Phase Space Tweezers for Tailoring Cavity Fields by Quantum Zeno Dynamics

We discuss an implementation of quantum Zeno dynamics in a cavity quantum electrodynamics experiment. By performing repeated unitary operations on atoms coupled to the field, we restrict the field evolution in chosen subspaces of the total Hilbert space. This procedure leads to promising methods for tailoring nonclassical states. We propose to realize “tweezers” picking a coherent field at a point in phase space and moving it towards an arbitrary final position without affecting other nonoverlapping coherent components. These effects could be observed with a state-of-the-art apparatus.

Figure 1

(a) Proposed experimental scheme. A slow atomic beam extracted from a 2D-magneto-optical trap (bottom) forms an atomic fountain with atoms nearly at rest in the center of the high-quality microwave Fabry-Perot cavity $C$ (only one mirror shown). Sources $S$ and $S^{\prime }$ address, respectively, the dressed atomic levels and the cavity mode. Electrodes around the cavity mirrors generate the electric fields preparing the circular state shown in the center. (b) Scheme of the dressed atomic levels. The arrow indicates the photon-number selective transition addressed by $S$ for $s=1$.

Figure 2

(a) QZD dynamics in ${\mathcal{H}}_{<6}$. Ten snapshots of the field Wigner function $W(\xi )$ obtained after a number of steps indicated above each frame. The cavity is initially in its vacuum state, $s=6$ and $\beta =0.1$. The EC is plotted as a blue dashed line. (b) QZD dynamics in ${\mathcal{H}}_{>6}$. Same as (a) with an initial $\alpha =-5$ amplitude. (c) Same as (b), with an initial amplitude $\alpha =-4+i\sqrt{6}$. In (b) and (c) the successive frames correspond to the same step numbers as in (a).

Figure 3

Energy of the field as a function of the number of steps for a QZD dynamics inside ${\mathcal{H}}_{<6}$. Conditions are the same as for Fig. 2a, which presents snapshots of the first oscillation.

Figure 4

(a),(b) Initial and final Wigner functions $W(\xi )$ for a phase space tweezer operation. The first step ECs are depicted as solid lines in (a) and dotted lines in (b), the final ECs as solid lines in (b). The arrows in (b) indicate the two EC centers trajectories. (c) Cat created by a vacuum state crush operation. Initial (dotted lines) and final (solid line) ECs are plotted, with arrows indicating the motion of their centers. (d) Four-component cat created by three successive crushing operations.