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Kh. Kh. Shakov

Publications and source records attributed to Kh. Kh. Shakov.

9 recordsLinked to original sources
arXiv2006

Sudden switching in qubits

Analytic solutions are developed for two-state systems (e.g. qubits) strongly perturbed by a series of rapidly changing pulses, called `kicks'. The evolution matrix may be expressed as a time ordered product of evolution matrices for single kicks. Single, double, and triple kicks are explicitly considered, and the onset of observability of time ordering is examined. The effects of different order of kicks on the dynamics of the system are studied and compared with effects of time ordering in general. To determine the range of validity of this approach, the effect of using pulses of finite widths for 2s-2p transitions in atomic hydrogen is examined numerically.

quant-ph↗
arXiv2005

How Time Works in Quantum Systems: Overview of time ordering and time correlation in weakly perturbed atomic collisions and in strongly perturbed qubits

Time ordering may be defined by first defining the limit of no time ordering (NTO) in terms of a time average of an external interaction, V(t). Previously, time correlation was defined in terms of a similar limit called the independent time approximation (ITA). Experimental evidence for time correlation has not yet been distinguished from experimental evidence for time ordering.

quant-ph↗
arXiv2005

An overview of simply pulsed qubits

The behavior of simply pulsed qubits (quantum systems with two linearly independent states) may be characterized by the energy difference $ΔE$ between the two states of the qubit and by an external stimulating potential $V(t)$ that causes transitions between them. Thus, the operation of such quantum mechanical systems may be categorized in various regions that explicitly depend on $ΔE$ and $V(t)$. Limiting cases of degenerate, perturbative, and adiabatic regions are discussed. A comprehensive and illustrative map for simply pulsed qubits is presented that can be used as a visual tool for students. Furthermore, analytic solutions may be obtained when the interaction $V(t)$ is proportional to $δ(t-t_k)$, namely when a fast interaction, called a kick, is used.

quant-ph↗
arXiv2004

Time Ordering in Kicked Qubits

We examine time ordering effects in strongly, suddenly perturbed two-state quantum systems (kicked qubits) by comparing results with time ordering to results without time ordering. Simple analytic expressions are given for state occupation amplitudes and probabilities for singly and multiply kicked qubits. We investigate the limit of no time ordering, which can differ in different representations.

quant-ph↗
arXiv2003

Quantum time ordering and degeneracy. II: Coherent population transfer between degenerate states

We find conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate $n$-state atom, where transitions are caused by an external interaction. In systems with degenerate states there is no time ordering. Analytic expressions have been found for transition probabilities in a degenerate $n$-state atom interacting with a strong external field that gives a common time dependence to all of the transition matrix elements. Except for solving a simple $n^{th}$ order equation to determine eigenvalues of dressed states, the method is entirely analytic. These expressions may be used to control electron populations in degenerate $n$-state atoms. Examples are given for $n=2$ and $n=3$.

quant-ph↗
arXiv2003

Population control of 2s-2p transitions in hydrogen

We consider the time evolution of the occupation probabilities for the 2s-2p transition in a hydrogen atom interacting with an external field, V(t). A two-state model and a dipole approximation are used. In the case of degenerate energy levels an analytical solution of the time-dependent Shroedinger equation for the probability amplitudes exists. The form of the solution allows one to choose the ratio of the field amplitude to its frequency that leads to temporal trapping of electrons in specific states. The analytic solution is valid when the separation of the energy levels is small compared to the energy of the interacting radiation.

quant-ph↗
arXiv2003

Complete population transfer in a degenerate 3-level atom

We find conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate 3-level atom, where transitions are caused by an external interaction. Complete population transfer from an initially occupied state 1 to a designated state 2 occurs under two conditions. First, there is a constraint on the ratios of the transition matrix elements of the external interaction. Second, there is a constraint on the action integral over the interaction, or "area", corresponding to the phase shift induced by the external interaction. Both conditions may be expressed in terms of simple odd integers.

quant-ph↗
arXiv2003

Complete population transfer in degenerate n-state atoms

We find a set of conditions to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate n-state atom, where the transitions are caused by an external interaction.

quant-ph↗