Biasing the quantum vacuum to control macroscopic probability distributions

One of the most important insights of quantum field theory is that electromagnetic fields must fluctuate. Even in the vacuum state, the electric and magnetic fields have a nonzero variance, leading to ubiquitous effects such as spontaneous emission, the Lamb shift, the Casimir effect, and more. These "vacuum fluctuations" have also been harnessed as a source of perfect randomness, for example to generate perfectly random photonic bits. Despite these achievements, many potential applications of quantum randomness in fields such as probabilistic computing rely on controllable probability distributions, which have not yet been realized on photonic platforms. In this work, we show that the injection of vacuum-level "bias" fields into a multi-stable optical system enables a controllable source of "biased" quantum randomness. We demonstrate this concept in an optical parametric oscillator (OPO). Ordinarily, an OPO initiated from the ground state develops a signal field in one of two degenerate phase states (0 and $\pi$) with equal probability. By injecting bias pulses which contain less than one photon on average, we control the probabilities associated with the two output states, leading to the first controllable photonic probabilistic bit (p-bit). We shed light on the physics behind this process, showing quantitative agreement between theory and experiment. Finally, we demonstrate the potential of our approach for sensing sub-photon level fields by showing that our system is sensitive to the temporal shape of bias field pulses far below the single photon level. Our results suggest a new platform for the study of stochastic quantum dynamics in nonlinear driven-dissipative systems, and point toward possible applications in ultrafast photonic probabilistic computing, as well as the sensing of extremely weak fields

Photonic probabilistic machine learning using quantum vacuum noise

Probabilistic machine learning utilizes controllable sources of randomness to encode uncertainty and enable statistical modeling. Harnessing the pure randomness of quantum vacuum noise, which stems from fluctuating electromagnetic fields, has shown promise for high speed and energy-efficient stochastic photonic elements. Nevertheless, photonic computing hardware which can control these stochastic elements to program probabilistic machine learning algorithms has been limited. Here, we implement a photonic probabilistic computer consisting of a controllable stochastic photonic element - a photonic probabilistic neuron (PPN). Our PPN is implemented in a bistable optical parametric oscillator (OPO) with vacuum-level injected bias fields. We then program a measurement-and-feedback loop for time-multiplexed PPNs with electronic processors (FPGA or GPU) to solve certain probabilistic machine learning tasks. We showcase probabilistic inference and image generation of MNIST-handwritten digits, which are representative examples of discriminative and generative models. In both implementations, quantum vacuum noise is used as a random seed to encode classification uncertainty or probabilistic generation of samples. In addition, we propose a path towards an all-optical probabilistic computing platform, with an estimated sampling rate of ~ 1 Gbps and energy consumption of ~ 5 fJ/MAC. Our work paves the way for scalable, ultrafast, and energy-efficient probabilistic machine learning hardware

Synthesis and phase transition behaviours of new non-symmetric liquid crystal dimers

A new series of non-symmetric liquid crystal dimers N-(4-(n-(4-(benzothiazol-2-yl)phenoxy)alkyloxy)-4-nitro-benzylideneimine) containing benzothiazole and benzylideneaniline as the mesogenic core units connected by a flexible alkyl spacer, -(CH2)(n)-, with n ranging from 2 to 6, 8, 10 and 12 have been prepared. Their molecular structures were proposed via spectroscopic techniques. Mesomorphic properties were studied using differential scanning calorimetry and polarising optical microscopy. The results showed that the clearing temperatures decreased upon lengthening of the alkyl spacers. Whilst even member with the shortest alkyl spacer (n=2) exhibited nematic phase, the rest of even members (n=4, 6, 8, 10 and 12) possessed smectic and nematic properties. Nematic phase range gradually decreased from n=2 to n=12. Odd members are belonged to non-mesogenic compounds except for n=5 which exhibited monotropic (metastable) nematic phase

Synthesis and phase-transition behaviors of new symmetrical dimer liquid crystals containing benzothiazole unit

This article reports the synthesis and characterization of a series of homologous symmetrical dimers α,ω-bis[4-(6′-ethoxybenzothiazol-2′-yl)iminomethylphenoxy]alkane. Five members with different lengths of alkyl spacer groups of even parity varying from butyl (C4H8) to dodecyl (C12H24) were synthesized. Spectroscopic analysis (IR, 1H and 13C NMR) along with electron-ionization mass spectrometric techniques were employed to verify the molecular structures of the dimers. Differential scanning calorimeter was used for determination of the phase-transition temperature and associated enthalpy changes. Optical studies and mesophase identification were carried out using a polarizing optical microscope attached to hotstage. A diversity of phase-transition behavior was observed as the length of the alkyl spacer increased from C4H8 to C12H24. Almost all title compounds exhibited nematic phase except the dimer containing butyl spacer in which the mesomorphic property was absent

Synthesis and phase transition behaviours of laterally substituted liquid crystals containing methylhydroquinone: emerging of smectic C phase for higher homologues

A series of laterally substituted low-molar-mass liquid crystals with molecular geometry were constructed with three phenyl rings bridged through ester central groups as the rigid core and a lateral methyl group as the flexible part of a molecule, with a view to understanding and establishing the effect of molecular structure on liquid crystal behaviour. Low-molar-mass mesogens known as 1,4-bis[(4′-n-alkyloxybenzoyl)oxy]toluene with different number of carbon (n) at the alkyl chain have been prepared. Their molecular structures were proposed via physical measurements and spectroscopic techniques. Mesomorphic properties were studied by using differential scanning calorimetry, optical polarizing microscopy and powder X-ray diffraction techniques. The results showed that the melting points as well as the clearing temperatures decreased upon lengthening of the terminal alkyloxy chain lengths. Members with the shorter chain (n = 2–10) exhibited nematic phase. As for higher homologues, members with n = 12, 14, 16 and 18 showed polymorphism, whereby these compounds displayed both smectic and nematic properties

Mineral and Bone Disorder in Children with Chronic Kidney Disease Stage I to V (Predialysis)

To evaluate the mineral and bone disorders in children with chronic kidney disease (CKD) stage I to V predialysis. Methods: Pediatric subcohort of KNOW-CKD (KoreaN cohort study for Outcome in patients With CKD) enrolled children (younger than 20 years) with CKD stage I-V (pre-dialysis) from five major pediatric nephrology centers in Korea and collected medical data associated with CKD-mineral and bone disorder. Results: Total number of 300 patients (male:female=199:101) was included in this study. Serum phosphorus (mean ± standard deviation 4.89±0.75, 4.6±0.83, 4.63±0.85, 5.13±1.37, 5.35±1.2 from CKD stage I to V, p=0.0002), fibroblast growth factor (FGF)-23 (32.29±42.04, 41.33±41.00, 70.68±121.06, 67.9±66.95, 121.74±139.36, p=0.0030) and the prevalence of hyperphosphatemia (8.51%, 10.64%, 25.53%, 25.53%, 29.79%, p=0.010) increased as CKD progressed. Intact parathyroid hormone (iPTH) increased (40.84±40.37, 44.13±20.2, 78.93±65.21, 181.39±183.86, 313.85±324.95, p<0.001) and serum 1,25D3 level decreased (47.52±21.32, 37.43±12.26, 36.86±25.97, 28.29±15.81, 34.11±21.34, p<0.001) significantly as CKD aggravated. Serum iPTH (r=−0.608, p<0.0001) and FGF-23 (r=−0.4943, p<0.0001) showed negative correlation whereas 1,25D3 (r=0.3288, <0.0001) showed positive correlation with glomerular filtration rate. FGF-23 showed positive correlation with serum phosphorus (r=0.3342, p<0.0001), iPTH (r=0.3214, p<0.0001) and proteinuria (r=0.3609, p<0.0001), and negative correlation with urine phosphorus (r=−0.2597, p=0.0006). The prevalence of patients with increased alkaline phosphatase level increased significantly as CKD progressed (5.66%, 15.09%, 39.62%, 16.98%, 22.64%, p=0.042), which was due to increased prevalence of hyperparathyroidism (p<0.001). Active form vitamin D (0%, 3.77%, 11.88%, 40.74%, 68.89%, p<0.0001), calcium (2.13%, 0%, 9.90%, 4.44%, 62.22%, p<0.0001) and non-calcium phosphorous binders (0%, 0%, 0%, 0%, 13.33%, p<0.0001) were prescribed significantly more often in advanced CKD. Calcium x phosphorus was significantly increased in advanced CKD (11.59%, 17.39%, 28.26%, 21.01%, 21.74%, p=0.002). Conclusion: As CKD progressed, hyperphosphatemia, hyperparathyroidism and 1,25D3 deficiency increased, serum FGF-23 level increased and urinary phosphorus excretion decreased in children with CKD stage I to V predialysis