Resonant second harmonic generation between 1550 nm and 775 nm with normalized outside efficiency > 3.8 × 10 −4 mW −1 is demonstrated in a gallium phosphide microdisk supporting high-Q modes at visible (Q ∼ 10 4 ) and infrared (Q ∼ 10 5 ) wavelengths. The double resonance condition is satisfied for a specific pump power through intracavity photothermal temperature tuning using ∼ 360 µW of 1550 nm light input to a fiber taper and coupled to a microdisk resonance. Power dependent efficiency consistent with a simple model for thermal tuning of the double resonance condition is observed.
Unlike regular time evolution governed by the Schrödinger equation, standard quantum measurement appears to violate time-reversal symmetry. Measurement creates random disturbances (e.g., collapse) that prevents back-tracing the quantum state of the system. The effect of these disturbances is explicit in the results of subsequent measurements. In this way, the joint result of sequences of measurements depends on the order in time in which those measurements are performed. One might expect that if the disturbance could be eliminated this time-ordering dependence would vanish. Following a recent theoretical proposal [A. Bednorz et al 2013 New J.Phys. 15 15 15 023043], we experimentally investigate this dependence for a kind of measurement that creates an arbitrarily small disturbance, weak measurement. We perform various sequences of a set of polarization weak measurements on photons. We experimentally demonstrate that, although the weak measurements are minimally disturbing, their time-ordering affects the outcome of the measurement sequence for quantum systems.A fundamental open question in physics is the role of time in quantum mechanics [1][2][3].While observables such as position and momentum are represented by operators, time in the Schrödinger equation appears only as ordinary number-parameter, just as in classical mechanics [2]. In view of relativistic theories of physics which famously treat time and space on equal footing, this distinction is problematic. In fact, while Heisenberg's uncertainty principle between energy and time appears to suggest that a time operator conjugate to the total energy operator exists, attempts to create such an operator lead to contradictions [4].Similar issues confound attempts to create an observable for the time it takes for a particle to tunnel through a potential barrier, or even the time of arrival of a particle at a detector [5][6][7].Another issue is that it is widely believed that information is conserved in quantum physics. This follows from the unitary time-reversible evolution in the Schrödinger equation. Yet,
Observations of neurons in a resting brain and neurons in cultures often display spontaneous scale-free (SF) collective dynamics in the form of information cascades, also called ‘neuronal avalanches’. This has motivated the so called critical brain hypothesis which posits that the brain is self-tuned to a critical point or regime, separating exponentially-growing dynamics from quiescent states, to achieve optimality. Yet, how such optimality of information transmission is related to behavior and whether it persists under behavioral transitions has remained a fundamental knowledge gap. Here, we aim to tackle this challenge by studying behavioral transitions in mice using two-photon calcium imaging of the retrosplenial cortex (RSC)—an area of the brain well positioned to integrate sensory, mnemonic, and cognitive information by virtue of its strong connectivity with the hippocampus, medial prefrontal cortex, and primary sensory cortices. Our work shows that the response of the underlying neural population to behavioral transitions can vary significantly between different sub-populations such that one needs to take the structural and functional network properties of these sub-populations into account to understand the properties at the total population level. Specifically, we show that the RSC contains at least one sub-population capable of switching between two different SF regimes, indicating an intricate relationship between behavior and the optimality of neuronal response at the subgroup level. This asks for a potential reinterpretation of the emergence of self-organized criticality in neuronal systems.
The weak value, the average result of a weak measurement, has proven useful for probing quantum and classical systems. Examples include the amplification of small signals, investigating quantum paradoxes, and elucidating fundamental quantum phenomena such as geometric phase. A key characteristic of the weak value is that it can be complex, in contrast to a standard expectation value. However, typically only either the real or imaginary component of the weak value is determined in a given experimental setup. Weak measurements can be used to, in a sense, simultaneously measure non-commuting observables. This principle was used in the direct measurement of the quantum wavefunction. However, the wavefunction's real and imaginary components, given by a weak value, are determined in different setups or on separate ensembles of systems, putting the procedure's directness in question. To address these issues, we introduce and experimentally demonstrate a general method to simultaneously read out both components of the weak value in a single experimental apparatus. In particular, we directly measure the polarization state of an ensemble of photons using weak measurement. With our method, each photon contributes to both the real and imaginary parts of the weak-value average. On a fundamental level, this suggests that the full complex weak value is a characteristic of each photon measured.
We study a nonlinear interferometer consisting of two consecutive parametric amplifiers, where all three optical fields (pump, signal and idler) are treated quantum mechanically, allowing for pump depletion and other quantum phenomena. The interaction of all three fields in the final amplifier leads to an interference pattern from which we extract the phase uncertainty. We find that the phase uncertainty oscillates around a saturation level that decreases as the mean number N of input pump photons increases. For optimal interaction strengths, we also find a phase uncertainty below the shot-noise level and obtain a Heisenberg scaling N 1 . This is in contrast to the conventional treatment within the parametric approximation, where the Heisenberg scaling is observed as a function of the number of down-converted photons inside the interferometer.
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