Quantum Mechanical Superposition States Research Articles

Interactive homework to support student learning of measurement uncertainty in quantum mechanics

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] When thinking about measurement uncertainty in a laboratory experiment that features quantum mechanical effects, it is important to consider both the physical principles of underlying quantum theory (e.g., the uncertainty due to quantum mechanical superposition states) as well as the limitations of the measurement (e.g., the spread in outcomes due to instrumental imperfections). Prior research has found student difficulties with these sources of uncertainty both individually and in students’ ability to distinguish between them. Additionally, students are less likely to access ideas related to experimental uncertainty in quantum mechanical contexts unless explicitly prompted. In this work, we have developed a simulation-homework activity focused on the Stern-Gerlach experiment to help students develop an understanding for the different ways that modifying the quantum state, improving the experimental setup, or collecting more data, will affect the resulting outcome distribution. The activity uses a purpose-built interactive simulation, coupled with homework questions grounded in the literature on student thinking about uncertainty. We analyze the effectiveness of the activity with students in junior-level undergraduate quantum mechanics courses using pre- and post-testing. The results indicate that the activity was successful in helping students distinguish between quantum mechanical uncertainty and uncertainty caused by instrumental imperfections, and in increasing the accessibility of instrumental limitations in this context. The activity can thus support student understanding of the core concept of quantum uncertainty, as well as link between the often abstract nature of quantum theory and laboratory experiments with their limitations. Published by the American Physical Society 2024

Cellular automaton ontology, bits, qubits and the Dirac equation

Cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its ontological states that evolve by permutations, in this way never creating would-be quantum mechanical superposition states. We review and illustrate this with a classical Ising spin chain. It is shown that it can be related to the Weyl equation in the continuum limit. Yet, the model of discrete spins or bits unavoidably becomes a model of qubits by generating superpositions, if only slightly deformed. We study modifications of its signal velocity which, however, do not relate to mass terms. To incorporate the latter, we consider the Dirac equation in 1+1 dimensions and sketch an underlying discrete deterministic “necklace of necklaces” automaton that qualifies as ontological.

Mathematical Model for Excited State Fluid Dynamics

The rational mechanic’s research method is synthesized with the help of mathematical means such as generalized function analysis and tensor analysis. The basic definition of the fluctuation velocity generation is based on phenomenological physics in this article. The basic control equations of general excited state fluid dynamics applicable to the flowfield are obtained based on the basic principles of quantum mechanical superposition states. The simplified basic equations of the excited State are finally obtained through time and space discretization. The basic theory of excited state fluid dynamics is established, providing new ideas for the innovation and application of flow control, fluid mechanical engineering design, and other aspects of research work.

Orbital angular momentum superposition states in transmission electron microscopy and bichromatic multiphoton ionization

The coherent control of electron beams and ultrafast electron wave packet dynamics have attracted significant attention in electron microscopy as well as in atomic physics. In order to unify the conceptual pictures developed in both fields, we demonstrate the generation and manipulation of tailored electron orbital angular momentum (OAM) superposition states either by employing customized holographic diffraction masks in a transmission electron microscope or by atomic multiphoton ionization utilizing pulse-shaper generated carrier-envelope phase stable bichromatic ultrashort laser pulses. Both techniques follow similar physical mechanisms based on Fourier synthesis of quantum mechanical superposition states allowing the preparation of a broad set of electron states with uncommon symmetries. We describe both approaches in a unified picture based on an advanced spatial and spectral double slit and point out important analogies. In addition, we analyze the topological charge and discuss the control mechanisms of the free-electron OAM superposition states. Their generation and manipulation by phase tailoring in transmission electron microscopy and atomic multiphoton ionization is illustrated on a 7-fold rotationally symmetric electron density distribution.

Single Photon Randomness based on a Defect Center in Diamond

The prototype of a quantum random number generator is a single photon which impinges onto a beam splitter and is then detected by single photon detectors at one of the two output paths. Prior to detection, the photon is in a quantum mechanical superposition state of the two possible outcomes with –ideally– equal amplitudes until its position is determined by measurement. When the two output modes are observed by a single photon detector, the generated clicks can be interpreted as ones and zeros – and a raw random bit stream is obtained. Here we implement such a random bit generator based on single photons from a defect center in diamond. We investigate the single photon emission of the defect center by an anti-bunching measurement. This certifies the “quantumness” of the supplied photonic input state, while the random “decision” is still based on the vacuum fluctuations at the open port of the beam-splitter. Technical limitations, such as intensity fluctuations, mechanical drift, and bias are discussed. A number of ways to suppress such unwanted effects, and an a priori entropy estimation are presented. The single photon nature allows for a characterization of the non-classicality of the source, and allows to determine a background fraction. Due to the NV-center’s superior stability and optical properties, we can operate the generator under ambient conditions around the clock. We present a true 24/7 operation of the implemented random bit generator.

Multidimensional Spectral Fingerprints of a New Family of Coherent Analytical Spectroscopies.

Triply resonant sum frequency (TRSF) and doubly vibrationally enhanced (DOVE) spectroscopies are examples of a recently developed family of coherent multidimensional spectroscopies (CMDS) that are analogous to multidimensional NMR and current analytical spectroscopies. CMDS methods are particularly promising for analytical applications because their inherent selectivity makes them applicable to complex samples. Like NMR, they are based on creating quantum mechanical superposition states that are fully coherent and lack intermediate quantum state populations that cause quenching or other relaxation effects. Instead of the nuclear spin states of NMR, their multidimensional spectral fingerprints result from creating quantum mechanical mixtures of vibrational and electronic states. Vibrational states provide spectral selectivity, and electronic states provide large signal enhancements. This paper presents the first electronically resonant DOVE spectra and demonstrates the capabilities for analytical chemistry applications by comparing electronically resonant TRSF and DOVE spectra with each other and with infrared absorption and resonance Raman spectra using a Styryl 9 M dye as a model system. The methods each use two infrared absorption transitions and a resonant Raman transition to create a coherent output beam, but they differ in how they access the vibrational and electronic states and the frequency of their output signal. Just as FTIR, UV-vis, Raman, and resonance Raman are complementary methods, TRSF and DOVE methods are complementary to coherent Raman methods such as coherent anti-Stokes Raman spectroscopy (CARS).

Applications of the New Family of Coherent Multidimensional Spectroscopies for Analytical Chemistry.

A new family of vibrational and electronic spectroscopies has emerged, comprising the coherent analogs of traditional analytical methods. These methods are also analogs of coherent multidimensional nuclear magnetic resonance (NMR) spectroscopy. This new family is based on creating the same quantum mechanical superposition states called multiple quantum coherences (MQCs). NMR MQCs are mixtures of nuclear spin states that retain their quantum mechanical phase information for milliseconds. The MQCs in this new family are mixtures of vibrational and electronic states that retain their phases for picoseconds or shorter times. Ultrafast, high-intensity coherent beams rapidly excite multiple states. The excited MQCs then emit bright beams while they retain their phases. Time-domain methods measure the frequencies of the MQCs by resolving their phase oscillations, whereas frequency-domain methods measure the resonance enhancements of the output beam while scanning the excitation frequencies. The resulting spectra provide multidimensional spectral signatures that increase the spectroscopic selectivity required for analyzing complex samples.

Phase control and diagnostic of quantum mechanical superposition states

We report experiments on the control of the phase η in quantum mechanical superposition states which emerge in electromagnetically induced transparency, |ψ〉 = (|1〉 + eiη|2〉)/√2. We interpret our findings in terms of the measurement role that spontaneous emission and the light fields play in selecting the optically dark and bright superpositions. A phase-switching tool is introduced which enables the rapid measurement of the absolute depth of the dark-state minimum and its absolute position on the frequency scale without detuning the lasers. The phase-switching technique allows one to determine the relative phase η in an ensemble of quantum mechanical superposition states of a system in a minimally invasive way.

NMR Quantum Simulation of Localization Effects Induced by Decoherence

The loss of coherence in quantum mechanical superposition states limits the time for which quantum information remains useful. Similarly, it limits the distance over which quantum information can be transmitted. Here, we investigate in a nuclear spin-based quantum simulator, the localization of the size of spin clusters that are generated by a Hamiltonian driving the transmission of information, while a variable-strength perturbation counteracts the spreading. We find that the system reaches a dynamic equilibrium size, which decreases with the square of the perturbation strength.

Multiple Quantum Coherence Spectroscopy

Multiple quantum coherences provide a powerful approach for studies of complex systems because increasing the number of quantum states in a quantum mechanical superposition state increases the selectivity of a spectroscopic measurement. We show that frequency domain multiple quantum coherence multidimensional spectroscopy can create these superposition states using different frequency excitation pulses. The superposition state is created using two excitation frequencies to excite the symmetric and asymmetric stretch modes in a rhodium dicarbonyl chelate and the dynamic Stark effect to climb the vibrational ladders involving different overtone and combination band states. A monochromator resolves the free induction decay of different coherences comprising the superposition state. The three spectral dimensions provide the selectivity required to observe 19 different spectral features associated with fully coherent nonlinear processes involving up to 11 interactions with the excitation fields. The different features act as spectroscopic probes of the diagonal and off-diagonal parts of the molecular potential energy hypersurface. This approach can be considered as a coherent pump-probe spectroscopy where the pump is a series of excitation pulses that prepares a multiple quantum coherence and the probe is another series of pulses that creates the output coherence.

Proton transfer across hydrogen bonds: From reaction path to Schrödinger's cat

Abstract We review recent studies of the interconversion mechanism of OH···O hydrogen-bonded centrosymmetric dimers through proton transfer in the prototype crystals of potassium hydrogen carbonate (KHCO3) and benzoic acid (C6H5COOH). The point at issue is whether the proton distributions at various temperatures arise from classical statistical mixtures of tautomers or quantum mechanical superposition states. A related issue is whether it is possible to probe a quantum superposition without inducing decoherence and classicality. We show that neutron diffraction can realize decoherence-free measurements for strictly defined scattering geometries and thus evidence macroscopic quantum correlations. We present a theoretical framework for decoherence-free macroscopically entangled states of the sublattice of protons. The neutron diffraction cross-section of protons is enhanced by a factor of ~45, compared to regular Bragg diffraction, and quantum correlations are observed with remarkable contrast. At elevated temperatures, up to 300 K, quantum correlations are unaffected by proton transfer. The crystal is a coherent superposition of macroscopic tunnelling states, like Schrödinger's cat in a superposition of dead and alive states.

Multiphoton transitions in a macroscopic quantum two-state system.

We have observed multiphoton transitions between two macroscopic quantum-mechanical superposition states formed by two opposite circulating currents in a superconducting loop with three Josephson junctions. Resonant peaks and dips of up to three-photon transitions were observed in spectroscopic measurements when the system was irradiated with a strong rf-photon field. The widths of the multiphoton absorption dips are shown to scale with the Bessel functions in agreement with theoretical predictions derived from the Bloch equation or from a spin-boson model.

Phase properties of Schrödinger cat states of light decaying in phase-sensitive reservoirs

We study phase properties of quantum mechanical superposition states decaying into phase-sensitive reservoirs. We show that the Wigner phase quasiprobability distribution reflects the quantum interference effects very well while the Pegg–Barnett and the Husimi phase probability distributions are quite insensitive with respect to the character of the quantum interference between component states. We study in detail phase properties of the even coherent state which decays into the thermal and the squeezed reservoirs. In thermal reservoirs the phase of the superposition state becomes randomized under the influence of thermal fluctuations. The higher the number of thermal photons the faster the randomization process is. On the other hand we show that depending on the relative phase between the superposition state and the phase-sensitive reservoir the process of phase randomization can be either enhanced or completely suppressed.