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At least 505 records · Page 28Linked to original sources
arXiv2013

Bell inequality and nonlocality in a two-dimensional mixed spin systems

In this paper, we use Bell inequality and nonlocality to study the bipartite correlation in an exactly soluble two-dimensional mixed spin system. Bell inequality turns out to be a valuable detector for phase transitions in this model. It can detect not only the quantum phase transition, but also the thermal phase transitions, of the system. The property of bipartite correlation in the system is also analyzed. In the quantum anti-ferromagnetic phase, the Bell inequality is violated thus nonlocality is present. It is interesting that the nonlocality is enhanced by thermal fluctuation, and similar results have not been observed in anti-ferromagnetic phase. In the ferromagnetic phase, the quantum correlation turns out to be very novel, which cannot be captured by entanglement or nonlocality.

quant-ph↗
arXiv2013

Zitterbewegung in Bogoliubov's System

We show that Bogoliubov's quasiparticle in superfluid $^3He-B$ undergoes the Zitterbewegung, as a free relativistic Dirac's electron does. The expectation value of position, as well as spin, of the quasiparticle is obtained and compared with that of the Dirac's electron. In particular, the Zitterbewegung of Bogoliubov's quasiparticle has a frequency approximately $10^5$ lower than that of an electron, rendering a more promising experimental observation.

quant-ph↗
arXiv2013

Probing surface electric field noise with a single ion

We report room-temperature electric field noise measurements combined with in-situ surface characterization and cleaning of a microfabricated ion trap. We used a single-ion electric field noise sensor in combination with surface cleaning and analysis tools, to investigate the relationship between electric field noise from metal surfaces in vacuum and the composition of the surface. These experiments were performed in a novel setup that integrates ion trapping capabilities with surface analysis tools. We find that surface cleaning of an aluminum-copper surface significantly reduces the level of electric field noise, but the surface does not need to be atomically clean to show noise levels comparable to those of the best cryogenic traps. The post-cleaning noise levels are low enough to allow fault-tolerant trapped-ion quantum information processing on a microfabricated surface trap.

physics.atom-ph↗
arXiv2013

Jacobi polynomials and SU(2,2)

A ladder structure of operators is presented for the Jacobi polynomials, J_n^(a,b)(x), with parameters n, a and b integers, showing that they are related to the unitary irreducible representation of SU(2,2) with quadratic Casimir C_SU(2,2)=-3/2. As they determine also a base of square-integrable functions, the universal enveloping algebra of su(2,2) is homomorphic to the space of linear operators acting on the L^2 functions defined on (-1,+1) x Z x Z/2.

math-ph↗
arXiv2013

Compton Effect in the Medium with Non-unity Refractive Index

The foundations of the modern quantum theory of electro-magnetic radiation and its interaction with medium are constituted by the Einstein's theory of photo-effect and the theory of Compton effect. However, in the theory proposed by Compton and subsequent refinements, the medium features in explicit form are not generally accounted at all. This theory is based on the relationship between the photon momentum and its energy that may take place only in vacuum, but not in a medium with non-unity refractive index n. Here, we use Abraham's representation for the momentum of a photon in medium for the creation of a new consistent Compton effect theory accounting for media features. A new condition under which anomalous Compton effect is possible, is defined. In our case, due to the photon scattering on a moving electron, the photon's energy can increase when the electron velocity is above a threshold value, in analogy with the Vavilov-Cherenkov radiation effect. In our theory we also provide a new description of the parameters for scattered electrons, which is important for the experimental determination of the dependence of the Compton effect in medium on refractive index n.

physics.gen-ph↗
arXiv2013

Dispelling the Quantum Spooks -- a Clue that Einstein Missed?

It is well-known that Bell's Theorem and other No Hidden Variable theorems have a "retrocausal loophole", because they assume that the values of pre-existing hidden variables are independent of future measurement settings. (This is often referred to, misleadingly, as the assumption of "free will".) However, it seems to have gone unnoticed until recently that a violation of this assumption is a straightforward consequence of time-symmetry, given an understanding of the quantization of light that would have seemed natural to Einstein after 1905. The new argument shows precisely why quantization makes a difference, and why time-symmetry alone does not imply retrocausality, in the classical context. It is true that later developments in quantum theory provide a way to avoid retrocausality, without violating time-symmetry; but this escape route relies on the "ontic" conception of the wave function that Einstein rejected. Had this new argument been noticed much sooner, then, it seems likely that retrocausality would have been regarded as the default option for hidden variables theories (a fact that would then have seemed confirmed by Bell's Theorem and the No Hidden Variable theorems). This paper presents these ideas at a level intended to be accessible to general readers.

physics.hist-ph↗
arXiv2013

High Performance Information Reconciliation for QKD with CASCADE

It is widely accepted in the quantum cryptography community that interactive information reconciliation protocols, such as cascade, are ineffcient due to the communication overhead. Instead, non-interactive information reconciliation protocols based on i.e. LDPC codes or, more recently, polar codes have been proposed. In this work, we argue that interactive protocols should be taken into consideration in modern quantum key distribution systems. In particular, we demonstrate how to improve the performance of cascade by proper implementation and use. Our implementation of cascade reaches a throughput above 80 Mbps under realistic conditions. This is more than four times the throughput previously demonstrated in any information reconciliation protocol.

quant-ph↗
arXiv2013

Generalization of the hypervirial and Feynman-Hellman theorems

Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is carried on for most general second order differential equation, which involves all physically interesting cases, such as Schrödinger and two-body Klein-Gordon equations with singular potentials. Some physical consequences are discussed. The connection with Feynman-Hellmann like theorems are also considered and some relevant differences are underlined.

math-ph↗
arXiv2013

Improving the Gutzwiller Ansatz with Matrix Product States

The Gutzwiller variational wavefunction (GVW) is commonly employed to capture correlation effects in condensed matter systems such as ferromagnets, ultracold bosonic gases, correlated superconductors, etc. By noticing that the grand-canonical and number-conserving Gutzwiller Ansätze are in fact the zero-order approximation of an expansion in the truncation parameter of a Matrix Product State (MPS), we argue that MPSs, and the algorithms used to operate on them, are not only flexible computational tools but also a unifying theoretical framework that can be used to generalize and improve on the GVW. In fact, we show that a number-conserving GVW is less efficient in capturing the ground state of a quantum system than a more general MPS which can be optimized with comparable computational resources. Moreover, we suggest a corrected time-dependent density matrix renormalization group algorithm that ensures the conservation of the expectation value of the number of particles when a GVW or a MPS are not explicitly number-conserving. The GVW dynamics obtained with our algorithm compares very well with the exact one in 1D. Most importantly, the algorithm works in any dimension for a GVW. We thus expect it to be of great value in the study of the dynamics of correlated quantum systems.

cond-mat.quant-gas↗
arXiv2013

A brief discussion on the possible bound states for a class of singular potentials

The one-dimensional Schrödinger equation for a class of potentials $V(|x|)$ which vanish at infinity and present dominant singularity at the origin in the form $α/|x|^β$ ($0<β\leq 2$) is investigated. The Hermiticity of the operators related to observable physical quantities is used to determinate the proper boundary conditions. Double degeneracy and exclusion of symmetric solutions, consonant the value of $β$, are discussed. Explicit solutions for the hydrogen atom and the Kratzer potential are presented.

quant-ph↗
arXiv2013

Cooperative Enhancement of Energy Transfer in a High-Density Thermal Vapor

We present an experimental study of energy transfer in a thermal vapor of atomic rubidium. We measure the fluorescence spectrum in the visible and near infra-red as a function of atomic density using confocal microscopy. At low density we observe energy transfer consistent with the well-known energy pooling process. In contrast, above a critical density we observe a dramatic enhancement of the fluorescence from high-lying states that is not to be expected from kinetic theory. We show that the density threshold for excitation on the D1 and D2 resonance line corresponds to the value at which the dipole-dipole interactions begins to dominate, thereby indicate the key role of these interactions in the enhanced emission.

physics.atom-ph↗
arXiv2013

Zeros in Bosonic Wave-Function Result in Local Anti-Bunching: Refining Feynman's argument

The effect of boson bunching is frequently mentioned and discussed in the literature. This effect is the manifestation of bosons tendency to "travel" in clusters. One of the core arguments for boson bunching was formulated by Feynman in his well-known lecture series and has been frequently used ever since. By comparing the scattering probabilities of two bosons and of two non-identical particles, Feynman concluded: "We have the result that it is twice as likely to find two identical Bose particles scattered into the same state as you would calculate assuming the particles were different." [1]. Indeed, in most scenarios, this reasoning is valid, however, as it is shown in this paper, there are cases, even in the most ordinary scattering scenarios, where this reasoning is invalid, and in fact the opposite occurs: boson anti-bunching appears. Similarly, it is shown that at exactly the same scenarios, fermions bunch together.

quant-ph↗
arXiv2013

A model with two quantum particles similar to the hydrogen atom

The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and stationary state wave functions of a real hydrogen atom. In this paper we modify the model replacing the Coulomb interaction by the interaction of the proton and the electron with the classical electromagnetic field serving as an intermediary transmitting the electromagnetic interaction of these two charged quantum particles.

quant-ph↗
arXiv2013

Multi-channel scattering problems: Analytical approach for exact solution using Green's functions

We have proposed an analytical approach for exact solution of multi-channel scattering problems, in presence of Dirac Delta function couplings. Our solution is quite general and is valid for any set of potentials, if the Green's functions of the uncoupled potentials are known at the crossing point. Using our model, it is possible to express N-channel problem by N independent `single' channel problems and hence one can have a realistic solution of multi-channel scattering problem. In this paper we have shown that transition probability from first diabatic potential to any other potential can be easily evaluated using a very simple analytical formula - which only require value of eigenfunction of first uncoupled potential and value of Green's function of other uncoupled potential, at the crossing.

quant-ph↗
arXiv2013

Data Structures in Classical and Quantum Computing

This survey summarizes several results about quantum computing related to (mostly static) data structures. First, we describe classical data structures for the set membership and the predecessor search problems: Perfect Hash tables for set membership by Fredman, Komlós and Szemerédi and a data structure by Beame and Fich for predecessor search. We also prove results about their space complexity (how many bits are required) and time complexity (how many bits have to be read to answer a query). After that, we turn our attention to classical data structures with quantum access. In the quantum access model, data is stored in classical bits, but they can be accessed in a quantum way: We may read several bits in superposition for unit cost. We give proofs for lower bounds in this setting that show that the classical data structures from the first section are, in some sense, asymptotically optimal - even in the quantum model. In fact, these proofs are simpler and give stronger results than previous proofs for the classical model of computation. The lower bound for set membership was proved by Radhakrishnan, Sen and Venkatesh and the result for the predecessor problem by Sen and Venkatesh. Finally, we examine fully quantum data structures. Instead of encoding the data in classical bits, we now encode it in qubits. We allow any unitary operation or measurement in order to answer queries. We describe one data structure by de Wolf for the set membership problem and also a general framework using fully quantum data structures in quantum walks by Jeffery, Kothari and Magniez.

quant-ph↗
arXiv2013

The Fate of the Quantum

Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other conceptual obstacles. Here, it is shown how mappings can be formulated that relate quantum systems to classical systems. By generalizing these ideas, one gets quite general models in which quantum mechanics and classical mechanics can merge. It is helpful to have some good model examples such as string theory. It is suggested that notions such as 'super determinism' and 'conspiracy' should be looked at much more carefully than in the, by now, standard arguments.

quant-ph↗