Time ordering in kicked qubits

Abstract

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.

Sudden switching in two-state systems

“…Of course, for a finite-width pulse, i.e. β = 0, time-ordering effects do begin to appear even in the interaction picture [30]. We note that the time ordering effect in the interaction picture is independent of the measurement time t, though it does depend on the pulse width τ through the β parameter.…”

“…(vi) A sudden pulse [29] or series of sudden pulses (single or multiple kicks). The basic validity condition [30] is that the external field is sharply tuned in time, i.e. ∆Eτ << 1, where τ is the width of the pulse.…”

“…In the Schrödinger picture, time ordering effects are present even for a single ideal kick, specifically the time ordering between the interaction and the free evolution preceding and following the kick [30]. The time ordering effect vanishes in either the degenerate limit ∆Et → 0 or in the perturbative limit α → 0.…”

“…The limit of no time ordering, i.e. T → 1 in (8), may in principle be generally obtained [30] by replacing t 0 V I (t ′ )dt with V t, where V is an average (constant) value of the interaction. In the case of two kicks of the same magnitude and opposite signs, it is then straightforward to show that, Û(0)−kk…”

Time Ordering Effects on Hydrogen Zeeman-Stark Line Profiles in Low-Density Magnetized Plasmas

“…For plasma conditions and magnetic fields encountered in the divertor of present and future tokamaks, an accurate model for the line shape of the hydrogen isotopes should include Zeeman and Stark effects, and retain the dynamics of the ion-emitter interaction. Since we then have to solve a quantum time-dependent problem, understanding the role of time ordering becomes an important issue both from the fundamental and computational points of view (note, this problem is also investigated in other contexts, e.g., [1][2][3]). Time ordering has already been studied in the Stark broadening literature, but generally for the electron broadening [4][5][6][7].…”