Complementarity lies at the heart of conceptual foundation of orthodox quantum mechanics. The wave-particle duality makes it impossible to tell which slit each particle passes through and still observe an interference pattern in a Young's double-slit experiment. In this paper, this duality is appraised under the standard formulation of quantum mechanics for atom interferometers. It is found that the internal freedoms like electronic states of an atom can be used to detect the which-path information of each atom while uphold the interference pattern of atoms when the center-of-mass motion of atoms is detected.
We study both the wave-like behavior and particle-like behavior in a general Mach-Zehnder interferometer with its asymmetric beam splitter. A error-free measurement in the detector is used to extract the which-path information. The fringe visibility V and the which-path information Ipath are derived: their complementary relation V + Ipath less than or equal to 1 are found, and the condition for the equality is also presented.
Trace-distance-based complementarity relations in a multipath interferometer
School of Mathematics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学数学学院）；School of Science, Beijing Information Science and Technology University（北京信息科技大学理学院）；Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院量子信息中心）
Wave-particle duality and complementarity principle stand at the conceptual core of quantum theory in its orthodox Copenhagen interpretation. They imply that the wave behavior and particle behavior of quantum objects are mutually exclusive to each other in experimental observation. Here we make a systematic analysis using the elementary methodology of quantum mechanics upon Young`s two-slit interferometer and Mach-Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern (wave nature) and which-way information (particle nature) of quantum objects. We desig…
Illustration of quantum complementarity using single photons interfering on a grating
最近由S. S. Afshar等人的理论被解释为违反了玻尔的互补原理，即干涉可见度和双光路干涉仪中的哪一路信息之间的互补原理。我们复制了这个实验，使用真正的单光子脉冲在一个双路波前分裂干涉仪中传播，该干涉仪是用菲涅耳双棱镜实现的，然后是一个具有可调透射狭缝的光栅。发现用可分辨性参数D表征的干涉可见度V和哪条路径信息的测量值服从互补关系V^2+D^2=<1。这一结果表明，实验可以完美地解释的量子力学的哥本哈根解释。
Two complementary observables can be measured simultaneously so that the exact individual distributions can be recovered by a proper data inversion. We apply this program to the paradigmatic example of the Young interferometer from the classical and quantum points of view. We show complete parallelism between complementarity in the quantum and classical theories. In both domains, complementarity manifests in a pathological behavior for the inferred joint distribution.
Standard quantum physics prevents the existence of a joint statistics for complementary observables. Nevertheless, a joint distribution for complementary observables can be derived from their imperfect simultaneous measurement followed by a suitable data inversion. Quantumness is reflected then in the pathologies of the inferred distribution. We apply this program to the paradigmatic example of complementarity: the wave-particle duality in a Young interferometer.
Often cited dictums in Quantum Mechanics include "observation disturbance causes loss of interference" and "ignorance is interference". In this paper we propose and describe a series of experiments with modified Mach-Zehnder interferometers showing that one has to be careful when applying such dictums. We are able to show that without interacting in any way with the light quantum (or quanta) expected to behave "wave-like", interference fringes can be lost by simply gaining (or having the potential to gain) the which-path knowledge. Erasing this information may revive the interference fringes. …
The complementarity relation between the visibility and the spectral distinguishability of frequency-displaced photonic wave-packets in a Hong-Ou-Mandel interferometer is studied. An experimental definition of $K$, the distinguishability parameter, is proposed and tested for the $K^2+\mathcal{V}^2\leq 1$ complementarity inequality when a consistent visibility parameter is defined. The results show that the spectral distinguishability is, indeed, complementary to the visibility and that the quantum aspect of the two-photon interference phenomenon can be examined by employing weak-coherent state…
We describe spontaneous parametric down-conversion experiments in which induced coherence across two coupled interferometers results in high-visibility single-photon interference. Opening additional photon channels allows "which-path" information and reduces the visibility of the singlephoton interference, but results in nearly perfect visibility when photons are counted in coincidence. A simplified theoretical model accounts for these complementary observations and attributes them directly to the relations among the vacuum fields at the different crystals.
An experimental test of quantum complementarity principle based on single neutral atom trapped in a blue detuned bottle trap was here performed. A Ramsey interferometer was used to assess the wavelike behavior or particle-like behavior with second $π/2$-rotation on or off. The wavelike behavior or particle-like behavior is characterized by the visibility $V$ of the interference or the predictability $P$ of which-path information, respectively. The measured results fulfill the complementarity relation $P^2+V^2\leq1$. Imbalance losses were deliberately introduced to the stem and find the complem…
To test the principle of complementarity and wave-particle duality quantitatively, we need a quantum composite system that can be controlled by experimental parameters. Here, we demonstrate that a double-path interferometer consisting of two parametric downconversion crystals seeded by coherent idler fields, where the generated coherent signal photons are used for quantum interference and the conjugate idler fields are used for which-path detectors with controllable fidelity, is useful for elucidating the quantitative complementarity. We show that the source purity $μ_s$ is tightly bounded by …
Complementarity and Young's interference fringes from two atoms
本文计算了三维简谐势中两个全同原子J= 1/2到J=1/2跃迁的共振荧光干涉图样。原子的热运动也包括在内。与实验[Eichmann et al.，物理修订版信函70，2359（1993）]。与一些理论预测相反，但与本计算一致，可以观察到大于50%的条纹可见度与偏振选择检测。条纹可见度对偏振的依赖性有一个简单的解释，基于原则上是否可能确定哪个原子发射光子。
Since the uncertainty about an observable of a system prepared in a quantum state is usually described by its variance, when the state is mixed, the variance is a hybrid of quantum and classical uncertainties. Besides that, complementarity relations are saturated only for pure, single-quanton, quantum states. For mixed states, the wave-particle quantifiers never saturate the complementarity relation and can even reach zero for a maximally mixed state. So, to fully characterize a quanton it is not sufficient to consider its wave-particle aspect; one has also to regard its correlations with othe…
We utilize IBM's quantum computers to perform a full quantum simulation of the optical quantum eraser (QE) utilizing a Mach-Zehnder interferometer with a variable partially-polarizing beam splitter (VPPBS) at the input. The use of the VPPBS motivates us to introduce the entangled quantum eraser, for which the path information is erased using a Bell-basis measurement. We also investigate the behavior of the wave aspect, i.e., the quantum coherence, as well as the particle character, represented by the predictability and entanglement, as delineated in complete complementarity relations (CCRs). A…
The quantum correlation of light and atomic collective excitation can be used to compose an SU(1,1)-type hybrid light-atom interferometer, where one arm in optical SU(1,1) interferometer is replaced by the atomic collective excitation. The phase-sensing probes include not only the photon field but also the atomic collective excitation inside the interferometer. For a coherent squeezed state as the phase-sensing field, the phase sensitivity can approach the Heisenberg limit under the optimal conditions. We also study the effects of the loss of light field and the dephasing of atomic excitation …
Atomic Interferometer has two quantum unitary gates that must be realized for quantum sensing purposes from atomic gravimeter and atomic interferometer gyroscope. An optimal cost function which define the distance between two unitary operator is defines and based on it a pulse based stochastic gradient descent algorithm is derived for implementation of atomic mirror and atomic beam-splitter gates. By using numerical optimal control for those gate realization, we achieved to gate fidelity of 0.995 and 0.998 for mirror and beam-splitter gates, respectively. For this research, a two-level atomic …
Coherent wave splitting is crucial in interferometers. Normally, the waves after this splitting are of the same type. But recent progress in interaction between atom and light has led to the coherent conversion of photon to atomic excitation. This makes it possible to split an incoming light wave into a coherent superposition state of atom and light and paves the way for an interferometer made of different types of waves. Here we report on a Rabi-like coherent-superposition oscillation observed between atom and light and a coherent mixing of light wave with excited atomic spin wave in a Raman …
Atomic Kapitza-Dirac (KD) scattering in the classical standing wave of lights is widely used to make the laser-pulsed atom interferometers. In this theoretical work, we show that the dielectric nanoparticle can be used as a weak light source to generate atomic KD scattering and make atom interferometer. We consider a cavity system consisting of atoms and a single nanoparticle, where the nanoparticle is illuminated by the external laser pulses. Atoms and the cavity mirrors are not illuminated by the laser beam, so nanoparticle acts as a pulsed source to excite the cavity mode which non-resonant…
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）
We derive an expression for the phase shift of an atom interferometer in a gravitational field taking into account both the finite duration of the light pulses and the effect of a small perturbing potential added to a stronger uniform gravitational field, extending the well-known results for rectangular pulses and at most quadratic potentials. These refinements are necessary for a correct analysis of present day high resolution interferometers.
Based on modern quantum measurement theory, we use Zurek's "triple model" to study, from the viewpoint of quantum information theory, the wave and particle nature of a photon in a symmetric Mach-Zehnder interferometer. In the process of quantum measurement, the state of both the system and the detector is not an entangled state but a correlated state. We find that the information gain about the photon is related to the correlations (including classical and quantum correlations) between the photon and the detector. We also derive the relationship between the information gain and the fringe visi…
Enhanced Raman scattering can be obtained by injecting a seeded light field which is correlated with the initially prepared collective atomic excitation. This Raman amplification process can be used to realize atom-light hybrid interferometer. We numerically calculate the phase sensitivities and the signal-to-noise ratios of this interferometer with the method of homodyne detection and intensity detection, and give their differences between this two methods. In the presence of loss of light field and atomic decoherence the measure precision will be reduced which can be explained by the break o…
Quantum non-demolition (QND) measurement is an important tool in the field of quantum information processing and quantum optics. The atom-light hybrid interferometer is of great interest due to its combination of atomic spin wave and optical wave, which can be utilized for photon number QND measurement via the AC-Stark effect. In this paper, we present an SU(1,1)-SU(2)-concatenated atom-light hybrid interferometer, and theoretically study the QND measurement of photon number. Compared to the traditional SU(2) interferometer, the signal-to-noise ratio (SNR) in a balanced case is improved by a g…
We propose quantum circuits to test interferometric complementarity using symmetric two-way interferometers coupled to a which-path detector. First, we consider the two-qubit setup in which the controlled transfer of path information to the detector subsystem depletes interference on the probed subspace, testing the visibility-distinguishability trade-off via minimum-error state discrimination measurements. Next, we consider the quantum eraser setup, in which reading out path information in the right basis recovers an interference pattern. These experiments are then carried out in an IBM super…
