Asymmetric Gaussian harmonic steering in second-harmonic generation

Abstract

Intracavity second-harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterized, both theoretically and experimentally. We show that it can be a source of continuous-variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering. [3,4], is one of the central features which differentiates quantum mechanics from classical physics. It has previously been shown that SHG can be used to produce entangled fields at the two frequencies [5,6], later called "harmonic entanglement" by Grosse et al. [7].EPR expressed the original paradox in terms of position and momentum measurements. The essential step in their argument was to introduce correlated (entangled) states of at least two particles which persisted when the particles become spatially separated. According to EPR, depending on which property of one group of particles that was measured, a prediction with some certainty of the values of physical quantities of the other group of particles could be made. If these properties were represented by noncommuting operators (such as position and momentum), the Heisenberg uncertainty principle could seemingly be violated. The EPR conclusion was therefore that the description of physical reality given by quantum mechanics is not complete.In this Rapid Communication we use the continuousvariable (CV) characterization of EPR first put on a mathematical footing by Reid [8], using quadrature amplitudes, which have the same mathematical properti...

Quantum behaviour of open pumped and damped Bose–Hubbard trimers

“…This raised the possibility that the considered state could be asymmetric, with the two observers not agreeing on whether the bipartite system exhibited EPR-steering or not. This asymmetric steering has been predicted in optical [40][41][42] and atomic systems [43], and measured in the laboratory [44], all using Gaussian measurements. It is now established that it is a general property, and may exist for any possible measurements [45].…”

Quantum behaviour of pumped and damped triangular Bose–Hubbard systems

“…When one of the pair (EP R ij , EP R ji ) is less than one and the other is more than one, we have a phenomenon known as asymmetric Gaussian steering. This property has been predicted in optical [40,41,42] and atomic systems [43], and measured in the laboratory [44]. It is now established that it is a general property, and may also exist for non-Gaussian measurements [45].…”

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“…The opposite has happened with modes 1 and 3, with their steering now being symmetric. The symmetry properties of the EPR steering can be controlled by adjusting the cavity loss rates, as was also found with intracavity second harmonic generation [36].…”