Using parity kicks for decoherence control

Decoherence is the process which limits our ability to maintain pure quantum states, or their linear superpositions. It is the phenomenon by which the classical world appears from the quantum one [1]. In more physical terms it is described as the rapid destruction of the phase relation between two, or more, quantum states of a system caused by the entanglement of these states with different states of the environment. The present widespread interest in decoherence is due to the fact that it is the main limiting factor for quantum information processing. We can store information, indeed, in two-level quantum systems, known as qubits, which can become entangled each other, but decoherence can destroy any quantum superposition, reducing the system to a mixture of states, and the stored information is lost. For this reason decoherence control is now becoming a rapidly expanding field of investigation. In a series of previous papers [2–5] we have faced the control of decoherence by actively modifying the system’s dynamics through a feedback loop. This procedure turned out to be very effective, in principle [4], to slow down the decoherence of the only one experiment [6], up to present, in which the decoherence of a mesoscopic superposition was detected. The main limiting aspect of this procedure is connected with the need of a measurement. In order to do the feedback in the appropriate way, one has first to perform a measurement and then the result of this measurement can be used to operate the feedback. However, any physical measurement is subject to the limitation associated with a non-unit detection efficiency. We have shown [5] that with detection efficiency approaching unity the quantum superposition of states stored in a cavity can be protected against decoherence for many decoherence times tdec, where tdec is defined as the cavity relaxation time divided by the average photon number [7]. We wish now to face the problem of eliminating the measurement in controlling the decoherence. We show, here, how it is possible to inhibit decoherence through the application of suitable open-loop control techniques to the system of interest, that is, by using appropriately shaped time-varying control fields. To be more specific, decoherence can be inhibited by subjecting a system to a sequence of very frequent parity kicks, i.e., pulses designed in such a way that their effect is equivalent to the application of the parity operator on the system. The paper is organized as follows: In section II the parity kicks method is presented in its generality and it is shown how decoherence and dissipation are completely frozen in the limit of infinitely frequent pulses. In Section III the method is applied to the case of a damped harmonic oscillator, as for example, a given normal mode of a system of trapped ions. In Section IV the numerical results corresponding to this case are presented showing that a considerable decoherence suppression is obtained when the parity kicks repetition rate becomes comparable to the typical timescale of the environment. In Section V the possibility of applying this scheme to harness the decoherence of the center-of-mass motion in ion traps are discussed.