arXiv subjects

D. Sokolovski

Publications and source records attributed to D. Sokolovski.

At least 73 records · Page 4Linked to original sources

arXiv2011

Self-intersecting Regge trajectories in multi-channel scattering

We present a simple direct method for calculating Regge trajectories for a multichannel scattering problem. The approach is applied to the case of two coupled Thomas-Fermi type potentials, used as a crude model for electron-atom scattering below the second excitation threshold. It is shown that non-adiabatic interaction may cause formation of loops in Regge trajectories. The accuracy of the method is tested by evaluating resonance contributions to elastic and inelastic integral cross sections.

quant-ph↗

arXiv2011

Measurement of non-commuting spin components using spin-orbit interaction

We analyze the physical meaning of a possible experiment aimed at the simultaneous measurement of two non-commuting spin components. We demonstrate that switching of a strong spin-orbit interaction, e.g., in a solid state or a cold-atom system, for a short period of time simulates a simultaneous von Neumann measurement of spin components, $σ_x$ and $σ_y$. By mapping spin dynamics onto coordinate-space motion, such a measurement determines time averages of $σ_x$ and $σ_y$ which, unlike their instantaneous values, may be evaluated simultaneously to an arbitrary accuracy.

quant-ph↗

arXiv2011

Multiple anion formation in low energy electron collisions with Tl atoms: Regge-pole prediction

The complex angular momentum (CAM) calculated low-energy 0 < E < 5 eV electron elastic total cross section (TCS) for In is benchmarked through its recently measured electron affinity (Walter et al, Phys. Rev. A 82, 032507 (2010)). The TCSs for Tl and Ga atoms are then calculated using the CAM method. From the dramatically sharp resonances in the TCSs binding energies for Tl^{-} and Ga^{-} negative ions formed during the collisions are extracted and compared with existing values. Three stable bound negative ions of Tl are predicted.

physics.atom-ph↗

arXiv2011

The Hartman effect and weak measurements "which are not really weak"

We show that in wavepacket tunnelling localisation of the transmitted particle amounts to a quantum measurement of the delay it experiences in the barrier. With no external degree of freedom involved, the envelope of the wavepacket plays the role of the initial pointer state. Under tunnelling conditions such 'self measurement' is necessarily weak, and the Hartman effect just reflects the general tendency of weak values to diverge, as post-selection in the final state becomes improbable. We also demonstrate that it is a good precision, or 'not really weak' quantum measurement: no matter how wide the barrier d, it is possible to transmit a wavepacket with a width σ small compared to the observed advancement. As is the case with all weak measurements, the probability of transmission rapidly decreases with the ratio σ/d.

quant-ph↗

arXiv2011

Classification of resonance Regge trajectories and a modified Mulholland formula

We employ a simple potential model to analyse the effects which a Regge trajectory, correlating with a bound or a metastable state at zero angular momentum, has on an integral cross section. A straightforward modification of the Mulholland formula of Macek et al is proposed for more efficient separation of the resonance contribution.

quant-ph↗

arXiv2011

Zeno effect and ergodicity in finite-time quantum measurements

We demonstrate that an attempt to measure a non-local in time quantity, such as the time average $\la A\ra_T$ of a dynamical variable $A$, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator $\a$. Conversely, in a long measurement of $\la A\ra_T$ to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which von Neumann ensemble average of $\a$ coincides with $\la A\ra_T$. Both effects are conveniently analysed in terms of singularities and critical points of the corresponding amplitude distribution and the Zeno-like behaviour is shown to be a consequence of conservation of probability.

quant-ph↗

arXiv2010

Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate

We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a `coherent' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power law) or rapid (Gaussian) decoherence of the mean values themselves.

quant-ph↗

arXiv2010

Atomic Fock states by gradual trap reduction: from sudden to adiabatic limits

We investigate the possibility to form high fidelity atomic Fock states by gradual reduction of a quasi one dimensional trap containing spin polarized fermions or strongly interacting bosons in the Tonk-Girardeau regime. Making the trap shallower and simultaneously squeezing it can lead to the preparation of an ideal atomic Fock state as one approaches either the sudden or the adiabatic limits. Nonetheless, the fidelity of the resulting state is shown to exhibit a non-monotonic behaviour with the time scale in which the trapping potential is changed.

quant-ph↗

arXiv2010

On causality, apparent 'superluminality' and reshaping in barrier penetration

We consider tunnelling of a non-relativistic particle across a potential barrier. It is shown that the barrier acts as an effective beam splitter which builds up the transmitted pulse from the copies of the initial envelope shifted in the coordinate space backwards relative to the free propagation. Although along each pathway causality is explicitly obeyed, in special cases reshaping can result an overall reduction of the initial envelope, accompanied by an arbitrary coordinate shift. In the case of a high barrier the delay amplitude distribution (DAD) mimics a Dirac $δ$-function, the transmission amplitude is superoscillatory for finite momenta and tunnelling leads to an accurate advancement of the (reduced) initial envelope by the barrier width. In the case of a wide barrier, initial envelope is accurately translated into the complex coordinate plane. The complex shift, given by the first moment of the DAD, accounts for both the displacement of the maximum of the transmitted probability density and the increase in its velocity. It is argued that analysing apparent 'superluminality' in terms of spacial displacements helps avoid contradiction associated with time parameters such as the phase time.

quant-ph↗

arXiv2009

Accurate "superluminal" transmission via entanglement, superoscillations and quasi-Dirac distributions

We analyse a system in which, due to entanglement between the spin and spatial degrees of freedom, the reduced transmitted state has the shape of the freely propagating pulse translated in the complex co-ordinate plane. In the case an apparently "superluminal" advancement of the pulse the delay amplitude distribution is found to be a peculiar approximation to the Dirac delta-function, and the transmission coefficient exhibits a well-defined super-oscillatory window. Analogies with potential tunnelling and the Wheeler's delayed choice experiment are highlighted.

quant-ph↗

arXiv2009

Regge resonances in low-energy electron elastic cross sections for Ge, Sn and Pb atoms: manifestations of stable excited anions

Low-energy E < 2 eV electron elastic collisions with Ge, Sn and Pb atoms yield stable excited Ge-, Sn- and Pb- anions. The recent Regge-pole methodology is used with Thomas-Fermi type potential incorporating the crucial core-polarization interaction to calculate elastic total and Mulholland partial cross sections. For excited Ge- and Sn- anions the extracted binding energies from the unique characteristic sharp Regge resonances manifesting stable excited states formed during the collisions agree excellently with experimental values; for Pb- the prediction requires experimental verification. The calculated differential cross sections also yield the binding energies.

physics.atom-ph↗

arXiv2009

Weak values, 'negative probability' and the uncertainty principle

A quantum transition can be seen as a result of interference between various pathways(e.g. Feynman paths) which can be labelled by a variable $f$. An attempt to determine the value of f without destroying the coherence between the pathways produces a weak value of $\bar{f}$. We show $\bar{f}$ to be an average obtained with amplitude distribution which can, in general, take negative values which, in accordance with the uncertainty principle, need not contain information about the actual range of the values $f$ which contribute to the transition. It is also demonstrated that the moments of such alternating distributions have a number of unusual properties which may lead to misinterpretation of the weak measurement results.We provide a detailed analysis of weak measurements with and without post-selection. Examples include the double slit diffraction experiment,weak von Neumann and von Neumann-like measurements, traversal time for an elastic collision, the phase time, the local angular momentum(LAM) and the 'three-box case' of {\it Aharonov et al}

quant-ph↗

arXiv2009

Feynman-path analysis of Hardy's paradox: measurements and the uncertainty principle

Hardy's paradox is analysed within Feynman's formulation of quantum mechanics. A transition amplitude is represented as a sum over virtual paths which different intermediate measurements convert into different sets of real pathways. Contradictory statements emerge when applying to the same statistical ensemble. The "strange" weak values result is also investigated in this context.

quant-ph↗

arXiv2009

Qubit residence time measurements with a Bose-Einstein condensate

We show that an electrostatic qubit located near a Bose-Einstein condensate trapped in a symmetric double-well potential can be used to measure the duration the qubit has spent in one of its quantum states. The stronq, medium and weak measurement regimes are analysed and a new type of Zeno effect is discussed. The analogy between the residence and the traversal (tunnelling) times is highlighted.

quant-ph↗

arXiv2009

Unusual decoherence in qubit measurements with a Bose-Einstein condensate

We consider an electrostatic qubit located near a Bose-Einstein condensate (BEC) of noninteracting bosons in a double-well potential, which is used for qubit measurements. Tracing out the BEC variables we obtain a simple analytical expression for the qubit's density-matrix. The qubit's evolution exhibits a slow ($\propto1/\sqrt{t}$) damping of the qubit's coherence term, which however turns to be a Gaussian one in the case of static qubit. This stays in contrast to the exponential damping produced by most classical detectors. The decoherence is, in general, incomplete and strongly depends on the initial state of the qubit.

quant-ph↗

arXiv2009

Novel Electron Spectroscopy of Tenuously and Weakly Bound Negative Ions

A novel method is proposed that uses very slow electron elastic collisions with atoms to identify their presence through the observation of tenuously bound (electron impact energy, E<0.1 eV) and weakly bound (E<1 eV) negative ions, formed as Regge resonances during the collisions.

physics.atom-ph↗

arXiv2004

On the relation between the Hartree-Fock and Kohn-Sham approaches

We show that the Hartree-Fock (HF) results cannot be reproduced within the framework of Kohn-Sham (KS) theory because the single-particle densities of finite systems obtained within the HF calculations are not $v$-representable, i.e., do not correspond to any ground state of a $N$ non-interacting electron systems in a local external potential. For this reason, the KS theory, which finds a minimum on a different subset of all densities, can overestimate the ground state energy, as compared to the HF result. The discrepancy between the two approaches provides no grounds to assume that either the KS theory or the density functional theory suffers from internal contradictions.

cond-mat.other↗

arXiv2004

Path summation and quantum measurements

We propose a general theoretical approach to quantum measurements based on the path (histories) summation technique. For a given dynamical variable A, the Schrödinger state of a system in a Hilbert space of arbitrary dimensionality is decomposed into a set of substates, each of which corresponds to a particular detailed history of the system. The coherence between the substates may then be destroyed by meter(s) to a degree determined by the nature and the accuracy of the measurement(s) which may be of von Neumann, finite-time or continuous type. Transformations between the histories obtained for non-commuting variables and construction of simultaneous histories for non-commuting observables are discussed. Important cases of a particle described by Feynman paths in the coordinate space and a qubit in a two dimensional Hilbert space are studied in some detail.

quant-ph↗