Difference Squeezing Research Articles

Sum Squeezing, Difference Squeezing, Higher-Order Antibunching and Entanglement of Two-Mode Photon-Added Displaced Squeezed States

In this paper, we study some higher-order nonclassical properties and intermodal entanglement that may arise in the so called two-mode photon-added displaced squeezed state. We derive analytical expressions for the degree of sum squeezing and difference squeezing, which are interesting kinds of two-mode squeezing, as well as for the degree of antibunching to any orders. We also examine the degree of entanglement between the two modes using the existing Hillery-Zubairy criterion. Based on the derived expressions we analyze in detail the behavior of these nonclassical effects and entanglement depending on the parameters involved.

Robust generation of bright two-color entangled optical beams from a phase-insensitive optical parametric amplifier

Bright two-color continuous variable (CV) entangled optical beams at 0.8 and 1.5 μm are generated by utilizing a phase-insensitive optical parametric amplifier with only 1.5 μm signal field injected. Without locking the relative phase between the signal and pump fields, the amplitude quadrature difference squeezing of 3.30 dB and phase quadrature sum squeezing of 3.35 dB are observed, which satisfy the entanglement criterion. The demonstrated scheme here eliminates the necessity of precise phase control between the signal and pump fields and enables robust generation of two-color CV entangled states.

Detection of Sum and Difference Squeezing

Sum and difference squeezing was defined by Hillery who showed that these turn into normal squeezing in sum and difference frequency generation. We re-examine this using an intense coherent pump mode and with a much better approximation. Our results are valid for much larger interaction times and therefore enable detection of smaller sum and difference squeezings, in principle., Moreover, if both, our and Hillary's results are regarded holding, our results lead to more squeezing.

Testing nonclassicality in multimode fields: A unified derivation of classical inequalities

We consider a way to generate operational inequalities to test nonclassicality (or quantumness) of multimode (or multiparty) bosonic fields that unifies the derivation of many known inequalities and allows to propose new ones. The nonclassicality criteria are based on Vogel's criterion corresponding to analyzing the positivity of multimode P functions or, equivalently, the positivity of matrices of expectation values of, e.g., creation and annihilation operators. We analyze not only monomials, but also polynomial functions of such moments, which can sometimes enable simpler derivations of physically relevant inequalities. As an example, we derive various classical inequalities which can be violated only by nonclassical fields. In particular, we show how the criteria introduced here easily reduce to the well-known inequalities describing: (a) multimode quadrature squeezing and its generalizations including sum, difference and principal squeezing, (b) two-mode one-time photon-number correlations including sub-Poisson photon-number correlations and effects corresponding to violations of the Cauchy-Schwarz and Muirhead inequalities, (c) two-time single-mode photon-number correlations including photon antibunching and hyperbunching, and (d) two- and three-mode quantum entanglement. Other simple inequalities for testing nonclassicality are also proposed. We have found some general relations between the nonclassicality and entanglement criteria, in particular, those resulting from the Cauchy-Schwarz inequality. It is shown that some known entanglement inequalities can be derived as nonclassicality inequalities within our formalism, while some other known entanglement inequalities can be seen as sums of more than one inequality derived from the nonclassicality criterion. This approach enables a deeper analysis of the entanglement for a given nonclassicality.

Sum and Difference Squeeze Properties of Entangle Coherent States

A kind of entangle coherent states is constructed. According to dual mode field’s sum and difference operators defined by Mark Hillery, its squeezing properties are investigated by means of numerical calculation. Results show that the states appear sum and difference squeezing effect under the given conditions.

SQUEEZING EFFECTS IN THE SUM AND DIFFERENCE OF THE FIELD AMPLITUDE IN THE RAMAN PROCESS

Under the short-time approximation, Giri and Gupta1 investigated the sum and difference squeezing of the field amplitude in the Raman process. The relations between the normal squeezing and the sum and difference squeezing of the field amplitude are explicitly exhibited. They argued that the sum and difference squeezing of the field amplitude are essentially the squeezing in higher-order sense. Upon verification of the results of Giri and Gupta, we observe that the entire calculations and the conclusions thereof are misleading and baseless. To substantiate our claim, we give the correct expressions for the useful variances. Interestingly, there is no possibility of getting normal squeezing, sum squeezing and difference squeezing of the input state prepared in coherent state.

SQUEEZING EFFECTS IN THE SUM AND DIFFERENCE OF THE FIELD AMPLITUDE IN THE RAMAN PROCESS

Sum and difference squeezing of the field amplitude are higher-order squeezing effects. These effects are studied in the Raman process under the short-time approximation based on a fully quantum mechanical approach. It is shown that for uncorrelated modes, the normal squeezing in the sum and difference-frequency field depends on the sum and difference squeezing of input field modes respectively, which can generate normal squeezing in the sum and difference-frequency field mode. All the possibilities for obtaining sum and difference squeezing in two modes and its dependence on squeezing of individual field modes are investigated. We have also shown that if the high-frequency mode is in a coherent state and the low-frequency mode is squeezed, the field state will be difference squeezed if the amplitude of the high-frequency mode is large enough; otherwise the state may or may not be difference squeezed. If both modes are squeezed, then the state may or may not be difference squeezed. These higher-order squeezing effects are useful in the production of squeezing in the Raman process.

The revival–collapse phenomenon in the quadrature field components of the two-mode multiphoton Jaynes–Cummings model

In this paper we consider a system consisting of a two-level atom in an excited state interacting with two modes of a radiation field prepared initially in $l$-photon coherent states. This system is described by two-mode multiphoton (, i.e., $k_1, k_2$) Jaynes-Cummings model (JCM). For this system we investigate the occurrence of the revival-collapse phenomenon (RCP) in the evolution of the single-mode, two-mode, sum and difference quadrature squeezing. We show that there is a class of states for which all these types of squeezing exhibit RCP similar to that involved in the corresponding atomic inversion. Also we show numerically that the single-mode squeezing of the first mode for $(k_1,k_2)=(3,1)$ provides RCP similar to that of the atomic inversion of the case $(k_1,k_2)=(1,1)$, however, sum and difference squeezing give partial information on that case. Moreover, we show that single-mode, two-mode and sum squeezing for the case $(k_1,k_2)=(2,2)$ provide information on the atomic inversion of the single-mode two-photon JCM. We derive the rescaled squeezing factors giving accurate information on the atomic inversion for all cases. The consequences of these results are that the homodyne and heterodyne detectors can be used to detect the RCP for the two-mode JCM.

Experimental Characterization of Quantum-Correlated Twin Beams and a Quantum Channel with Twin Beams

We report the generation and characterization of quantum-correlated twin beams and their application to a quantum channel. Compared with our previous results, the characterization of twin beams and the quantum channel have been studied with 7.0-dB intensity difference squeezing. The measured inference variance of twin beams is decreased to 0.40 ± 0.02. For the quantum channel, the bit error rate will be 0.035 by using 7.0-dB intensity difference squeezing compared with our previous result of 0.067 by using 4.9-dB intensity difference squeezing.

Multimode difference squeezing

We define a type of multimode difference-squeezed states and show explicitly that these states are entirely embedded within the non-classical domain. We then contrast multimode difference squeezing with normal squeezing. We further analyse its delicate dependence on the modal states. All these studies emphasize the role of the concept of difference squeezing as a helpful theoretical tool for how to prepare the input modes to generate a squeezed output mode in a proper multiwave nonlinear process. Finally, we also discuss the possible connection between difference squeezing and a symmetry group.

Quantum variances and squeezing of output field from NOPA

The quadrature phase squeezing of coupled-mode and intensity difference squeezing between signal and idler mode of output field from continuous nondegenerate optical parametric amplifier (NOPA) are theoretically analyzed and compared. The calculation results provide design references for nonclassical light generation system.

Difference squeezing in four-wave difference-frequency generation

The multimode difference squeezing of the electromagnetic field in the four-wave mixing process is investigated under the short-time approximation based on a fully quantum mechanical approach. It is shown that for uncorrelated modes the normal squeezing in the difference-frequency field depends on the difference squeezing of input field modes, which can generate normal squeezing in the difference-frequency field mode. Various possibilities for obtaining difference squeezing in three modes and its dependence on squeezing of individual field modes are investigated. If one of the high-frequency modes is squeezed and the other two modes are in coherent states, difference squeezing can be generated when the amplitude of the low-frequency mode is large enough. Difference squeezing can be generated in the three modes if one of the high-frequency modes is in a coherent state and the other two modes are difference squeezed. It is also shown that when the low-frequency mode is in a coherent state and the high-frequency modes are sum squeezed, then difference squeezing can be generated for large amplitude of the low-frequency mode.

The amplitude-squared, sum and difference squeezing in the interaction of two quantized field modes with a two-level atom

The sum, difference and amplitude-squared squeezing are investigated for a generalized Jaynes-Cummings model with two field modes. Different initial states for the two-level atom are considered, and the dependence on the relative phases between the atomic and field coherent states is investigated.

Squeezing of two light fields coupled by a two-photon transition in a cavity

We calculate the squeezing for the sum and the difference of the two output beams. The effects of spontaneous emission on the squeezing are included. While spontaneous emission degrades the sum squeezing, no degradation is found for the difference squeezing, because of the correlation of the two photons spontaneously emitted. But the phase-shift induced by the atomic absorption can improve the squeezing for a given quadrature.

Sum and difference squeezing of the electromagnetic field.

Sum and difference squeezing are both higher-order, two-mode squeezing effects. Sum squeezing is turned into normal squeezing by sum-frequency generation. The operators that are used to define it form a representation of the su(1,1) Lie algebra. Difference squeezing can generate normal squeezing through difference-frequency generation. The operators that characterize it form a representation of the su(2) Lie algebra. Both are nonclassical effects. For uncorrelated modes the presence of squeezing in at least one of the modes is a necessary condition for the existence of either sum or difference squeezing. If the modes are correlated this is no longer true. Both sum and difference squeezing can be generated by combining a squeezed mode with one in a coherent state. Sum squeezing is also produced by a parametric amplifier. In order to better illustrate some of these effects a pictorial representation of sum squeezing is presented.