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Register a new userLosses-based test of wave-particle duality with Mach-Zehnder interferometers
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Wave-particle duality of photons with losses in the Mach-Zehnder interferometer (MZI) is investigated experimentally and theoretically. The experiment is done with the standard MZI with the beam splitter or the beam merger being continuously varied. The losses are deliberately introduced either inside the MZI (the two arms between the beam splitter and beam mergers) or outside the MZI (after the beam merger). It is proved that the unbalanced losses have great influence on the predictability $P$ (particle nature) and visibility $V$ (wave nature). For the former case the duality inequality holds while for the later the duality inequality is ``violated. We get $P^2+V^2>1$. This ``violation could be eliminated in principle by switching the two paths and detectors and then averaging the results. The observed results can be exactly explained theoretically. The experiment is done with coherent beam, instead of single photons, and we have proved that they are exactly equivalent in duality experiment with MZI.
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Possible paths of a photon passing through a nested Mach-Zehnder interferometer on its way to a detector are analyzed using the consistent histories formulation of quantum mechanics, and confirmed using a set of weak measurements (but not weak values). The results disagree with an analysis by Vaidman [ Phys. Rev. A 87 (2013) 052104 ], and agree with a conclusion reached by Li et al. [ Phys. Rev. A 88 (2013) 046102 ]. However, the analysis casts serious doubt on the claim of Salih et al. (whose authorship includes Li et al.) [ Phys. Rev. Lett. 110 (2013) 170502 ] to have constructed a protocol for counterfactual communication: a channel which can transmit information even though it contains a negligible number of photons.
The Mach-Zehnder interferometric setup quantitatively characterizing the wave-particle duality implements in fact a joint measurement of two unsharp observables. We present a necessary and sufficient condition for such a pair of unsharp observables to be jointly measurable. The condition is shown to be equivalent to a duality inequality, which for the optimal strategy of extracting the which-path information is more stringent than the Jaeger-Shimony-Vaidman-Englert inequality.
We study theoretically electronic Mach-Zehnder interferometers built from integer quantum Hall edge states, showing that the results of recent experiments can be understood in terms of multiparticle interference effects. These experiments probe the visibility of Aharonov-Bohm (AB) oscillations in differential conductance as an interferometer is driven out of equilibrium by an applied bias, finding a lobe pattern in visibility as a function of voltage. We calculate the dependence on voltage of the visibility and the phase of AB oscillations at zero temperature, taking into account long range interactions between electrons in the same edge for interferometers operating at a filling fraction $ u=1$. We obtain an exact solution via bosonization for models in which electrons interact only when they are inside the interferometer. This solution is non-perturbative in the tunneling probabilities at quantum point contacts. The results match observations in considerable detail provided the transparency of the incoming contact is close to one-half: the variation in visibility with bias voltage consists of a series of lobes of decreasing amplitude, and the phase of the AB-fringes is practically constant inside the lobes but jumps by $pi$ at the minima of the visibility. We discuss in addition the consequences of approximations made in other recent treatments of this problem. We also formulate perturbation theory in the interaction strength and use this to study the importance of interactions that are not internal to the interferometer.
We theoretically studied the quantum Cram{e}r-Rao bound of an actively correlated Mach-Zehnder interferometer (ACMZI), where the quantum Fisher information obtained by the phase-averaging method can give the proper phase-sensing limit without any external phase reference. We numerically calculate the phase sensitivities with the method of homodyne detection and intensity detection in the presence of losses. Under lossless and very low loss conditions, the ACMZI is operated in a balanced case to beat the standard quantum limit (SQL). As the loss increases, the reduction in sensitivity increases. However within a certain range, we can adjust the gain parameters of the beam recombination process to reduce the reduction in sensitivity and realize the sensitivity can continue to beat the SQL in an unbalanced situation. Our scheme provides an optimization method of phase estimation in the presence of losses.
In a recent paper, arXiv:1604.04596, Griffiths questioned - based on an informative consistent-histories (CH) argument - the counterfactuality, for one of the bit choices, of Salih et al.s protocol for communicating without sending physical particles, Phys. Rev. Lett. 110, 170502 (2013). Here, we first show that for the Mach-Zehnder version used to explain our protocol, no family of consistent histories exists where any history has the photon travelling through the communication channel, thus rendering the question of whether the photon was in the communication channel meaningless from a CH viewpoint. We then show that for the actual Michelson-type protocol, there are consistent-histories families that include histories where the photon travels through the communication channel. We show that the probability of finding the photon in the communication channel is zero - thus proving complete counterfactuality.
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