Interference and ‘which way’ information

An overview is given of typical examples of interference experiments that confirm the general quantum mechanical rule that distinguishability of the paths destroys interference. It will be shown that path information can be gained in different ways: from the screen's or the atom's recoil in Young-type optical experiments; from the spontaneously emitted photon in atom optics; and from the idler photon, in a striking interference experiment with a photon pair being involved. In all cases, the physical mechanism that actually makes the interference pattern disappear is elucidated.     

Single-photon wavefront-splitting interference

We present a new realization of the textbook experiment consisting in single-photon interference based on the pulsed, optically excited photoluminescence of a single colour centre in a diamond nanocrystal. Interferences are created by wavefront-splitting with a Fresnel’s biprism and observed by registering the “single-photon clicks” with an intensified CCD camera. This imaging detector provides also a real-time movie of the build-up of the single-photon fringes. We perform a second experiment with two detectors sensitive to photons that follow either one or the other interference path. Evidence for single photon behaviour is then obtained from the absence of time coincidence between detections in these two paths. Electronic supplementary material Online Material -- Movies showing the built-up of the interference pattern Gradual build-up of the interference pattern can be observed in the animated movies presented hereafter.     

Controlled decoherence in multiple beam Ramsey interference

We have scattered photons from an interfering path of a multiple beam Ramsey interference experiment realized with a cesium atomic beam. It is demonstrated that in multiple beam interference the decoherence from photon scattering cannot only lead to a decrease but, under certain conditions, also to an increase of the Michelson fringe contrast. In all cases, the atomic quantum state loses information with photon scattering, as "which-path" information is carried away by the photon field. We outline an approach to quantify this which-path information from observed fringe signals, which allows for an appropriate measure of decoherence in multiple path interference.     

Some realizable joint measurements of complementary observables

Noncommuting quantum observables, if considered asunsharp observables, are simultaneously measurable. This fact is exemplified for complementary observables in two-dimensional state spaces. Two proposals of experimentally feasible joint measurements are presented for pairs of photon or neutron polarization observables and for path and interference observables in a photon split-beam experiment. A recent experiment proposed and performed by Mittelstaedt, Prieur, and Schieder in Cologne is interpreted as a partial version of the latter example.Work partly supported by the DFG, Bonn, and the BMFT, Bonn.Dedicated to Professor Ulrich Hauser on the occasion of his 60th birthday, November 1986.     

基于马赫-曾德尔干涉仪的单个光子操控

分别利用空间和光纤马赫—曾德尔干涉仪对空间和光纤传输中的单个光子的干涉现象进行了研究,干涉对比度可达到90％以上,实现了空间和光纤中的单个光子的路由操控。实验采用脉冲调制加衰减的方法产生单个光子,获得了每个脉冲中只包含0．1个光子的准单光子源。通过改变压电换能器的电压控制马赫—曾德尔干涉仪的单个光子在两个输出端的选择,实现了光子在节点上的路由。采用同步符合检测技术,利用重复频率为1kHz,脉冲宽度为100ns的同步信号对输出信号进行符合,实现了量子效率高于70％,暗计数小于0．2s^-1的单光子高灵敏度检测,观测到了单个光子在相位操控下出射到两个输出端的有序分配现象。验证了基于马赫—曾德尔干涉仪的单个光子路由操控实现的可能性。     

Wave-particle duality using the Compton effect

Thought experiments based on the double-slit interferometer had a crucial role to develop ideas concerning the wave-particle duality and the Bohr's complementarity principle. Ideally, a slit with a sufficiently low mass recoils due to the passage of the photon. This motion denounces the path taken by the light and suppresses any attempt to observe an interference pattern. In real life, however, available which-way information in such a setup is significantly impaired by the typical magnitudes of photons and slits, making the verification of the effect almost impossible. Here, we extend this discussion by applying similar ideas to the Mach-Zehnder interferometer. That is, we study the consequences of the beam-splitter recoil, during the passage of the photon, over the interference pattern produced by the device. Unlike the double-slit experiment, this recoil can now be encoded in the wavelength of the photon itself, which, in principle, is more easily accessed. Fortuitously, the model used to describe the interaction between the idealized beam-splitter and the photon clearly indicates that an interferometer based on Compton's effect could be build to study wave-particle duality. We follow this hint, finding realistic experimental parameters needed to observe the trade-off between wave and corpuscular behaviors in such a modified interferometer.     

Quantum Nonlocality of Photon Pairs in Interference in a Mach-Zehnder Interferometer

Nonlocal character of entangled photon pairs generated in spontaneous parametric downconversion is demonstrated. One photon from a pair propagates through a Mach-Zehnder interferometer and is detected in coincidence-count measurement with its twin. Width of the coincidence-count interference pattern (measured for various values of path difference in the Mach-Zehnder interferometer) depends on spectral width of the twin as a result of entanglement of photons in a pair. The experimental setup is analyzed for a Gaussian spectral filter and a Fabry-Perot resonator. It is shown that nonlocal interference is much stronger for cw pumping in comparison with femtosecond pulsed pumping for values of parameters commonly used in spontaneous parametric downconversion experiments.     

Quantum information and microscopic measuring instruments

The consideration of measuring instruments as macroscopic bodies leads to neglect of the microscopic processes that occur during measurements. This disregard is not justified in general cases. As an example of measurements using microscopic instruments, the scattering of a photon by an electron with electron interference at two slits(Compton effect) was used. The amount of information that can be obtained in such a process is inversely proportional to the wavelength of the incident photon. At large photon wavelengths(soft measurements), the pure state of the electron can be disrupted by an arbitrarily small extent; accordingly, the amount of information extracted in such an experiment is also arbitrarily small. It is shown that the energy price for a bit obtained in such a measurement tends toward a constant value for increasing the photon wavelength. Microscopic instruments can be used in situations where energy costs for measurements are important.     

Quantum nonlocality and interference in frequency domain

The experiment is proposed which should demonstrate that if the filter providing the spectral selection is placed in the route of one photon of the entangled pair produced by spontaneous down-conversion and the photon is detected behind it then the interference appears in the (distant) Mach-Zehnder interferometer placed in the route of the other photon of the pair even if the optical path difference through the interferometer greatly exceeds the coherence length of the light and if the spectra of these two photons do not overlap. The theoretical analysis is carried out and physical interpretation is discussed.     

Fiber-based source of photon pairs at telecom band with high temporal coherence and brightness for quantum information processing

We experimentally demonstrate a bright pulsed source of correlated photon pairs at the 1550 nm telecom band by pumping 300 m dispersion-shifted fiber with a 4 ps pulse train. We investigate the coherence property of the source by measuring the second-order intensity correlation function g(2) of individual signal (idler) photons. A preliminary Hong-Ou-Mandel-type two-photon interference experiment with two such sources confirms the high temporal and spatial coherence of the source. The source is suitable for multiphoton quantum interference of independent sources, which is required in quantum information processing.     

两个独立全光纤多通道光子纠缠源的Hong-Ou-Mandel干涉

独立光子源的干涉是实现复杂量子体系应用(比如多光子纠缠态产生和量子隐形传态等)的核心技术.利用100 GHz密集波分复用技术,实现了1.55μm全光纤多通道独立纠缠光子源的Hong-Ou-Mandel干涉,在不去除暗符合(随机符合计数)的情况下,可见度为53.2%±8.4%,去除暗符合可见度可达到82.9%±5.3%.给出了关于色散位移光纤中基于自发四波混频过程产生的单光子光谱纯度严格的理论描述,模拟了抽运脉冲宽度和滤波器带宽对单光子光谱纯度的影响,并给出了理论上的最佳条件(最佳的抽运脉冲宽度为8 ps,高斯滤波器带宽为40 GHz及以下).在测量Hong-Ou-Mandel干涉之前,先测量了液氮冷却状态下的色散位移光纤关联光子源的符合和随机符合比率,在抽运功率为23μW的情况下,最大比率可以达到131.Hong-Ou-Mandel干涉在高精度光学测量、测量装置无关的量子密钥分配等应用中扮演着极为重要的角色.     

Interference of multimode photon echoes generated in spatially separated solid-state atomic ensembles

High-visibility interference of photon echoes generated in spatially separated solid-state atomic ensembles is demonstrated. The solid-state ensembles were LiNbO(3) waveguides doped with erbium ions absorbing at 1.53 microm. Bright coherent states of light in several temporal modes (up to 3) are stored and retrieved from the optical memories using two-pulse photon echoes. The stored and retrieved optical pulses, when combined at a beam splitter, show almost perfect interference, which demonstrates both phase preserving storage and indistinguishability of photon echoes from separate optical memories. By measuring interference fringes for different storage times, we also show explicitly that the visibility is not limited by atomic decoherence. These results are relevant for novel quantum-repeater architectures with photon-echo based multimode quantum memories.     

Multiple-beam Ramsey interference and quantum decoherence

We study the effect of photon scattering from a path of a four-beam atomic interference setup, which is based on a cesium atomic beam and two subsequent optical Ramsey pulses projecting the atoms onto a multilevel dark state. While in two-beam interference, any attempt to keep track of an interfering path reduces the fringe contrast, we demonstrate that photon scattering in a multiple-path arrangement cannot only lead to a decrease, but - under certain conditions - also to an increase of the interference contrast. The results are confirmed by a density-matrix calculation. We are aware that in all cases the “which-path” information carried away by the scattered photons leads to a loss of information that is contained in the atomic quantum state. An approach to quantify this “which-path” information using observed fringe signals is presented; it allows for an appropriate measure of quantum decoherence in multiple-path interference. Received: 27 July 2000 / Published online: 6 December 2000     

Entanglement generation by Fock-state filtration

We demonstrate a Fock-state filter which is capable of preferentially blocking single photons over photon pairs. The large conditional nonlinearities are based on higher-order quantum interference, using linear optics, an ancilla photon, and measurement. We demonstrate that the filter acts coherently by using it to convert unentangled photon pairs to a path-entangled state. We quantify the degree of entanglement by transforming the path information to polarization information; applying quantum state tomography we measure a tangle of T=(20+/-9)%.     

Comprehensive experimental test of quantum erasure

In an interferometer, path information and interference visibility are incompatible quantities. Complete determination of the path will exclude any possibility of interference, rendering zero visibility. However, it is, under certain conditions, possible to trade the path information for improved (conditioned) visibility. This procedure is called quantum erasure. We have performed such experiments with polarization-entangled photon pairs. Using a partial polarizer, we could vary the degree of entanglement between the object and the probe. We could also vary the interferometer splitting ratio and thereby vary the a priori path predictability. This allowed us to test quantum erasure under a number of different experimental conditions. All experiments were in good agreement with theory. Received 15 July 2001 and Received in final form 30 November 2001     

Diffraction of entangled photon pairs by ultrasonic waves

In this paper, we have presented and established a new theoretical formulation of photon optics based on photon path and Feynman path integral idea. We have used Feynman path integral approach to discuss Fraunhofer, Fresnel diffraction of single photon and entangled photon pairs by ultrasonic wave and obtained the following results: i) quantum state and probability distribution of single photon and entangled photon pairs by Fraunhofer and Fresnel ultrasonic diffraction, ii) oblique incidence Raman-Nath and Bragg diffraction conditions, iii) total correlation state and its probability distribution. Our calculation results are in agreement with the experiment results. Comparing one-photon and two-photon diffraction effects by ultrasonic waves, we have found that two-photon diffraction by ultrasonic waves is also a sub-wavelength diffraction.     

Observation of scissors modes in solid state systems with a SQUID

The occurrence of scissors modes in crystals that have deformed ions in their unit cells was predicted some time ago. The theoretical value of their energy is rather uncertain, however, ranging between ten and a few tens of eV, with the corresponding widths of 10^?7 to 10^?6 eV. Their observation by resonance fluorescence experiments therefore requires a photon spectrometer covering a wide energy range with a very high resolving power. Here, a new experiment is proposed and discussed in which such difficulties are overcome by measuring with a superconducting quantum interference device (SQUID) the variation of the magnetic field associated with the excitation of scissors modes.     

First-order photon interference of a single photon from a single quantum dot

Photon interference indicating wave-like nature of a single photon emitted from a single quantum dot is demonstrated. Photon state as a superposition of two orthogonal linear polarization modes is prepared inside a solid-state single photon source, which causes the first-order interference analogous to the Young’s double slit experiment. The lack of which-mode information is essential for observing the single photon interference.     

Another proof that the future can influence the present

A modified Young double-slit experiment proposed by Wootters and Zurek is considered in which a system P of parallel plates covered with a photographic emulsion has been set up in the region where we would normally expect the central interference fringes. Because under certain conditions P makes it possible to conclude with much more than50% certainty through which of the two slits each particular photon passed, the relevant interference pattern becomes blurred. It is proved that this implies a retroactive effect because the setup of P and the interaction of photons with P appear to influence the momentum transferred to the photons by the edges of the slits at an earlier stage of the experiment.     

Measurement-based entanglement under conditions of extreme photon loss

The act of measuring optical emissions from two remote qubits can entangle them. By demanding that a photon from each qubit reaches the detectors, one can ensure that no photon was lost. But retaining both photons is rare when loss rates are high, as in Moehring et al. where 30 successes occurred per 10(9) attempts. We describe a means to exploit the low grade entanglement heralded by the detection of a lone photon: A subsequent perfect operation is quickly achieved by consuming this noisy resource. We require only two qubits per node, and can tolerate both path length variation and loss asymmetry. The impact of photon loss upon the failure rate is then linear; realistic high-loss devices can gain orders of magnitude in performance and thus support quantum computing.