A quantum memory protocol of controlled ac Stark echoes (CASE) based on a double rephasing photon echo scheme via controlled Rabi flopping is proposed. The double rephasing scheme of photon echoes inherently satisfies the no-population inversion requirement for quantum memories, but the resultant absorptive echo remains a fundamental problem. Herein, it is reported that the first echo in the double rephasing scheme can be dynamically controlled so that it does not affect the second echo, which is accomplished by using unbalanced ac Stark shifts. Then, the second echo is coherently controlled to be emissive via controlled coherence conversion. Finally a near perfect ultralong CASE is presented using a backward echo scheme. Compared with other methods such as dc Stark echoes, the present protocol is all-optical with advantages of wavelength-selective dynamic control of quantum processing for erasing, buffering, and channel multiplexing.
We study echoes and what we call ``revival echoes'' for a collection of atoms that are described by a single quantum wave function and are confined in a weakly anharmonic trap. The echoes and revival echoes are induced by applying two successive temporally localized potential perturbations to the confining potential, one at time
t=0, and a smaller one at time $t=\ensuremath{\tau}$. Pulselike responses in the expectation value of position $\ensuremath{\langle}x(t)\ensuremath{\rangle}$ are predicted at $t\ensuremath{\approx}n\ensuremath{\tau}$ (
n=2,3,...) and are particularly evident at $t\ensuremath{\approx}2\ensuremath{\tau}$. While such echoes are familiar from previous work, a result of our study is the finding of revival echoes. Revivals (but not echoes) occur even if the second perturbation is absent. In particular, in the absence of the second perturbation, the response to the first perturbation dies away but then reassembles, producing a response at revival times
mTx (
m=1,2,...). The existence of such revivals is due to the discreteness of the quantum levels in a weakly anharmonic potential, and has been well studied previously. If we now include the second perturbation at $t=\ensuremath{\tau}$, we find temporally localized responses, revival echoes, both before and after $t\ensuremath{\approx}m{T}_{x}$ [e.g., at $t\ensuremath{\approx}m{T}_{x}\ensuremath{-}n\ensuremath{\tau}$ (prerevival echoes) and at $t\ensuremath{\approx}m{T}_{x}+n\ensuremath{\tau}$, (postrevival echoes)] where
m and
n are
1,2,.... One notable point is that, depending on the form of the perturbations, the ``principal'' revival echoes at $t\ensuremath{\approx}{T}_{x}\ifmmode\pm\else\textpm\fi{}\ensuremath{\tau}$ can be much larger than the echo at $t\ensuremath{\approx}2\ensuremath{\tau}$. We develop a perturbative model for these phenomena, and compare its predictions to the numerical solutions of the time-dependent Schr\"odinger equation. The scaling of the size of the various echoes and revival echoes as a function of the symmetry of the perturbations applied at
t=0 and $t=\ensuremath{\tau}$, and of the size of the external perturbations is investigated. The quantum recurrence and revival echoes are also present in higher moments of position, $\ensuremath{\langle}{x}^{p}(t)\ensuremath{\rangle}$,
p>1. Recurrences are present at $t\ensuremath{\approx}m{T}_{x}/j$, and dominant prerevival and postrevival echoes occur at fractional shifts of $\ensuremath{\tau}$ [i.e. $t\ensuremath{\approx}(m{T}_{x}\ifmmode\pm\else\textpm\fi{}\ensuremath{\tau})/j$] where the
m=1,2,... and the integer values of
j are determined by
p. Additionally, we use the Gross-Pitaevskii equation to study the effect of atom-atom interactions on these phenomena. We find that echoes and revival echoes become more difficult to discern as the size of the second perturbation is increased and/or as the atom-atom interactions become stronger.