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Tracking coherences in a dissipative ocean: Analysing and controlling Br2/Ar matrix

Heide Ibrahim

Published Jan 1, 2008• 1 citation
Publisher

Abstract

With the model system of a diatomic molecule embedded in a rare gas matrix (Br2/Ar), a method is introduced to enhance buried coherent structures and thus to prepare them out of an overwhelming, but incoherent background. Therefore, phase controlled pulse sequences are superimposed, which are generated with a pulse shaper in a direct way based on spectroscopic information. This requires a precise knowledge on the energetic signatures of the target state. This was accomplished via high resolution excitation spectroscopy covering 630 to 540 nm of the X(v′′ = 0)→B(v′) transition. Narrow zero phonon lines (ZPL) were observed with isotopic resolution from v′ = 2 to v′ = 19. They are accompanied by broad phonon sidebands (PSB), which reflect the matrix phonon density of states. With higher excitation energy, a broadening of ZPL and an increase in PSB due to an increase in matrix influence was observed and quantified. Two energetic positions were identified, where repulsive states cross the B-state. The time resolved pump – probe experiments were carried out with ultrashort and thus energetically very broad laser pulses. The B-state dynamics is completely superimposed by A-state dynamics in single pump - probe experiments with 590 nm. However, with the pulse trains the wave packets were created delayed by the B vibrational roundtrip time, which interfere constructively or destructively and thus select spectrally, depending on the relative phase. The required phase adjusted pulse trains were generated by impressing the molecular spectroscopic signature on the spectral composition of the ultrashort pulse. A phase dependent control scheme requires persisting electronic coherence. This was first determined in experiments with double pulses with a Michelson interferometer to at least 1.5 ps, which corresponds to the length of the experimental pulse sequence. In the case of constructive interference due to ZPL excitation, the B vibrational progression builds up and A-state dynamics is suppressed, successfully, since it adds up incoherently to an unmodulated background. Because of this, a surprisingly long coherence of more than 1 ps - also in the PSB - was determined, due to an inverse experiment, based on destructive interference. Since the efficiency of predissociation depends on the coupling strength of the molecule to the matrix, it was specifically attenuated or enhanced by excitation with wave packets which are predominantly composed of ZPL or PSB. Thereby, the dynamical development of predissociation could be determined. My work thus introduces a combination of spectrally sharp defined excitation and time resolved interrogation, which can only be achieved by the coherent superposition of elongated pulse trains. Further on, simulations on the free molecule in first order perturbation theory were carried out, to investigate the temporal behaviour of the interfering wave packets.

DOI
10.17169/refubium-7008

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With the model system of a diatomic molecule embedded in a rare gas matrix (Br2/Ar), a method is introduced to enhance buried coherent structures and thus to prepare them out of an overwhelming, but incoherent background. Therefore, phase controlled pulse sequences are superimposed, which are generated with a pulse shaper in a direct way based on spectroscopic information. This requires a precise knowledge on the energetic signatures of the target state. This was accomplished via high resolution excitation spectroscopy covering 630 to 540 nm of the X(v′′ = 0)→B(v′) transition. Narrow zero phonon lines (ZPL) were observed with isotopic resolution from v′ = 2 to v′ = 19. They are accompanied by broad phonon sidebands (PSB), which reflect the matrix phonon density of states. With higher excitation energy, a broadening of ZPL and an increase in PSB due to an increase in matrix influence was observed and quantified. Two energetic positions were identified, where repulsive states cross the B-state. The time resolved pump – probe experiments were carried out with ultrashort and thus energetically very broad laser pulses. The B-state dynamics is completely superimposed by A-state dynamics in single pump - probe experiments with 590 nm. However, with the pulse trains the wave packets were created delayed by the B vibrational roundtrip time, which interfere constructively or destructively and thus select spectrally, depending on the relative phase. The required phase adjusted pulse trains were generated by impressing the molecular spectroscopic signature on the spectral composition of the ultrashort pulse. A phase dependent control scheme requires persisting electronic coherence. This was first determined in experiments with double pulses with a Michelson interferometer to at least 1.5 ps, which corresponds to the length of the experimental pulse sequence. In the case of constructive interference due to ZPL excitation, the B vibrational progression builds up and A-state dynamics is suppressed, successfully, since it adds up incoherently to an unmodulated background. Because of this, a surprisingly long coherence of more than 1 ps - also in the PSB - was determined, due to an inverse experiment, based on destructive interference. Since the efficiency of predissociation depends on the coupling strength of the molecule to the matrix, it was specifically attenuated or enhanced by excitation with wave packets which are predominantly composed of ZPL or PSB. Thereby, the dynamical development of predissociation could be determined. My work thus introduces a combination of spectrally sharp defined excitation and time resolved interrogation, which can only be achieved by the coherent superposition of elongated pulse trains. Further on, simulations on the free molecule in first order perturbation theory were carried out, to investigate the temporal behaviour of the interfering wave packets.
Electronic and vibrational coherences of Cl2 embedded in solid Ar are investigated by exciting to the B state with a phase-locked pulse pair from an unbalanced Michelson interferometer, where the chirp difference matches the B state anharmonicity. Recording the A' --> X fluorescence after relaxation is compared to probing to charge transfer states by a third pulse. The three-pulse experiment delivers more details on the decoherence processes. The signal modulation due to phase tuning up to the third vibrational round-trip time indicates that the electronic coherence in the B <-- X transition is preserved for more than 660 fs in the solid Ar environment where many body electronic interactions take place. Vibrational coherence lasts longer than 3 ps according to the observed half revival of the wavepacket. Control of the coupling between wavepacket motion and lattice oscillation is demonstrated by tuning the relative phase between the phase-locked pulses, preparing wavepackets predominantly composed of either zero-phonon lines or phonon side bands.
Electronic and vibrational coherences in the B 3 Π(0 + u ) ← X 1 Σ + g transition of chlorine (Cl 2 ) molecules doped in an argon matrix are investigated by exciting with a pulse pair whose relative phase is scanned for every time delay step. The spacing and position of the generated spectral comb are controlled by the delay and relative phase of the pulses. The B 3 Π(0 + u ) ← X 1 Σ + g excitation spectrum shows a progression of zero phonon lines which are decoupled from the lattice and of phonon side bands which originate from a concerted excitation of intramolecular and lattice vibrations. The molecular anharmonicity is compensated for by applying a negative chirp difference of the two pulses, which leads to an asymmetry in the signal around time zero. Absolute phase values are determined from spectral positions in the measured comb patterns. They are used to calculate fringe patterns and to simulate interferograms by a multiplication with the excitation spectrum which are compared with the measured ones in detail. From simulated interferograms of zero phonon lines and phonon side bands, we show that the two contributions can be selected with a large contrast by a time delay of two molecular vibrational periods.
With a train of 5 phase controlled ultrashort pulses, we enhance a coherent vibronic transition to exceed a dominant incoherent background. The interference in the chromophore generates a spectral comb which is adjusted to a progression of internal Br2 vibrations coupled to phonons of the surrounding Ar lattice. It steers the mode-specific phase evolution of the system. The trains are generated by straightforward programing of the spectral comb in a pulse shaper unit. Excitations involving several hundred degrees of freedom remain coherent on a picosecond time scale.
Time-resolved, electronically resonant, coherent anti-Stokes Raman scattering is used to prepare and interrogate vibronic coherences of molecular iodine in matrix Ar. Coherences that involve evolution on the excited B(3Π0u) state, first- and third-order coherences, decay in less than one vibrational period (τ<300 fs). In contrast, as many as 200 vibrational periods of motion can be observed for Raman-prepared wave packets consisting of zero-phonon vibrational superpositions on the ground electronic state (second-order coherence). Packets consisting of v=4, 5 and v=3, 4, 5 on the X(1Σg) state decay with a half-life of 10±1 ps at 31 K, allowing a more accurate measure of vibrational level spacings and decoherence time than has been possible in frequency domain. The harmonic frequency of the molecule is reduced by 1.5 cm−1 (0.7%) in the matrix. The lack of recurrence in the excited electronic state ensures that the resonant anti-Stokes scattering arises only from the negative momentum component of the Raman packet. This momentum filter, which should be ubiquitous in condensed media, leads to a signal with deeper modulation than in the gas phase.
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.
Any real system, no matter how well isolated, unavoidably interacts with the environment. This interaction makes the evolution of a quantum system nonunitary and destroys the coherence of quantum superpositions. This process, known as decoherence, is widely regarded as the most important and fundamental obstacle to the practical realization of quantum information processing. On the other hand, the objectives of quantum control are predicated on the ability to manipulate the system coherently over a period of time. Quantum control has been applied successfully to several experimental systems and coupling such a controlled system to an environment makes the study of coherence loss possible. The standard model of decoherence is formulated in terms of a system, defined by the observables that can be measured, and a reservoir, de¯ned by those degrees of freedom that are not accessed by observation. The vibrational and rotational degree of freedom of diatomic molecules form an experimental model of such a system and bath 1. The nature of the ro-vibrational coupling does not allow a Decoherence Free Subspace, instead we try to identify a Decoherence Resistant Subspace using closed loop control. We set up a learning control loop experiment to monitor the coherence in a vibrational wavepacket, consisting of about 6 vibrational states of the A(1Σ+g ) electronic state, excited by a shaped, ultrashort optical pulse, and then to determine the pulse shape that yielded the longest coherence lifetime. The coherence of the vibrational wavepacket was monitored by measuring the fluorescence quantum beats from the outer turning point of the wave packet's trajectory. The closed loop controller altered the shape of the driving optical pulse to maximize the the depth of modulation of the quantum beats at a prescribed time after excitation, within the constraints of the laser system. The outcome of this closed loop control experiment shows an improvement of the beat decay constant of about 60%, as shown in Fig. (1), a result which occurs for several di®erent pulse shapes. Our experiments show that a number of interesting decoherence-resistant excitations exist. The nature of the dephasing was examined theoretically. Using measured optical pulse shapes, we simulated numerically the molecular wavepacket in the limit of perturbation theory. The experiment and simulations show that there are di®erent mechanisms contributing to the decoherence resistant excitation. The shaped pulse reduces the °uctuations in the wave packet spatial extent, which in turn changes the system reservoir coupling. Other components of the optimal pulse are a sequence of pulses that creates constructive interference of the vibrational wavepacket at the desired time, and chirp which compensates for the anharmonicity of the adiabatic potential. The experimental results show general agreement with numerical simulations. We conclude that wavepackets resistant to dephasing do exist,and that learning algorithms provide an effcient means for finding them.