We have constructed an atom interferometer of the Mach-Zehnder type, operating with a supersonic beam of lithium. Atom diffraction uses Bragg diffraction on laser standing waves. With first order diffraction, our apparatus has given a large signal and a very good fringe contrast (74%), which we believe to be the highest ever observed with atom interferometers. This apparatus will be applied to high sensitivity measurements
We present a precision gravimeter based on coherent Bragg diffraction of freely falling cold atoms. Traditionally, atomic gravimeters have used stimulated Raman transitions to separate clouds in momentum space by driving transitions between two internal atomic states. Bragg interferometers utilize only a single internal state, and can therefore be less susceptible to environmental perturbations. Here we show that atoms extracted from a magneto-optical trap using an accelerating optical lattice are a suitable source for a Bragg atom interferometer, allowing efficient beamsplitting and subsequen…
We explore the possibility of implementing a Heisenberg-limited Mach-Zehnder interferometry via an array of trapped ions, which obey a quantum Ising model within a transverse field. Based upon adiabatic processes of increasing the Ising interaction and then decreasing the transverse field, we demonstrate a perfect transition from paramagnetism to ferromagnetic states, which can be used as the beam splitter for the multi-ion Mach-Zehnder interferometry. The achieved NOON state of the ions enables the Heisenberg-limited interferometry. Using currently available techniques for ultracold ions, we …
We show how to implement a Mach-Zehnder interferometry based upon a string of trapped ions with artificial nonlinear interactions. By adiabatically sweeping down/up the coupling strength between two involved internal states of the ions, we could achieve the beam splitting/recombination. Based on current techniques for manipulating trapped ions, we discuss the experimental feasibility of our scheme and analyze some undesired uncertainty under realistic experimental environment.
A method for mitigating the readout delay characteristic of Bragg-based atom interferometry is presented, utilizing an asymmetric Mach-Zehnder interferometer sequence to generate spatial fringes that are read out while still overlapped. The time of flight after the final beamsplitter is engineered to facilitate constructive overlap of the fringes on the output states. A noise analysis performed using a precision atom interferometer is presented, comparing the traditional separated symmetric scheme with that of the separated and overlapped asymmetric scheme showing no significant increase in sh…
This paper presents the first realisation of a simultaneous $^{87}$Rb -$^{85}$Rb Mach-Zehnder atom interferometer with Bose-condensed atoms. A number of ambitious proposals for precise terrestrial and space based tests of the Weak Equivalence Principle rely on such a system. This implementation utilises hybrid magnetic-optical trapping to produce spatially overlapped condensates with a duty cycle of 20s. A horizontal optical waveguide with co-linear Bragg beamsplitters and mirrors is used to simultaneously address both isotopes in the interferometer. We observe a non-linear phase shift on a no…
We show that no local, hidden variable model can be given for two-channel states exhibiting both a sufficiently high interference visibility and a sufficient degree of anticorrelation in a Mach-Zehnder interferometer.
We suggest a self-testing teleportation configuration for photon q-bits based on a Mach-Zehnder interferometer. That is, Bob can tell how well the input state has been teleported without knowing what that input state was. One could imagine building a "locked" teleporter based on this configuration. The analysis is performed for continuous variable teleportation but the arrangement could equally be applied to discrete manipulations.
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…
We demonstrate that networks of locally connected processing units with a primitive learning capability exhibit behavior that is usually only attributed to quantum systems. We describe networks that simulate single-photon beam-splitter and Mach-Zehnder interferometer experiments on a causal, event-by-event basis and demonstrate that the simulation results are in excellent agreement with quantum theory.
The employment of path entangled multiphoton states enables measurement of phase with enhanced precision. It is common practice to demonstrate the unique properties of such quantum states by measuring super-resolving oscillations in the coincidence rate of a Mach-Zehnder interferometer. Similar oscillations, however, have also been demonstrated in various configurations using classical light only; making it unclear what, if any, are the classical limits of this phenomenon. Here we derive a classical bound for the visibility of super-resolving oscillations in a Mach-Zehnder. This provides an ea…
We present a method for intrusion detection which is based on the Mach-Zehnder interference effect. This device provides monitored surveillance by continuously measuring the intensity of light collected by a pair of photodetectors. We find that our protocol allows for the detection of intrusion attempts which employ path- redirection and/or intercept-resend techniques. Expectation values for the registered output flux are provided for normal and interrupted operation.
A new scheme for generating amplitude squeezed light by means of soliton self-phase modulation is experimentally demonstrated. By injecting 180-fs pulses into an equivalent Mach-Zehnder fiber interferometer, a maximum noise reduction of $4.4 \pm 0.3$ dB is obtained ($6.3 \pm 0.6$ dB when corrected for losses). The dependence of noise reduction on the interferometer splitting ratio and fiber length is studied in detail.
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…
We give an analytical result for the quantum Fisher information of entangled coherent States in a lossy Mach-Zehnder Interferometer recently proposed by J. Joo et al. [Phys. Rev. Lett. 107, 083601(2011)]. For small loss of photons, we find that the entangled coherent state can surpass the Heisenberg limit. Furthermore, The formalism developed here is applicable to the study of phase sensitivity of multipartite entangled coherent states.
We propose a scheme to achieve a Mach-Zehnder interferometry using a quantized Bose-Josephson junction with negative charging energy. The quantum adiabatic evolution through a dynamical bifurcation is used to accomplish the beam splitting and recombination. The negative charging energy ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. A feasible detection procedure is also presented. The scheme should be realizable with current technology.
Using spontaneous parametric down conversion and a 50:50 beam splitter, we generate coaxial polarization-entangled photon pairs, of which the two photons are far separated from each other. The photons are then sent one by one through one port of a modified Mach-Zehnder interferometer. We observe interference fringes with a periodicity half of the single-photon wavelength, independent of the distance between the photons. This feature can find applications in quantum-enhanced measurement.
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 effect of quantum motion in a Mach-Zehnder interferometer where ultracold, two-level atoms cross a $π/2 $-$π$-$π/2$ configuration of separated, laser illuminated regions. Explicit and exact expressions are obtained for transmission amplitudes of monochromatic, incident atomic waves using recurrence relations which take into account all possible paths: the direct ones usually considered in the simple semiclassical treatment, but including quantum motion corrections, and the paths in which the atoms are repeatedly reflected at the fields.
We investigate the dependence of the fidelity of a Mach-Zehnder quantum interferometer on the prior information about the phase, for Fock state input and for maximally entangled (N00N) state input. For no prior information, the fidelity for Fock state input is greater than for N00N state input. In the limit of a narrow distribution describing the prior information, we find that both Fock and N00N state inputs lead to nearly equal fidelity.
The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for factoring $N$ by means of an N-slit interference experiment is translated into an experiment with a single Mach-Zehnder interferometer. With dispersive phase shifters the ratio of the coherence length to wavelength limits the numbers that can be factored. A conservative estimate permits $N \approx 10^7$. It is furthermore shown, that sine and cosine Fourier coefficients of a real periodic function can be obtained with such an interferometer.
We experimentally demonstrate that a long distance actively stabilized Mach-Zehnder fibre optical interferometer can be used to reliably implement the GV95 quantum cryptography protocol employing orthogonal states. A proof-of-principle experiment using an interferometer composed of 1 km of spooled optical fibres connecting Alice and Bob is performed. The active stabilisation against phase drifts is done with a classical channel wavelength-multiplexed with the quantum channel and a high stable visibility implying a QBER of 2.2 % is shown.
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 theoretically analyze a Mach-Zehnder interferometer with trapped condensates, and find that it is surprisingly stable against the nonlinearity induced by inter-particle interactions. The phase sensitivity, which we study for number squeezed input states, can overcome the shot noise limit and be increased up to the Heisenberg limit provided that a Bayesian or Maximum-Likelihood phase estimation strategy is used. We finally demonstrate robustness of the Mach-Zehnder interferometer in presence of interactions against condensate oscillations and a realistic atom counting error.
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…
We discuss complementarity and uncertainty in a gedanken Which-Way (Welcher-Weg) experiment in a Mach-Zehnder interferometer. Although a Welcher-Weg measurement can be performed with only a negligible amount of momentum change in the detector itself, the change in the interference pattern must correspond to a change in the momentum distribution of the particle. Entanglement between the Mach-Zehnder interferometer and the Welcher-Weg measurement introduces orthogonality that disables the interference of the particle, but simultaneously, it also generates a momentum transfer between the particle…
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 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 rel…
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…
We study the coherent transport of single photon in a one-dimensional coupled-resonator-array, "non-locally" coupled to a two-level system. Since its inherent structure is a Mach-Zehnder interferometer, we explain the destructive interference phenomenon of the transmission spectrums according to the effect of which-way detection. The quantum realization of the present model is a nano-electromechanical resonator arrays with two nearest resonators coupled to a single spin via their attached magnetic tips. Its classical simulation is a waveguide of coupled defected cavity array with double coupli…
The best performance of a Mach-Zehnder interferometer is achieved with the input state |N_T/2 + 1>|N_T/2-1 > + |N_T/2 - 1>|N_T/2+1>, being N_T the total number of atoms/photons. This gives: i) a phase-shift error confidence C_{68%}=2.67/N_T with ii) a single interferometric measurement. Different input quantum states can achieve the Heisenberg scaling ~ 1/N_T but with higher prefactors and at the price of a statistical analysis of two or more independent measurements.
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…
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.
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.
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…
The high inertial sensitivity of atom interferometers has been used to build accelerometers and gyrometers but this sensitivity makes these interferometers very sensitive to the laboratory seismic noise. This seismic noise induces a phase noise which is large enough to reduce the fringe visibility in many cases. We develop here a model calculation of this phase noise in the case of Mach-Zehnder atom interferometers and we apply this model to our thermal lithium interferometer. We are thus able to explain the observed dependence of the fringe visibility with the diffraction order. The dynamical…
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 …
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…
Atom interferometers are very sensitive to accelerations and rotations. This property, which has some very interesting applications, induces a deleterious phase noise due to the seismic noise of the laboratory and this phase noise is sufficiently large to reduce the fringe visibility in many experiments. We develop a model calculation of this phase noise in the case of Mach-Zehnder atom interferometers and we apply this model to our thermal lithium interferometer. We are able to explain the observed phase noise which has been detected through the rapid dependence of the fringe visibility with …
We are developing a Quantum Interactive Learning Tutorial (QuILT) on a Mach-Zehnder Interferometer with single photons to expose upper-level students in quantum mechanics courses to contemporary applications. The QuILT strives to help students develop the ability to apply fundamental quantum principles to physical situations and explore differences between classical and quantum ideas. The QuILT adapts visualization tools to help students build physical intuition about quantum phenomena and focuses on helping them integrate qualitative and quantitative understanding. We also discuss findings fr…
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…
Photon counting measurements are analyzed for obtaining a classical phase parameter in linear Mach Zehnder interferometer (MZI), by the use of phase estimation theories. The detailed analysis is made for four cases: a) Coherent states inserted into the interferometer. b) Fock number state inserted in one input port of the interferometer and the vacuum into the other input port. c) Coherent state inserted into one input port of the interferometer and squeezed-vacuum state in the other input port. d) Exchanging the first beam-splitter (BS1) of a MZI by a non-linear system which inserts a NOON st…
We study a single-electron pulse injected into the chiral edge-state of a quantum Hall device and subject to a capacitive Coulomb interaction. We find that the scattered multi-particle state remains unentangled and hence can be created itself by a suitable classical voltage-pulse $V(t)$. The application of the inverse pulse $-V(-t)$ corrects for the shake-up due to the interaction and resurrects the original injected wave packet. We suggest an experiment with an asymmetric Mach-Zehnder interferometer where the application of such pulses manifests itself in an improved visibility.
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 …
