We propose an experiment that permits observation of the de Broglie two-photon wave packet behavior for a pair of photons, using a Mach-Zehnder interferometer. It is based on the use of pulsed lasers to generate pairs of photons via spontaneous parametric down-conversion and the post-selection of events. It differs from previous realizations by the use of a third time-correlated photon to engineer the state of the photons. The same technique can give us which-path information via an ``interaction-free'' experiment and can be used in other experiments on the foundations of quantum mechanics related to wave-particle duality and to nonlocality.
Mach-Zehnder interferometer for in-situ characterization of atom traps
German Aerospace Center (DLR)（德国航空航天中心）；Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm（乌尔姆大学量子物理研究所与集成量子科学技术中心）
In this paper, we have estimated the temperature dependent path predictability for an electronic Mach-Zehnder interferometer. The increment of path predictability can directly be associated with stronger decoherence process. We have also theoretically predicted that placing two detectors in both the paths, which are at the same equilibrium temperature with the system, erases all the memory of path information and hence acts like a quantum eraser.
We study the wave-particle duality in a general Mach-Zehnder interferometer with an asymmetric beam splitter from the viewpoint of quantum information theory. The correlations(including the classical correlation and the quantum correlation) between the particle and the which-path detector are derived when they are in pure state or mixed state at the output of Mach-Zehnder interferometer. It is found that the fringe visibility and the correlations are effected by the asymmetric beam splitter and the input state of the particle. The complementary relations between the fringe visibility and the c…
Mach-Zehnder interferometer, a powerful tool for a wide variety of measurements, has been realized with Bose-Einstein condensates in recent experiments. In this report, we propose and analyze a realizable scheme for performing a Heisenberg-limited Mach-Zehnder interferometry with dipolar spin-1 condensate. Based upon adiabatic processes of sweeping the transverse magnetic field, we demonstrate a perfect phase transition, which accomplishes the beam splitter, phase shifter and recombiner as for a Mach-Zehnder interferometer. The attractive dipolar interaction ensures the existence of a path-ent…
An ideal experiment is designed to determine the past of a particle in the nested Mach-Zehnder interferometer (MZI) by using standard quantum mechanics with quantum non-demolition measurements. We find that when the photon reaches the detector, it only follows one arm of the outer interferometer and leaves no trace in the inner MZI; while when it goes through the inner MZI, it cannot reach the detector. Our result obtained from the standard quantum mechanics is contradict to the statement based on two state vector formulism, "the photon did not enter the (inner) interferometer, the photon neve…
Griffiths [Phys. Rev. A 94, 032115 (2016)] analyzed, in the framework of consistent histories interpretation, the controversy regarding the approach to the past of a quantum particle introduced by Vaidman [Phys. Rev. A 87, 052104 (2013)]. I argue that Griffith's criticism of my approach using analysis of experiments with weak probes is unfounded.
The correctness of the consistent histories analysis of weakly interacting probes, related to the path of a particle, is maintained against the criticisms in the Comment, and against the alternative approach described there, which receives no support from standard (textbook) quantum mechanics.
We study the sensitivity of a Mach-Zehnder interferometer that contains in addition to the phase shifter a non-linear element. By including both elements in a cavity or a loop that the light transverses many times, a non-linear kicked version of the interferometer arises. We study its sensitivity as function of the phase shift, the kicking strength, the maximally reached average number of photons, and damping due to photon loss for an initial coherent state. We find that for vanishing damping Heisenberg-limited scaling of the sensitivity arises if squeezing dominates the total photon number. F…
Potocek and Ferenczi [Phys. Rev. A 92, 023829 (2015)] provided an analysis of the experimental evidence obtained by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] for the surprising behaviour of photons passing through an interferometer, in particular, motion on disconnected paths. Potocek and Ferenczi reproduced the results of the experiment, but when analyzing its modification, they claimed that the reasoning of Danan et al., which led to disconnected paths, is erroneous. It is argued here that the criticism of Potocek and Ferenczi is unfounded.
While much of the technical analysis in the preceding Comment [1] is correct, in the end it confirms the conclusion reached in my previous work [2]: a consistent histories analysis provides no support for the claim of counterfactual quantum communication put forward in [3]
We present the results of a theoretical work discussing the propagation of an electromagnetic wave through nested Mach-Zehnder interferometers using classical optics and standard quantum theory. We show that some seemingly surprising effects at first sight, which are often explained in the literature using the two-state vector formalism (TSVF), are a direct consequence of destructive or constructive interference and thus there is no need for the unconventional TSVF formulation. We show that the probability of a photon detection derived from the weak value used in TSVF can be interpreted as the…
Bartkiewicz et al. [Phys. Rev. A 91, 012103 (2015)] provided an alternative analysis of experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] which presented surprising evidence regarding the past of photons passing through an interferometer. They argued that the quantity used by Danan et al. is not a suitable which-path witness, and proposed an alternative. It is argued that the quantum and classical analyses of Bartkiewicz et al. are inconsistent and both are inappropriate for describing the past of photons in a properly working interferometer.
In this work we investigate the problem of simultaneous estimation of phases using generalised three- and four-mode Mach-Zehnder interferometer. In our setup, we assume that the phases are placed in each of the modes in the interferometer, which introduces correlations between estimators of the phases. These correlations prevent simultaneous estimation of all these phases, however we show that we can still obtain the Heisenberg-like scaling of precision of joint estimation of any subset of $d-1$ phases, $d$ being the number of modes, within completely fixed experimental setup, namely with the …
A one-dimensional waveguide enables a single two-level emitter to route the propagation of a single photon, as to provide a quantum mirror or a quantum beamsplitter. Here we present a fully-quantum Mach-Zehnder interferometer (QMZ) for single-photon pulses comprised of two quantum beamsplitters. We theoretically show how nonlinearities of the QMZ due to photon-emitter detunings and to the spectral linewidth of the pulse contribute to the versatility of the device with respect to the classical-beamsplitters scenario. We employ a quantum dynamics framework to obtain analytical expressions for th…
We propose and experimentally demonstrate two-photon interference effects in a Mach-Zehnder interferometer in which two different kinds of two-photon states are prepared by introducing a time delay between the two input photons. The two-photon states are simultaneously prepared in a symmetrically superposed state with two temporally separated photons in two different spatial modes or in the same spatial mode within the interferometer. We observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simulta…
Recently, new physics for unconditional security in a classical key distribution (USCKD) in a frame of a double Mach-Zehnder interferometer has been proposed and demonstrated as a proof of principle, where the unconditional security is unaffected by the no-cloning theorem of quantum key distribution protocols. Due to environmental phase fluctuations caused by temperature variations, atmospheric turbulences, or mechanical vibrations, active phase locking seems to be necessary for the two-channel transmission layout of USCKD. Here, the two-channel layout of USCKD is demonstrated to be an environ…
In this article, we consider the possibility of manipulation of quantum signals, ensured by the use of the tripod-type atomic memory cell. We show that depending on a configuration of driving fields at the writing and reading, such a cell allows both to store and transform the signal. It is possible to provide the operation of the memory cell in a Mach-Zehnder interferometer mode passing two successive pulses at the input. We proposed a procedure of partial signal read out that provides entanglement between the retrieved light and the atomic ensemble. Thus, we have shown that tripod atomic cel…
We demonstrated the first-order interference between coherent light at 1580 nm and 795 nm by using frequency-domain Mach-Zehnder interferometer (MZI). The MZI is implemented by two frequency-domain BSs based on a second-order nonlinear optical effect in a periodically-poled lithium niobate waveguide with a strong pump light. We achieved the visibility of over 0.99 at 50% conversion efficiencies of the BSs. Toward photonic quantum information processing, sufficiently small background photon rate is necessary. From the measurement results with a superconducting single photon detector, we discuss…
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 …
A nonlinear phase shift is introduced to a Mach-Zehnder interferometer (MZI), and we present a scheme for enhancing the phase sensitivity. In our scheme, one input port of a standard MZI is injected with a coherent state and the other input port is injected with one mode of a two-mode squeezed-vacuum state. The final interference output of the MZI is detected with the method of active correlation output readout. Based on the optimal splitting ratio of beam splitters, the phase sensitivity can beat the standard quantum limit and approach the quantum Cramér-Rao bound. The effects of photon loss …
We theoretically studied the quantum Cramér-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. …
Quantum theory allows direct measurement of the average of a non-Hermitian operator using the weak value of the positive semidefinite part of the non-Hermitian operator. Here, we experimentally demonstrate the measurement of weak value and average of non-Hermitian operators by a novel interferometric technique. Our scheme is unique as we can directly obtain the weak value from the interference visibility and the phase shift in a Mach Zehnder interferometer without using any weak measurement or post selection. Both the experiments discussed here were performed with laser sources, but the result…
Many works have stated that nonlinear interactions can improve phase sensitivity beyond the Heisenberg limit scaling of $1/N$ with $N$ being the mean photon number. This raises some open questions---among them the conclusive sensitivity limits with respect to single-mode inputs. Namely, when one of two inputs is vacuum, is there a shot-noise-style sensitivity bound on a nonlinear Mach-Zehnder interferometer? Within the reach of second-order nonlinear phase shifts, we make an attempt to provide an answer to this question. Based upon phase-averaging approach, this puzzle is partially resolved wi…
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 v…
Quantum-enhanced phase sensitivity in an all-fiber Mach-Zehnder interferometer
Université Côte d’Azur, CNRS, Institut de physique de Nice（尼斯大学，法国国家科学研究中心，尼斯物理研究所）；Télécom Paris-LTCI, Institut Polytechnique de Paris（巴黎电信学院-信息与通信研究所，巴黎理工学院）
Based on heralded interference on a six-port Mach-Zehnder interferometer, we propose protocols to generate a series of multiphoton states in primary output port, by injecting a coherent state in primary input port and two Fock states in two ancillary input ports, and measuring two Fock states in two ancillary output ports. Only manipulating at the single-photon level (i.e, |0> or |1>) in all ancillary ports, we generate sixteen types (six categories) of multiphoton nonclassical states, whose state vectors are unified as superposition of a new coherent state, a single-photon added coherent stat…
Recently, a scheme based on the method of weak measurements to register the trajectories of photons passing through a nested Mach-Zehnder interferometer was proposed [L. Vaidman, Phys. Rev. A \textbf{87}, 052104 (2013)] and then realized [A. Danan, D. Farfurnik, S. Bar-Ad, et al., Phys. Rev. Lett. \textbf{111}, 240402 (2013)]. Interpreting the results of the experiment, the authors concluded that "the photons do not always follow continuous trajectories". It is shown in this work that these results can be easily and clearly explained in terms of traditional classical electrodynamics or quantum…
In this paper we address the problem of optimizing an unbalanced Mach-Zehnder interferometer, for a given pure input state and considering a specific detection scheme. While the optimum transmission coefficient of the first beam splitter can be uniquely determined via the quantum Fisher information only [Phys. Rev. A 105, 012604 (2022)], the second beam splitter transmission coefficient is detection-scheme dependent, too. We systematically give analytic solutions for the optimum transmission coefficient of the second beam splitter for three types of widely used detection schemes. We provide de…
Entanglement distillation is the process of concentrating entanglement from a given quantum state. We present a technique for distillation of bi-partite polarization entanglement using interferometry. This technique can be optimized to extract maximal entanglement from any pure or mixed entangled state. A model for this method is presented and in particular we present experimental results for pure states when using polarizing Mach-Zehnder interferometers. These experimentally distilled states always demonstrate an increased violation of Bell's inequality.
