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Physical Review A

Reconstructing wave packets by quantum-state holography

Ilya Sh. Averbukh, M. Shapiro, C. Leichtle, Wolfgang P. Schleich

Published Mar 1, 1999• 38 citations
Publisher

Abstract

We analyze and further develop our method of quantum-state holography for reconstructing quantum superposition states in molecules or atoms [Phys. Rev. Lett. 80, 1418 (1998)]. The technique is based on mixing the unknown object state with a known reference state generated in the same system by two delayed laser pulses, and detecting the total time- and frequency-integrated fluorescence as a function of the delay. The feasibility of the method is demonstrated by reconstructing various vibrational wave packets in sodium dimers. Both the cases of completely controlled and noisy relative phase between the laser pulses are considered. In the latter case, we use the technique of coherence observation by interference noise to recover the interference component of the fluorescence signal. Our results clearly demonstrate the robustness of quantum-state holography and the high quality of reconstruction even in the presence of the external noise.

DOI
10.1103/physreva.59.2163

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We analyze and further develop our method of quantum-state holography for reconstructing quantum superposition states in molecules or atoms [Phys. Rev. Lett. 80, 1418 (1998)]. The technique is based on mixing the unknown object state with a known reference state generated in the same system by two delayed laser pulses, and detecting the total time- and frequency-integrated fluorescence as a function of the delay. The feasibility of the method is demonstrated by reconstructing various vibrational wave packets in sodium dimers. Both the cases of completely controlled and noisy relative phase between the laser pulses are considered. In the latter case, we use the technique of coherence observation by interference noise to recover the interference component of the fluorescence signal. Our results clearly demonstrate the robustness of quantum-state holography and the high quality of reconstruction even in the presence of the external noise.
We present a method for performing quantum state holography, with which we completely characterize the amplitude and phase of an attosecond electron wave packet. Our approach is an extension of a recent publication [J. Mauritsson et al., Phys. Rev. Lett. 105, 053001 (2010)] in which we demonstrated experimentally that the energies and amplitudes of an attosecond electron wave packet can be characterized using attosecond electron interferometry. Here we show theoretically that attosecond electron interferometry can be extended to retrieve the phases of all the states that make up the wave packet. We demonstrate the feasibility of our method by analyzing a wave packet created by a shake-up process. We show that our method can successfully retrieve arbitrary phases and/or lifetimes added to the component eigenstates.
A method is presented for reconstructing the quantum state of vibrational wave packets in diatomic molecules by a heterodyne experiment. After the preparation of a wave packet, a femtosecond laser pulse interferes with the induced polarization and the resulting signal is frequency filtered and measured by a photodetector. The conditions are analyzed under which the resulting time- and frequency-resolved photocurrent contains the information needed to recover the quantum state of the prepared wave packet. It is shown that the vibrational wave function in the excited electronic state can be measured directly without the need of involved numerical reconstruction. Simulations of the proposed experiment are performed for sodium dimers.
Studies of wave packet dynamics often involve phase-selective measurements of coherent optical signals generated from sequences of ultrashort laser pulses. In wave packet interferometry (WPI), the separation between the temporal envelopes of the pulses must be precisely monitored or maintained. Here we introduce a new (and easy to implement) experimental scheme for phase-selective measurements that combines acousto-optic phase modulation with ultrashort laser excitation to produce an intensity-modulated fluorescence signal. Synchronous detection, with respect to an appropriately constructed reference, allows the signal to be simultaneously measured at two phases differing by 90 degrees. Our method effectively decouples the relative temporal phase from the pulse envelopes of a collinear train of optical pulse pairs. We thus achieve a robust and high signal-to-noise scheme for WPI applications, such as quantum state reconstruction and electronic spectroscopy. The validity of the method is demonstrated, and state reconstruction is performed, on a model quantum system--atomic Rb vapor. Moreover, we show that our measurements recover the correct separation between the absorptive and dispersive contributions to the system susceptibility.
Experimental and theoretical work is presented on the control of wave packet dynamics in atomic and molecular systems. Using sequences of phase-locked optical pulses, the link between optical phase and quantum mechanical phase is explored in the Na atom and Naj dimer, representing a step towards the logical engineering of quantum states in more complicated systems. A novel apparatus, constructed to study and control the vibrational dynamics of vibrational wave packets on the Na ionic potential surface, is described in chapter 3. Theoretical simulations for proposed experiment are presented in chapter 4. Control is achieved by exploiting the phase-evolution of the constituent vibrational quantum states within the wave packet superposition. The phase relationship and the accumulated phase difference between the various components of the wave packet is determined, and a sequence of phase-locked optical pulses is employed to selectively enhance or depopulate specific vibrational states, or sets of vibrational states. The quantum state composition of the resulting wave packet, and the efficiency of the control scheme, is determined by calculating the multi-pulse response of the time-dependent vibrational state populations. In chapter 5, the quantum interference between Rydberg electron wave packets in the Na atom is investigated using pairs of phase-locked wave packets, allowing manipulation of the total orbital angular momentum of Na Rydberg atoms. Initially the wave packet is composed of a superposition of s and d Rydberg series. Exploitation of the difference between the quantum defects of the two series allows specific angular momentum compositions within the resultant wave packet to be engineered. Experimentally, this final quantum state distribution is analysed in the frequency domain using state selective field ionisation, and in the time domain using the optical Ramsey method. The theoretical calculations show how the phase difference between pairs of optical pulses is linked to the corresponding Rydberg frequency spectrum, therefore enabling the control of the quantum state composition of the wave packets.
We study wave packet interferometry (WPI) considering the laser pulse fields both classical and quantum mechanically. WPI occurs in a molecule after subjecting it to the interaction with a sequence of phase-locked ultrashort laser pulses. Typically, the measured quantity is the fluorescence of the molecule from an excited electronic state. This signal has imprinted the interference of the vibrational wave packets prepared by the different laser pulses of the sequence. The consideration of the pulses as quantum entities in the analysis allows us to study the entanglement of the laser pulse states with the molecular states. With a simple model for the molecular system, plus several justified approximations, we solve for the fully quantum mechanical molecule-electromagnetic field state. We then study the reduced density matrices of the molecule and the laser pulses separately. We calculate measurable corrections to the case where the fields are treated classically.