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Photonics

Gain Saturation Modified Quantum Noise Effect on Preparing a Continuous-Variable Entanglement

Saeid Vashahri-Ghamsari, Bing He

Published Aug 30, 2022• 0 citations
Publisher

Abstract

We examine the gain saturation effect in non-Hermitian systems of coupled gain–loss waveguides and whispering-gallery-mode microresonators, through which a continuous-variable (CV) entanglement of light fields is generated. Here, we consider squeezed vacuum inputs for coupled waveguide setup and coherent drive for coupled microresonators, and study the influence from the saturation of the used optical gain. Unlike the ideal situation without gain saturation, it is possible to generate stabilized entanglement measured by logarithmic negativity under gain saturation. Both types of setups realize steady CV entanglement, provided that the gain saturation is sufficiently quick. Particularly, with the coupled microresonators which are pumped by coherent drive, the created CV entanglement is actually out of the gain noise with a squeezing characteristic, under the condition of fast saturation of the initial optical gain.

DOI
10.3390/photonics9090620

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We examine the gain saturation effect in non-Hermitian systems of coupled gain–loss waveguides and whispering-gallery-mode microresonators, through which a continuous-variable (CV) entanglement of light fields is generated. Here, we consider squeezed vacuum inputs for coupled waveguide setup and coherent drive for coupled microresonators, and study the influence from the saturation of the used optical gain. Unlike the ideal situation without gain saturation, it is possible to generate stabilized entanglement measured by logarithmic negativity under gain saturation. Both types of setups realize steady CV entanglement, provided that the gain saturation is sufficiently quick. Particularly, with the coupled microresonators which are pumped by coherent drive, the created CV entanglement is actually out of the gain noise with a squeezing characteristic, under the condition of fast saturation of the initial optical gain.
Gain saturation is ubiquitous but has not been fully explored in the newly developed field of non-Hermitian optics. On the other hand, the nonclassical properties of light are highly relevant to the gain saturation that influences the quantum noise accompanying light amplification. In this paper, we systematically examine the gain saturation effects in a non-Hermitian system of coupled gain-loss waveguides. We explain the impact of gain saturation on a quantum light field dynamically evolving in the coupled system. In contrast to the ideal situation without gain saturation, one can achieve a quasisteady state under the gain saturation. Moreover, gain saturation reduces the influence of amplification noise and thereby better preserves such quantum features as entanglement. We illustrate the effects of gain saturation by examining the time evolution of the Wigner function, entanglement of the light fields, and the cross-correlation function between the two output modes. Significant differences exist between unsaturated and saturated situations, especially for low photon numbers.
We study a system of two coupled waveguides respectively carrying optical damping and optical gain in addition to squeezing elements in one or both waveguides. Such a system is expected to generate highly entangled light fields in the two waveguides. Especially, if the light fields are strong enough, a macroscopic, continuous-variable entanglement can be achieved. We, however, show that the degree of the created entanglement is significantly affected by the quantum noises associated with the amplification and dissipation. The entanglement for the different configurations of the setup is quantified to illustrate how the quantum noises limit such entanglement as well as determine its actual time evolution patterns. In contrast to its sensitivity to the quantum noises, the degree of entanglement is irrelevant to the input light intensities, given the inputs in coherent states.
We explore in detail the possibility of intracavity generation of continuous-variable (CV) entangled states of light beams under mode phase-locked conditions. We show that such quantum states can be generated in a self-phase-locked nondegenerate optical parametric oscillator (NOPO) based on type II phase-matched down-conversion combined with a linear mixer of two orthogonally polarized modes of the subharmonics in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both subthreshold and above-threshold operational regimes. We show that the system providing high-level phase coherence between two generated modes, unlike the ordinary NOPO, also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the CV entanglement as two-mode squeezing and show that the maximal degree of the integral two-mode squeezing (which is 5050%50 relative to the level of vacuum fluctuations) is achieved at the pump field intensity close to the generation threshold of a self-phase-locked NOPO, provided that the constant of linear coupling between the two polarizations is much less than the mode detunings. The peculiarities of CV entanglement for the case of unitary, nondissipative dynamics of the system under consideration are also cleared up.
We develop a method for generating a more squeezed than single-mode squeezed vacuum (SMSV) state by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more of 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ~ 5 dB and least quadrature variance in the corresponding range of initial squeezing. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with non-unit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal photon subtraction. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of odd number of photons (say, 3 photons) allows the implementation of the measurement-induced even CV state which is several times brighter than the initial state and has lower quadrature noise.
We develop a method to generate nonclassical light with a larger quadrature squeezing than one of the single-mode squeezed vacuum (SMSV) states by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more than 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ∼5dB, and less quadrature variance. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with nonunit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal measurement of photons in the auxiliary mode. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of an odd number of photons (say, 3 photons) in auxiliary mode allows the implementation of the measurement-induced even CV state, which is several times brighter than the initial state, has lower quadrature noise, and is generated with greater probability.
We explore in detail the possibility of generation of continuous-variable (CV) entangled states of light fields with well-localized phases. We show that such quantum states, called entangled self-phase locked states, can be generated in nondegenerate optical parametric oscillator (NOPO) based on a type-II phase-matched down-conversion combined with polarization mixer in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both sub-threshold and above-threshold operational regimes. We show that the system providing relative phase coherence between two generated modes also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the entanglement as two-mode squeezing and show that CV entanglement is realized for both unitary, non-dissipative dynamics and for dissipative NOPO in the entire range of pump field intensities.