Quantum State Holography

We introduce a novel method for reconstructing quantum superposition states excited in molecules or atoms by short laser pulses. The technique is based on mixing the unknown object state with a known reference state generated in the same system by an additional delayed laser pulse, and detecting the total time-and frequency-integrated uorescence as a function of the delay. We demonstrate the feasibility of the method by reconstructing various vibrational wavepackets in sodium dimers. The problem of how to measure the wave function of a quantum system in amplitude and phase has attracted a lot of attention over the last few years 1]. Such a reconstruction has been achieved for only a few systems, such as a single mode of the electromagnetic eld 2,3], vibratory states of molecules 4], a single ion stored in a Paul trap 5], and an atomic beam 6]. In this Letter, we address the problem of measuring the quantum state of a molecule 4,7,8], and propose the concept of Quantum State Holography. In analogy to the ordinary optical holography, we interfere the object wave function to be measured with a known reference wave function. For this purpose, we employ a sequence of two time-delayed laser pulses which subsequently excite the object and the reference wave packet in the excited molecular potential. This is similar to recently introduced technique of wavepacket cross-interferometry 9]. The total incoherent uorescence 10] of the excited molecule, which is recorded as the function of the delay time , serves as a hologram. We show that these data contain enough information to extract the full quantum state of the object wave packet. Moreover, we demonstrate the feasibility of quantum state holography by numerically simulating the reconstruction of wave packets in a sodium dimer. The method is capable of determining wave packets in arbitrary potentials and is not restricted to weakly anharmonic molecules. Quantum state holography applied to a wavepacket in an excited molecular potential adds coherently the reference state j r i = e ii() P n b n jni to the object state j o i = P n a n e ?i!n jni which already has evolved for a time. Here, jni denotes the n?th vibrational state with energy E n = h! n in the excited molecular potential, and we allow for an additional phase () between the object and reference states. This relative phase is determined by the actual …