Two-path Interferometer Research Articles

Illustration of quantum complementarity using single photons interfering on a grating

A recent experiment performed by Afshar et al (2007 Found. Phys. 37 295–305) has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information (WPI) in a two-path interferometer. We have reproduced this experiment, using true single-photon pulses propagating in a two-path wavefront-splitting interferometer realized with a Fresnel's biprism, and followed by a grating with adjustable transmitting slits. The measured values of interference visibility V and WPI, characterized by the distinguishability parameter D, are found to obey the complementarity relation V2+D2⩽1. This result demonstrates that the experiment can be perfectly explained by the standard interpretation of quantum mechanics.

Quantum mechanical complementarity probed in a closed-loop Aharonov–Bohm interferometer

The complementarity principle1 demands that a particle reveals wave-like properties only when the different paths that it can take are indistinguishable2,3. The complementarity has been demonstrated in optics with pairs of correlated photons4,5 and in two-path solid-state interferometers with phase-coherent electrons6. In the latter experiment, a charge detector embedded near one path of a two-path electron interferometer provided which-path information3. Here, we report on electron dephasing in an Aharonov–Bohm ring interferometer7 via a charge detector adjacent to the ring. In contrast to the two-path interferometer, charge detection in the ring does not always provide path information. The interference was suppressed only when path information could be acquired, even if only in principle. This confirms that dephasing is not always induced by ‘disturbing’ the interfering particle through the interferometer–environment interactions: path information of the particle must be available too. Our experiment suggests that acquisition of which-path information is more fundamental than the back-action in understanding quantum mechanical complementarity.

WAVE-PARTICLE DUALITY IN MULTI-PATH INTERFEROMETERS: GENERAL CONCEPTS AND THREE-PATH INTERFEROMETERS

For two-path interferometers, the which-path predictability [Formula: see text] and the fringe visibility [Formula: see text] are familiar quantities that are much used to talk about wave-particle duality in a quantitative way. We discuss several candidates that suggest themselves as generalizations P of [Formula: see text] for multi-path interferometers, and treat the case of three paths in considerable detail. To each choice for the path knowledge P, the interference strength V — the corresponding generalization of [Formula: see text] — is found by a natural, operational procedure. In experimental terms, it amounts to finding those equal-weight superpositions of the path amplitudes which maximize P for the emerging intensities. Mathematically speaking, one needs to identify a certain optimum one among the Fourier transforms of the state of the interfering quantum object. Wave-particle duality is manifest, inasmuch as P = 1 implies V = 0 and V = 1 implies P = 0, whatever definition is chosen. The possible values of the pair (P,V) are restricted to an area with corners at (P,V) = (0,0), (P,V) = (1,0), and (P,V) = (0,1), with the shape of the border line from (1,0) to (0,1), depending on the particular choice for P and the induced definition of V.

Electronic Mach-Zehnder quantum eraser

We propose an electronic quantum eraser in which the electrons are injected into a mesoscopic conductor at the quantum Hall regime. The conductor is composed of a two-path interferometer which is an electronic analogue of the optical Mach-Zehnder interferometer, and a quantum point contact detector capacitively coupled to the interferometer. While the interference of the output current at the interferometer is shown to be suppressed by the which-path information, we show that the which-path information is erased by the zero-frequency cross correlation measurement between the interferometer and the detector output leads. We also investigate a modified setup in which the detector is replaced by a two-path interferometer.We show that the path distinguishability and the visibility of the joint detection can be controlled in a continuous manner, and satisfy a complementarity relation for the entangled electrons.

Entanglement, Dephasing, and Phase Recovery via Cross-Correlation Measurements of Electrons

Determination of the path taken by a quantum particle leads to a suppression of interference and to a classical behavior. We employ here a quantum "which path" detector to perform accurate path determination in a two-path Mach-Zehnder electron interferometer, leading to full suppression of the interference. Following the dephasing process we recover the interference by measuring the cross correlation between the interferometer and detector currents. Under our measurement conditions every interfering electron is dephased by approximately a single electron in the detector-leading to mutual entanglement of approximately single pairs of electrons.

Experimental Realization of Wheeler's Delayed-Choice Gedanken Experiment

Wave-particle duality is strikingly illustrated by Wheeler's delayed-choice gedanken experiment, where the configuration of a two-path interferometer is chosen after a single-photon pulse has entered it: Either the interferometer is closed (that is, the two paths are recombined) and the interference is observed, or the interferometer remains open and the path followed by the photon is measured. We report an almost ideal realization of that gedanken experiment with single photons allowing unambiguous which-way measurements. The choice between open and closed configurations, made by a quantum random number generator, is relativistically separated from the entry of the photon into the interferometer.

Charge detection in a closed-loop Aharonov-Bohm interferometer

We report on a study of complementarity in a two-terminal closed-loop Aharonov-Bohm interferometer. In this interferometer, the simple picture of two-path interference cannot be applied. We introduce a nearby quantum point contact to detect the electron in a quantum dot inserted in the interferometer. We found that charge detection reduces but does not completely suppress the interference even in the limit of perfect detection. We attribute this phenomenon to the unique nature of the closed-loop interferometer. That is, the closed-loop interferometer cannot be simply regarded as a two-path interferometer because of multiple reflections of electrons. As a result, there exist indistinguishable paths of the electron in the interferometer and the interference survives even in the limit of perfect charge detection. This implies that charge detection is not equivalent to path detection in a closed-loop interferometer. We also discuss the phase rigidity of the transmission probability for a two-terminal conductor in the presence of a detector.

Efficient comparison of path-lengths using Fourier multiport devices

We present a scheme for comparing effective path-lengths through a spatial region by using multipath generalizations of a Mach–Zehnder interferometer. This enables us to identify paths that have different lengths from the others with exponentially fewer measurements than would be required by repeated measurements with a standard two-path interferometer. We show that this scheme is extremely sensitive to small variations in the paths, which means it could be used to measure the variance of the path-lengths accurately and efficiently. Possible applications include accurately measuring spatial variations of potential fields and efficiently identifying which of many cavities contains an atom.

An electronic Mach-Zehnder interferometer.

Double-slit electron interferometers fabricated in high mobility two-dimensional electron gases are powerful tools for studying coherent wave-like phenomena in mesoscopic systems. However, they suffer from low visibility of the interference patterns due to the many channels present in each slit, and from poor sensitivity to small currents due to their open geometry. Moreover, these interferometers do not function in high magnetic fields--such as those required to enter the quantum Hall effect regime--as the field destroys the symmetry between left and right slits. Here we report the fabrication and operation of a single-channel, two-path electron interferometer that functions in a high magnetic field. This device is the first electronic analogue of the optical Mach-Zehnder interferometer, and opens the way to measuring interference of quasiparticles with fractional charges. On the basis of measurements of single edge state and closed geometry transport in the quantum Hall effect regime, we find that the interferometer is highly sensitive and exhibits very high visibility (62%). However, the interference pattern decays precipitously with increasing electron temperature or energy. Although the origin of this dephasing is unclear, we show, via shot-noise measurements, that it is not a decoherence process that results from inelastic scattering events.

All-fiber three-path Mach–Zehnder interferometer

We report the realization of a three-path Mach-Zehnder interferometer using single-mode fibers and two integrated 3 x 3 fiber couplers. We observed enhanced phase sensitivity, as compared with two-path interferometers, with a visibility of the interference pattern of more than 97%. This interferometer has an analog in two-photon interferometry, and we believe it to be the first nontrivial example of N x N multiport interferometers.

Neutron interferometry in a gravity field

Abstract Quantitative understanding of the effects of external forces in three-crystal neutron interferometry is achieved by realizing that the three-crystal system is in fact an eight-path interferometer and not the two-path interferometer of previous descriptions. The approach explains damping of the interferometer oscillations with increasing applied force, even for an ideal unbent crystal and a monochromatic beam.

Correlated laser spectral and intensity noise in short-path-difference interferometers

A novel technique has been developed for stabilising against drift and vibration the path difference of a Michelson two-path interferometer. The technique has enabled measurements to be made for the first time of semiconductor laser noise around individual interference fringes near to, and including, zero order. Minimum noise was not detected at zero path difference as had been expected: this characteristic may be explained by assuming partial correlation between the source intensity and demodulated spectral noises.

Anisotropic Electrical Properties of Coal

This study has made use of a two-path interferometer at microwave frequencies (9 GHz) to measure the dielectric constant and conductivity of coal as a function of direction of propagation and polarization of the electromagnetic wave within the coal. Four types of eastern bituminous coal of various rank and one type of eastern anthracite coal were studied, and the effects of the physical properties (rank and anisotropy, pyrite concentration and distribution, moisture content and other mineral matter concentration) on the conductivity and dielectric constant were investigated. In general, moisture increases the conductivity and dielectric constant: however, pyrite layers along the bedding planes of the bituminous coals cause a general increase in conductivity. The anthracites (higher rank coals) have larger values of conductivity (about a factor of 10) and permittivity (about a factor of 2 to 3) than the bituminous (lower rank) coals. Further, models of optical anisotropy seem to correlate quite well with the anisotropy of the electrical properties of anthracites. No distinct relationship was found between the direction of propagation and the electrical properties.

Optical fiber acoustic sensor utilizing mode-mode interference

A method for detecting sound using a single step-index multimode fiber is presented. The detected signal results from differences in acoustically induced phase shifts between two different waveguide modes propagating in the fiber. The relative sensitivity of this technique compared with a two-path interferometer was experimentally determined and agreed with that calculated using the fiber parameters. Because the sensitivity of this approach is proportional to the difference in propagation constants for modes in the fiber, it is approximately 10(-3) less sensitive than the single-mode interferometer arrangement.

Electrical Properties of Eastern Bituminous Coal as a Function of Frequency, Polarization and Direction of the Electromagnetic Wave, and Temperature of the Sample

The development of electromagnetic systems to detect and monitor an in situ underground coal gasification process requires a knowledge of the electrical properties of coal. Using a two-path interferometer at microwave frequencies (≃9 GHz), the samples of solid eastern bituminous coal were tested as a function of temperature, electric-field polarization, and direction of the coal samples. There were slight decreases in the dielectric constant and conductivity of coal as a function of temperature from ambient up to 700°F. However, there were significant variations in the conductivity as a function of polarization, with the vertical polarization possessing lower conductivity. Only slight changes in conductivity were detected as a function of direction, with the face cleats exhibiting somewhat higher losses. The dielectric constant remained essentially constant as a function of polarization and direction of the electromagnetic wave. Measurements of electrical properties of coal were also made in the 0.5-100-MHz region using capacitance techniques. In general, there was a decrease in the values of dielectric constant and an increase in conductivity as the frequency increased.