and the properties of this superposition state are discussed and contrasted with the other superposition states.
In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.
In this paper, we study some quantum properties of a superposition of displaced squeezed two-mode vacuum and single-photon states, such as the second-order correlation function, the Cauchy-Schwartz inequality, quadrature squeezing, quasiprobability distribution functions and purity. This type of states includes two mechanisms, namely, interference in phase space and entanglement. We show that these states can exhibit sub-Piossonian statistics, squeezing and deviate from the classical Cauchy-Schwartz inequality. Moreover, the amount of entanglement in the system can be increased by increasing the squeezing mechanism. In the framework of the quasiprobability distribution functions we show that the single-mode state can tend to thermal state based on the correlation mechanism. Generation scheme for such states is given.
In this paper, we study some quantum properties of a superposition of displaced squeezed two-mode vacuum and single-photon states, such as the second-order correlation function, the Cauchy-Schwartz inequality, quadrature squeezing, quasiprobability distribution functions and purity. This type of states includes two mechanisms, namely, interference in phase space and entanglement. We show that these states can exhibit sub-Piossonian statistics, squeezing and deviate from the classical Cauchy-Schwartz inequality. Moreover, the amount of entanglement in the system can be increased by increasing the squeezing mechanism. In the framework of the quasiprobability distribution functions we show that the single-mode state can tend to thermal state based on the correlation mechanism. Generation scheme for such states is given.
The near superposition of squeezed vacuum states (NSVS) is investigated in this article. The state appears to be a superposition of a squeezed vacuum state (SVS) and a derivative-squeezed vacuum state. We have shown that NSVS is significantly different from any regular superposition of two SVSs. NSVS, like SVS, displays only even photons, but with different distributions. In some cases, NSVS has no vacuum state. NSVS displays sub-Poissonian statistics for small values of the squeezing parameter. NSVS reveals linear and amplitude-squared squeezing, with amplitude-squared squeezing surpassing SVS in most cases. The minimum uncertainty is explored, and a possible method for generating NSVS is explained. We have discovered that NSVS exhibits a similar behavior for all phase differences except when it equals precisely zero. This phenomenon has been identified and could potentially enable more sensitive measurements.
Phase-space-interference approaches employ interference on the phase plane to explain a quantum state's photon-number distribution. This paper generalizes the approach so that knowledge of the photon-number distribution explains the state's quantum phase-plane distribution. The required generalization is as follows. The Bohr-Sommerfeld ``band'' or trajectory of the mixture of number states \ensuremath{\sim}(\ensuremath{\Vert}N〉〈N\ensuremath{\Vert}+\ensuremath{\Vert}M〉〈M\ensuremath{\Vert}) consists of two annuli centered on the origin. In contrast, the trajectory of the pure number state superposition \ensuremath{\sim}(\ensuremath{\Vert}N〉+\ensuremath{\Vert}M〉) (with M>N) contains additional interference structures, namely, (M-N) symmetrically positioned radial spokes connecting the annuli. These spokes intersect the circular band attributed to a photon-number state at (M-N) locations, with the resulting destructive interference eliminating states \ensuremath{\Vert}N+1〉 to \ensuremath{\Vert}M-1〉. These structures build state phase-plane quantum probability distributions, as we illustrate for the squeezed vacuum. This state is missing every odd-numbered photon number state, and thus its trajectory consists of a repeated pattern of two heavily emphasized bars eliminating every odd-numbered state. These bars sum to generate the traditional ``cigar'' shape of the squeezed state.