Observation of squeezing using cascaded nonlinearity

Kasai, Katsuyuki; Gao, Jiangrui; Fabre, Claude

doi:10.1209/epl/i1997-00418-8

Cited by 42 publications

(38 citation statements)

References 18 publications

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“…Below the oscillation threshold, they have been shown to generate squeezed vacuum states [1] and bi-partite entangled states. Above the oscillation threshold, they generate intensity correlated twin beams [2], squeezed reflected pump [3], bright bi-partite [4] or tri-partite [5] entangled states. Very impressive amounts of squeezing (11dB) have been recently observed below threshold [6].…”

Section: Pacs Numbersmentioning

confidence: 99%

Multimode nonclassical light generation through the optical-parametric-oscillator threshold

et al. 2010

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We show that an Optical Parametric Oscillator which is simultaneously resonant for several modes, either spatial or temporal, generates both below and above threshold a multimode non-classical state of light consisting of squeezed vacuum states in all the non-oscillating modes. We confirm this prediction by an experiment dealing with the degenerate TEM01 and TEM10 modes. We show the conservation of non-classical properties when the threshold is crossed. The experiment is made possible by the implementation of a new method to lock the relative phase of the pump and the injected beam. (11dB) have been recently observed below threshold [6]. Experimental results are less spectacular above threshold, because of the detrimental effect of the pump beam excess noise. Generally speaking, the non-classical properties increase when one approaches from below or from above the oscillation threshold, or any other bifurcation point of the non-linear dynamics of the device [7,8], but it is not always the case: for instance the signal-idler intensity difference squeezing is independent of the pumping level. This property of "non-critially squeezed light" has been further explored by the Valencia group[10] in the context of quantum imaging, which has found other squeezing effects that are independent of the pumping level. These effects are related to spatial symmetry-breaking, either translational[9] or rotational[10]: in a cavity of cylindrical symmetry, the parametric gain is the same for Gaussian modes TEM 01 where the two lobes are aligned along any direction in the transverse plane. However, above the oscillation threshold, a unique TEM 01 mode is produced. It is shown that this spontaneous symmetry breaking "induces" the generation of a squeezed vacuum state in the mode orthogonal to the emitted one with a squeezed value independent of the pumping level and clamped to its value at threshold. The emitted field is thus a two-mode non-classical field, made of the superposition of a bright mode and a vacuum-squeezed mode.In this paper, we show theoretically that this important result can be generalized to a much wider class of situations, involving either spatial or temporal modes, and we check experimentally that one can efficiently produce in this way multimode non-classical light.Let us envision the situation in which the cavity of the OPO is simultaneously resonant on several modes, which can be either spatial modes (Hermite-Gauss modes or more complicated patterns in transverse degenerate cavities), or frequency modes (separated by the free spectral range of the cavity). The annihilation operatorsâ ℓ associated with these different modes and the pump mode operatorb obey then the following well-known evolution equations, describing the effect of the parametric splitting of pump photons into couples of signal and idler photons respectively in modes ℓ and ℓ

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Section: Pacs Numbersmentioning

confidence: 99%

Multimode nonclassical light generation through the optical-parametric-oscillator threshold

et al. 2010

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“…These experimental systems have to include two parts for the second harmonic generation (SHG) firstly and then the parametric down-conversion, respectively. Besides, it has been experimentally demonstrated that the pump fields reflected from an optical cavity for intracavity SHG are the squeezed-state light fields because of the cascaded nonlinear interaction between subharmonic and harmonic fields inside the cavity [14] [15] . Z.Y.Ou [16] and C.Fabre et al [15] theoretically analyzed the quantum fluctuation and squeezing characteristics of the reflected subharmonic fields and calculated the spectra of squeezing.…”

Section: Introductionmentioning

confidence: 99%

Entanglement characteristics of subharmonic modes reflected from a cavity for type-II second-harmonic generation

Zhai

Gao

2004

Phys. Rev. A

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Quantum fluctuation and quantum entanglement of the pump field reflected from an optical cavity for type II second harmonic generation are theoretically analyzed. The correlation spectra between the quadratures of the reflected subharmonic fields are interpreted in terms of pump parameter, intracavity losses and normalized frequency. Large correlation degrees of both amplitude and phase quadratures can be accessed in a triple resonant cavity before the pitchfork bifurcation occurs. The two reflected subharmonic fields are in an entangled state with the quantum correlation of phase quadratures and anticorrelation of amplitude quadratures. The proposed system can be exploited to be a new source generating entangled states of continuous variables.

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“…This leads to both intensity and phase correlations between the three modes that extend to the quantum regime, and eventually culminate in tripartite entanglement as we show below. So far, physicists' interest has been concentrated on the signal and idler quantum correlations [19] or on the pump squeezing [20]. The full three-mode system has indeed genuine quantum properties [21], which are partly lost when one traces out the pump mode, although the signal and idler modes remain of course entangled [10].…”

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Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold Optical Parametric Oscillator

et al. 2006

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We calculate the quantum correlations existing among the three output fields (pump, signal, and idler) of a triply resonant non-degenerate Optical Parametric Oscillator operating above threshold. By applying the standard criteria [P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003)], we show that strong tripartite continuous-variable entanglement is present in this well-known and simple system. Furthermore, since the entanglement is generated directly from a nonlinear process, the three entangled fields can have very different frequencies, opening the way for multicolored quantum information networks. [3], all with different resonance frequencies. These systems will probably be used in nodes of quantum networks, implying the necessity of devising ways to address them without loss of quantum information. For networks with several nodes, multipartite entangled light beams will be important to carry out such tasks.Most of the current realizations of entangled light beams are implemented by combining squeezed beams on beam splitters [4,5,6,7,8,9]. The beam splitter transformation is linear and does not lead to entangled beams of different frequencies. In order to produce multicolored entangled beams it is important to generate them directly from a nonlinear process. In the case of bipartite two-color entanglement, this has been done very recently, in the above-threshold optical parametric oscillator (OPO) [10,11,12].The OPO is the best known and most widely used source of entangled continuous variables for quantum information purposes [13]. Nevertheless, focus thus far has been on the down-converted beams it produces, usually overlooking quantum properties of the pump beam. Recent proposals for direct generation of tripartite entanglement use so-called cascaded nonlinearities, combining down-conversion and sum/subtraction frequency generation [14], which are not present in standard OPOs. In this Letter, we theoretically demonstrate that the standard triply resonant above-threshold OPO naturally produces pump-signal-idler tripartite entanglement. We show that the down-converted and the pump fields' noises violate inequalities which are sufficient for witnessing entanglement [13]. We believe this to be the simplest and most practical proposal of a multicolored multipartite entanglement source to date.For tripartite systems with subsystems (k, m, n), if the state is partially separable, the density operator can be written in the form of a statistical mixture of reduced density operatorsρ i,km andρ i,n :with weights η i ≥ 0 satisfying i η i = 1. A necessary condition for separability of two sub-systems was demonstrated by Duan et al. [15], in the form of an inequality: if it is violated, there is bipartite entanglement. This criterion is easily checked experimentally by measuring second order moments of combinations of operators acting on each of the subsystems. The inequality presented in Ref.[15] for the variances of two combinations of positions and momenta (x j ,p j ) of subsystems j = {1, 2} can be readil...

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Observation of squeezing using cascaded nonlinearity

Cited by 42 publications

References 18 publications

Multimode nonclassical light generation through the optical-parametric-oscillator threshold

Multimode nonclassical light generation through the optical-parametric-oscillator threshold

Entanglement characteristics of subharmonic modes reflected from a cavity for type-II second-harmonic generation

Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold Optical Parametric Oscillator

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