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Modern Physics Letters A

A REAPPRAISAL OF TWO-MODE SQUEEZING AND INTERMODE COUPLING

Bijan Kumar Bagchi, Debajyoti Bhaumik

Published Apr 30, 2000• 2 citations
Publisher

Abstract

We study two-mode squeezing in the framework of generalized quantum condition and derive pedagogically the result that the two-mode squeezed state is factorizable in terms of the component single modes. We also examine the related problem of two-mode squeezing in the system of a pair of coupled oscillators and consider the effects of a sudden switching-on of the intermode coupling for these quadrature modes.

DOI
10.1142/s0217732300000815

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Squeezing the quantum fluctuations of the two-mode light due to the nonstationary coupling between the quadrature components q1{q}_{1}q1​ and q2{q}_{2}q2​ is examined. The \ensuremath{\delta}- and step-function mode couplings are considered. The conditions of weak and strong step-function coupling are distinguished, the latter being the condition of the instability for the classical counterpart of the quantum system under study. Under the conditions of weak coupling the quadrature squeezing is established in both a two-mode electromagnetic noise in thermal equilibrium (the thermal state) and a two-mode correlated coherent state (CCS). Squeezing in the thermal state is suppressed at a high temperature. The photon distribution function (PDF) in the thermal state reveals oscillatory behavior for both high and low temperature, the oscillations decrease while the temperature increases. The PDF in the CCS can be either oscillatory or smooth, whereas the photon statistics is essentially non-Poissonian. The nonclassical intermode photon-number correlations in the CCS are briefly studied.
Quantum squeezing, a major resource for quantum information processing and quantum metrology, is best analyzed in terms of the field quadratures - the quantum optical analogues of position and momentum, which form the continuous-variable formalism of quantum light. Degenerate squeezing admits a very helpful and simple description in terms of the single-mode quadrature operators, but the non-degenerate case, i.e. when the squeezing involves pairs of modes, requires a more complicated treatment involving correlations between the quadratures of the different modes. We introduce a generalized set of complex quadrature operators that treats degenerate and non-degenerate squeezing on equal footing. We describe the mode-pairs (and photon-pairs) as a single entity, generalizing the concept of single-mode quadrature operators to two-mode fields of any bandwidth. These complex operators completely describe the SU(1,1) algebra of two-photon devices and directly relate to observable physical quantities, like power and visibility. Based on this formalism, we discuss the measurement of optically-broad squeezed signals with direct detection, and present a compact set of phase-dependent observables that completely and intuitively determine the two-mode squeezed state, and quantify the degree of inseparability and entanglement between the modes.
Information theory allows us to make quantitative statements about the strength and nature of the correlations between systems. Application of this theory to the quantized electromagnetic field reveals a special role for the two-mode squeezed states. The nonclassical properties of these states arise from the intermode correlations, and we apply information-theoretic methods to determine the strength of the correlation between specific pairs of observables. This analysis leads to the important general result that for any correlated pure state a given pair of single-system observables contains at most only half the information about the correlations. We discuss the implications of this result for the distinction between classical and quantum systems.
The entanglement of general asymmetric pure Gaussian two-mode states is examined in terms of the coefficients of the quadrature components of the wave function. The entanglement criterion and the entanglement of formation are directly evaluated as a function of these coefficients, without the need for local unitary transformations. These reproduce results for the special case of symmetric pure states which employ a relation between squeezed states and Einstein-Podolsky-Rosen correlations. The modification of the quadrature coefficients and the corresponding entanglement due to application of various optical elements is also derived.
The one- and two-mode combination squeezed states are constructed by applying the operator U identical to exp(-i lambda (erQ1P2+e-rQ2P1)) or W identical to exp(-i lambda (erQ1Q2-e-rP1P2)) (where lambda , r are real; Qi, Pi, i=1, 2 are coordinate and momentum operators, respectively) to the vacuum state. When the condition tanh lambda <1/(1+cosh r) is satisfied, such states can have less fluctuations in one quadrature phase than the usual two-mode squeezed state. Here, the authors examine the higher-order squeezing properties for such states. The result shows that under the same conditions, these states can exhibit a stronger form of higher-order squeezing than the usual two-mode squeezed state.