arXiv subjects

Yakir Aharonov

Publications and source records attributed to Yakir Aharonov.

At least 37 records · Page 2Linked to original sources

arXiv2020

Green's Function for the Schrödinger Equation with a Generalized Point Interaction and Stability of Superoscillations

In this paper we study the time dependent Schrödinger equation with all possible self-adjoint singular interactions located at the origin, which include the $δ$ and $δ'$-potentials as well as boundary conditions of Dirichlet, Neumann, and Robin type as particular cases. We derive an explicit representation of the time dependent Green's function and give a mathematical rigorous meaning to the corresponding integral for holomorphic initial conditions, using Fresnel integrals. Superoscillatory functions appear in the context of weak measurements in quantum mechanics and are naturally treated as holomorphic entire functions. As an application of the Green's function we study the stability and oscillatory properties of the solution of the Schrödinger equation subject to a generalized point interaction when the initial datum is a superoscillatory function.

math.AP↗

arXiv2020

Magnetic forces in the absence of a classical magnetic field

It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest that the classical magnetic force can be seen as emerging entirely from the Aharonov-Bohm effect. Finally, the basic elements of a semi-classical theory that models the emergence of classical magnetic forces from fields with special symmetries are introduced.

quant-ph↗

arXiv2019

Schrödinger evolution of superoscillations with $δ$- and $δ'$-potentials

In this paper we study the time persistence of superoscillations as the initial data of the time dependent Schrödinger equation with $δ$- and $δ'$-potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converges in the topology of the entire function space $A_1(\mathbb{C})$. Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under $δ$- and $δ'$-potentials.

math-ph↗

arXiv2019

Topological bound states for quantum charges

We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a thought experiment with a cavity where two solenoids are sufficient to create bound states.

quant-ph↗

arXiv2019

Diffraction-Based Interaction-Free Measurements

We introduce diffraction-based interaction-free measurements. In contrast with previous work where a set of discrete paths is engaged, good quality interaction-free measurements can be realized with a continuous set of paths, as is typical of optical propagation. If a bomb is present in a given spatial region -- so sensitive that a single photon will set it off -- its presence can still be detected without exploding it. This is possible because, by not absorbing the photon, the bomb causes the single photon to diffract around it. The resulting diffraction pattern can then be statistically distinguished from the bomb-free case. We work out the case of single- versus double- slit in detail, where the double-slit arises because of a bomb excluding the middle region.

quant-ph↗

arXiv2019

Why physical understanding should precede the mathematical formalism - conditional quantum probabilities as a case-study

Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov-Bergmann-Lebowitz rule. In this short note we present a seemingly disturbing paradox that appears when applying the rule to systems with slightly broken degeneracies. In these cases we encounter a singular limit - the probability "jumps" when going from perfect degeneracy to negligibly broken one. We trace the origin of the paradox and solve it from both traditional and modern perspectives in order to highlight the physics behind it: the necessity to take into account the finite resolution of the measuring device. As a practical example, we study the application of the rule to the Zeeman effect. The analysis presented here may stress the general need to first consider the governing physical principles before heading to the mathematical formalism, in particular when exploring puzzling quantum phenomena.

quant-ph↗

arXiv2019

Modification of "Counterfactual communication protocols" which eliminates weak particle traces

Possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, was known for quarter of a century. The protocols of full communication, including transmitting unknown quantum states were proposed only few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace larger than the trace left by a single particle passing through the channel. This made the claim of counterfactuality of these protocols at best controversial. However, a simple modification of these recent protocols eliminates the trace in the transmission channel making all these protocols counterfactual.

quant-ph↗

arXiv2018

The Weak Reality that Makes Quantum Phenomena more Natural: Novel Insights and Experiments

While quantum reality can be probed through measurements, the Two-State-Vector formalism (TSVF) reveals a subtler reality prevailing between measurements. Under special pre- and post-selections, odd physical values emerge. This unusual picture calls for a deeper study. Instead of the common, wave-based picture of quantum mechanics, we suggest a new, particle-based perspective: Each particle possesses a definite location throughout its evolution, while some of its physical variables (characterized by deterministic operators, some of which obey nonlocal equations of motion) are carried by "mirage particles" accounting for its unique behavior. Within the time-interval between pre- and post-selection, the particle gives rise to a horde of such mirage particles, of which some can be negative. What appears to be "no-particle," known to give rise to Interaction-Free Measurement, is in fact a self-canceling pair of positive and negative mirage particles, which can be momentarily split and cancel out again. Feasible experiments can give empirical evidence for these fleeting phenomena. In this respect, the Heisenberg ontology is shown to be conceptually advantageous compared to the Schrödinger picture. We review several recent advances, discuss their foundational significance and point out possible directions for future research.

quant-ph↗

arXiv2018

Anomalous Weak Values Emerging from Strong Interactions between Light and Matter

Some predictions regarding pre- and post-selected states are far-reaching, thereby requiring validation with standard quantum measurements in addition to the customary weak measurements used so far, as well as other advanced techniques. We go further pursuing this goal, proposing two thought experiments which incorporate novel yet feasible validation methods of unconventional light-matter interactions. An excited atom traverses a Mach-Zehnder interferometer (MZI) under a special combination of pre- and post-selection. In the first experiment, photons emitted by the superposed atom, after being hit by two laser beams, are individually counted. Despite the interaction having definitely taken place, the numbers of photons emitted from each arm of the MZI are predicted, at the ensemble level, to be different from those expected with standard stimulated emission. In the second experiment, the atom spontaneously emits a photon while still in the MZI. This photon later serves as a strong measurement of the atom's energy upon hitting a photographic plate. The experiment is repeated to enable an interference effect of the emitted photons. Interestingly, the latter gives the appearance that the photons have been emitted by the atom from a position much farther from the two MZI arms L and R, as if in a "phantom arm" R'. These experiments also emphasize the key role of anomalous weak values in determining light-matter interactions. In fact, they present a straightforward realization of an entity we term counter-particles, namely pre- and post-selected states acting as if they have negative physical variables such as mass and energy. The novel verification methods we suggest for testing these predictions resemble weak measurements in some aspects, yet result from definite atomic transitions verified by the detected photons.

quant-ph↗

arXiv2018

Is the Quilted Multiverse Consistent with a Thermodynamic Arrow of Time?

Theoretical achievements, as well as much controversy, surround multiverse theory. Various types of multiverses, with an increasing amount of complexity, were suggested and thoroughly discussed in literature by now. While these types are very different, they all share the same basic idea: our physical reality consists of more than just one universe. Each universe within a possibly huge multiverse might be slightly or even very different from the others. The quilted multiverse is one of these types, whose uniqueness arises from the postulate that every possible event will occur infinitely many times in infinitely many universes. In this paper we show that the quilted multiverse is not self-consistent due to the instability of entropy decrease under small perturbations. We therefore propose a modified version of the quilted multiverse which might overcome this shortcoming. It includes only those universes where the minimal entropy occurs at the same instant of (cosmological) time. Only these universes whose initial conditions are fine-tuned within a small phase-space region would evolve consistently to form their "close" states at present. A final boundary condition on the multiverse may further lower the amount of possible, consistent universes. Finally, some related observations regarding the many-worlds interpretation of quantum mechanics and the emergence of classicality are discussed.

gr-qc↗

arXiv2017

Interaction-Free Effects Between Distant Atoms

A Gedanken experiment is presented where an excited and a ground-state atom are positioned such that, within the former's half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms have become entangled. Consequently, the "no exchange" result, apparently precluding entanglement, is non-locally established between the atoms by this very entanglement. This quantum-mechanical version of the ancient Liar Paradox can be realized with already existing transmission schemes, with the addition of Bell's theorem applied to the no-exchange cases. Under appropriate probabilities, the initially-excited atom, still excited, can be entangled with additional atoms time and again, or alternatively, exert multipartite nonlocal correlations in an interaction free manner. When densely repeated several times, this result also gives rise to the Quantum Zeno effect, again exerted between distant atoms without photon exchange. We discuss these experiments as variants of Interaction-Free-Measurement, now generalized for both spatial and temporal uncertainties. We next employ weak measurements for elucidating the paradox. Interpretational issues are discussed in the conclusion, and a resolution is offered within the Two-State Vector Formalism and its new Heisenberg framework.

quant-ph↗

arXiv2017

A Completely Top-Down Hierarchical Structure in Quantum Mechanics

Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest "atoms"? In the following paper we answer these questions on the negative for a specific class of systems and measurements. We begin with simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to new surprising effects within atomic and electromagnetic systems. A general construction based on pre- and post-selected ensembles is then suggested, where the N-body correlation can be genuinely perceived as a global property, as long as one is limited to preforming a small set of measurements which we term "strictly local". We conclude that within time-symmetric quantum mechanics and under certain boundary conditions, high-order correlations can determine low-order ones, but not vice versa. Moreover, the latter seem to provide no information at all regarding the former. This supports a top-down structure in many-body quantum mechanics.

quant-ph↗

arXiv2017

The Case of the Disappearing (and Re-Appearing) Particle

A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a particle superposed over three boxes. Under appropriate pre- and postselections, and with tunneling enabled between two of the boxes, it is possible to derive not only one, but three predictions for three different times within the intermediate interval. These predictions are moreover contradictory. The particle (when looked for using a projective measurement) seems to disappear from the first box where it would have been previously found with certainty, appearing instead within the third box, to which no tunneling is possible, and later re-appearing within the second. It turns out that local measurement (i.e. opening one of the boxes) fails to indicate the particle's presence, but subtler measurements performed on the two boxes together reveal the particle's nonlocal modular momentum spatially separated from its mass. Another advance of this setting is that, unlike other predictions of the TSVF that rely on weak and/or counterfactual measurements, the present one uses actual projective measurements. This outcome is then corroborated by adding weak measurements and the Aharonov-Bohm effect. The results strengthen the recently suggested time-symmetric Heisenberg ontology based on nonlocal deterministic operators. They can be also tested using the newly developed quantum router.

quant-ph↗

arXiv2016

On conservation laws in quantum mechanics

We raise fundamental questions about the very meaning of conservation laws in quantum mechanics and we argue that the standard way of defining conservation laws, while perfectly valid as far as it goes, misses essential features of nature and has to be revisited and extended.

quant-ph↗

arXiv2016

Realisation of Qudits in Coupled Potential Wells

Quantum computation strongly relies on the realisation, manipulation and control of qubits. A central method for realizing qubits is by creating a double-well potential system with a significant gap between the first two eigenvalues and the rest. In this work we first revisit the theoretical grounds underlying the double-well qubit dynamics, then proceed to suggest novel extensions of these principles to a triple-well qutrit with periodic boundary conditions, followed by a general d-well analysis of qudits. These analyses are based on representations of the special unitary groups SU(d) which expose the systems' symmetry and employ them for performing computations. We conclude with a few notes on coherence and scalability of d-well systems.

quant-ph↗

arXiv2016

Interference Energy Spectrum of the Infinite Square Well

Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the {interference energy spectrum} of the state. This name is appropriate because the same splitting procedure applied at the stationary nodes of any eigenstate does not change the measurable energy of the state. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations. An analytic derivation is given for the interference spectrum of a given wavefunction $Ψ(x,t)$ with $N$ known zeros located at points $s_i = (x_i, t_i)$. Numerical simulations were used to verify that a barrier can be rapidly raised at a zero of the wavefunction without significantly affecting it. The interpretation of this result with respect to the conservation of energy and the energy-time uncertainty relation is discussed, and the idea of alternate energy eigenbases is fleshed out. The question of whether or not a preferred discrete energy spectrum is an inherent feature of a particle's quantum state is examined.

quant-ph↗

arXiv2016

Comment on "Role of Potentials in the Aharonov-Bohm Effect"

Are the electromagnetic scalar and vector potentials dispensable? Lev Vaidman has suggested that local interactions of gauge-invariant quantities, e.g. magnetic torques, suffice for the description of all quantum electromagnetic phenomena. We analyze six thought experiments that challenge this suggestion. All of them have explanations in terms of $local$ interactions of gauge-dependent quantities, in addition, some have explanations in terms of nonlocal interactions of gauge-invariant quantities. We claim, however, that two of our examples have no gauge-invariant formal description and that, in general, no local description can dispense with electromagnetic potentials.

quant-ph↗

arXiv2016

Nonlocality of the Aharonov-Bohm Effect

Although the Aharonov-Bohm and related effects are familiar in solid state and high energy physics, the nonlocality of these effects has been questioned. Here we show, for the first time, that the Aharonov-Bohm effect has two very different aspects. One aspect is instantaneous and nonlocal; the other aspect, which depends on entanglement, unfolds continuously over time. While local, gauge-invariant variables may occasionally suffice for explaining the continuous aspect, we argue that they cannot explain the instantaneous aspect. Thus the Aharonov-Bohm effect is, in general, nonlocal.

quant-ph↗