Squeezed states in harmonic generation of a laser beam
Abstract
Harmonic generation processes are shown to minimize quantum fluctuations of the electromagnetic field in the fundamental as well as in every generated beam. For the harmonics, squeezing is additionally dependent on the polarisation properties of both beams.
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Cited by (41)
We study maximum simultaneous 2nth-order Hong and Mandel's squeezing of the most general the Hermitian operator, , and nth-order sub-Poissonian photon statistics (connected with expectation value of 2nth power of number fluctuation), in the most general superposition state, of two coherent states and . Here Hermitian operators X1,2 are defined by X1 + iX2 = a, the annihilation operator, complex numbers Z1,2, α, β are all arbitrary and the only restriction on these is the normalization condition of the state. We find a linear relationship between these two non-classical effects when the angle θ = arg(α + β) and . We show that maximum simultaneous 2nth-order Hong and Mandel's squeezing for the operator Xθ and nth-order sub-Poissonian photon statistics in the state occur for an infinite combinations with ; is a constant which depends on the order of squeezing, and with θ = arg(α + β) and . We also illustrate analytically and numerically by an example that both effects occur simultaneously for high-intensity field but for observation of such effects, sensitive settings of the parameters are required.
We study higher-order Hong and Mandel's squeezing of both quadrature components for an arbitrary 2nth order (n ≠ 1) considering the most general Hermitian quadrature operator, Xθ = X1 cos θ + X2 sin θ, in the orthogonal even coherent state defined by . Here and are even coherent states, |α〉 is coherent state, α = Aeiθα, , and . We find that maximum simultaneous 2nth-order Hong and Mandel's squeezing of both quadrature components Xθ and Xθ+π/2 in the state |ψ〉 occurs at θ = θα ± (π/4) for an arbitrary order 2n (n ≠ 1). We conclude that any large amount of higher-order squeezing in the state |ψ〉 can be obtained by choosing suitably a large 2n but in this case minimum values of the 2nth-order moments become less close to the corresponding best minimum values explored numerically so far. Variations of 2nth order squeezing for n = 2, 3 and 4, i.e., for fourth-order, sixth-order and eighth-order squeezing with different parameters have also been discussed.
Higher-order Hong-Mandel's squeezing in superposed coherent states
2011, Optics CommunicationsWe study 2nth order Hong and Mandel's squeezing of the Hermitian operator, Xθ ≡ X1cosθ + X2sinθ in the most general superposition state, |ψ〉 = Z1|α〉 + Z2|β〉 of two coherent states |α〉 and |β〉. Here operators X1,2 are defined by X1 + i X2 = a, the annihilation operator, angle θ and complex numbers Z1,2 , α, β are arbitrary and the only restriction on these is the normalization condition of |ψ〉. We find maximum 2nth-order Hong–Mandel squeezing of Xθ in the superposed coherent state |ψ〉 for an infinite combinations with , and with arbitrary values of (α + β) and θ. Here A2n is a constant which depends on the order of squeezing. The maximum percentage of 2nth order Hong–Mandel squeezing and their respective constants A2n have been reported for some values of n. We conclude that any large percentage of squeezing can be obtained by suitably choosing of the order 2n. For the order greater than 128 we obtained more than 99% higher-order squeezing at very low intensity of the optical field. Variations of higher-order squeezing with different parameters near its maxima have also been discussed.
Multiphoton quantum optics and quantum state engineering
2006, Physics ReportsWe present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter–radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms that are relevant for the conceptual investigations as well as for the practical applications of forefront aspects of modern quantum mechanics. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromagnetic field, either in discrete or in continuous variables, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.
Quantum variances in field modes of parametric down converter
2003, Optics CommunicationsParametric down converter is a device to generate quantum nonclassical states of light. Such states play a key role in studies of new quantum optical effects. Here we present an analysis of output quadrature variances in the signal, idler, and pump modes of the down converter. Our treatment in Schrödinger three-mode representation with quantized pump is based on multi-particle representation of the down converter wave function. This enables to trace behaviour of the wave amplitudes of the multi-particle correlated states with increase of the gain parameter and the input pump intensity. The developed method allows us to calculate minimum quadrature variances in the output modes as functions of the gain parameter and the pump amplitude. Special attention is given to pump output quantum quadrature variances. We show that the pump mode acquires new quantum properties different from input due to action of the down converter. We compare our results related to the separate signal and idler quantum quadrature variances with the ones following from the classical pump approximation.
Squeezing in the sum and difference fields in second harmonic generation
1999, Optics CommunicationsIn this article we show that, in intracavity second harmonic generation, a combined quadrature can be chosen which exhibits considerably more squeezing than the amplitude quadratures of the fundamental or second harmonic individually. We also investigate squeezing in single-pass travelling wave second harmonic generation, showing that previously published results are not accurate for arbitrary interaction length, with the behaviour obtained being qualitatively different.