Stochastic dynamics of a Josephson junction threshold detector

We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. Activation rate dependence on the third current cumulant includes an additional term originating from the back-action of the measurement circuit.Comment: 5 pages, 2 figures, discussion of experiment added, typos correcte

Noise suppression in inverse weak value based phase detection

We examine the effect of different sources of technical noise on inverse weak value-based precision phase measurements. We find that this type of measurement is similarly robust to technical noise as related experiments in the weak value regime. In particular, the measurements considered here are robust to additive Gaussian white noise and angular jitter noise commonly encountered in optical experiments. Additionally, we show the same techniques used for precision phase measurement can be used with the same technical advantages for optical frequency measurements.Comment: 6 pages, 4 figure

Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements

We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multi-particle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semi-weak polarization measurement based on Fresnel reflection. We also point out a non- trivial connection between specific two-party Leggett-Garg inequality violations and convex sums of strange weak values.Comment: 4 pages, 6 figure

Technical advantages for weak value amplification: When less is more

The technical merits of weak value amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak value amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which uses all of them). Using the Fisher information metric, we demonstrate that weak value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time correlated noise model, and find that a Fisher information analysis indicates that while the standard method can have much larger information about the detected parameter than the postselected technique. However, the estimator needed to gather the information is technically difficult to implement, showing that the inefficient (but practical) signal-to-noise estimation of the parameter is usually superior. We also describe other technical advantages unique to imaginary weak value amplification techniques, focusing on beam deflection measurements. In this case, we discuss combined noise types (such as detector transverse jitter, angular beam jitter before the interferometer and turbulence) for which the interferometric weak value technique gives higher Fisher information over conventional methods. We go on to calculate the Fisher information of the recently proposed photon recycling scheme for beam deflection measurements, and show it further boosts the Fisher information by the inverse postselection probability relative to the standard measurement case

Thermal correlators of anyons in two dimensions

The anyon fields have trivial $\alpha$-commutator for $\alpha$ not integer. For integer $\alpha$ the commutators become temperature-dependent operator valued distributions. The $n$-point functions do not factorize as for quasifree states.Comment: 14 pages, LaTeX (misprints corrected, a reference added

Gravitational sensing with weak value based optical sensors

Using weak values amplification angular resolution limits, we theoretically investigate the gravitational sensing of objects. By inserting a force-sensing pendulum into a weak values interferometer, the optical response can sense accelerations to a few 10's of $\mathrm{zepto}\text{-}\mathrm{g}/\sqrt{\mathrm{Hz}}$, with optical powers of $1~\mathrm{mW}$. We convert this precision into range and mass sensitivity, focusing in detail on simple and torsion pendula. Various noise sources present are discussed, as well as the necessary cooling that should be applied to reach the desired levels of precision.Comment: 9 pages, 4 figures, Quantum Stud.: Math. Found. (2018

On second-order differential equations with highly oscillatory forcing terms

We present a method to compute efficiently solutions of systems of ordinary differential equations that possess highly oscillatory forcing terms. This approach is based on asymptotic expansions in inverse powers of the oscillatory parameter,and features two fundamental advantages with respect to standard ODE solvers: rstly, the construction of the numerical solution is more efficient when the system is highly oscillatory, and secondly, the cost of the computation is essentially independent of the oscillatory parameter. Numerical examples are provided, motivated by problems in electronic engineering

Parity meter for charge qubits: an efficient quantum entangler

We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact. Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)]. Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter. Two applications of the parity meter are discussed: the measurement of Bell's inequality in charge qubits and the realization of a controlled NOT gate.Comment: 8 pages, 4 figures; v2: discussion of measurement time, references adde

Precision frequency measurements with interferometric weak values

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 kHz per root Hz with only 2 mW of continuous wave, single mode input power. We describe the measurement of a weak value and show how even higher frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.Comment: 4 pages, 3 figures, published in PR

Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification

We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 560 femtoradians and the linear travel of a piezo actuator down to 20 femtometers