This review emphasizes the physical principles underlying the dephasing of nonstationary vibrational states of molecules with multiple vibrational degrees of freedom. The motion of atoms within molecules can be described to a very good approximation by a many-level system of coupled anharmonic quantized oscillators. The separation of electronic and nuclear timescales, combined with weak symmetry breaking inherent in molecular structures, guarantees that the Hamiltonian can always be cast in a form that is local in the quantum state space of the molecular vibrations. The resulting nonexponential dephasing dynamics can be controlled with external fields to stabilize nonstationary quantum states, and both quantum–classical and fully quantum control formalisms are described. Coupled molecular vibrations interacting with external fields also offer prospects for quantum computing because vibrational level spacings can be made very large compared to thermal noise, and relaxation mechanisms such as infrared fluorescence are many orders of magnitude slower than the timescales required for coherence transfer. Finally, a toy model that provides insights into the interaction of vibrational degrees of freedom with 'solvent' modes is also discussed, and exhibits nonexponential dynamics in certain regimes.
This review emphasizes the physical principles underlying the dephasing of nonstationary vibrational states of molecules with multiple vibrational degrees of freedom. The motion of atoms within molecules can be described to a very good approximation by a many-level system of coupled anharmonic quantized oscillators. The separation of electronic and nuclear timescales, combined with weak symmetry breaking inherent in molecular structures, guarantees that the Hamiltonian can always be cast in a form that is local in the quantum state space of the molecular vibrations. The resulting nonexponential dephasing dynamics can be controlled with external fields to stabilize nonstationary quantum states, and both quantum–classical and fully quantum control formalisms are described. Coupled molecular vibrations interacting with external fields also offer prospects for quantum computing because vibrational level spacings can be made very large compared to thermal noise, and relaxation mechanisms such as infrared fluorescence are many orders of magnitude slower than the timescales required for coherence transfer. Finally, a toy model that provides insights into the interaction of vibrational degrees of freedom with 'solvent' modes is also discussed, and exhibits nonexponential dynamics in certain regimes.
Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available Hilbert space. The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimensions. Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes, including bosonic encoding schemes in quantum information, reliable and efficient measurement techniques, and quantum operations that allow various quantum simulations and quantum computation algorithms. We describe experiments using the vibrational modes, including the preparation of non-classical states, molecular vibronic sampling, and applications in quantum thermodynamics. We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.
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.
Summary form only given. One of the most enticing notions of modern optical physics is the idea that one can manipulate the quantum state of atoms and molecules, and thus engineer the properties of matter at its most fundamental level. Homonuclear diatomic molecules are model systems for studying quantum control. They have several degrees of freedom associated with different particles (three are particularly useful: the internuclear vibrational and rotational coordinates and the electronic coordinate) and each degree of freedom has a low dissipation rate as compared to its characteristic frequency. The coupling of the electronic and vibrational degree of freedom allows the preparation of arbitrary vibrational wave packets in both excited and ground electronic states of the molecules by the application of optical radiation.
Modern computational techniques used to simulate quantum chemistry are on the boundary of tractability due to the exponential growth of the molecular wavefunction, requiring a careful balance between molecule size and simulation accuracy. In recent years, quantum computing has risen in popularity as a potential alternative to conventional (classical) techniques; however, most methods rely on access to "digital" quantum computers composed of qubits and quantum gates, which at present are severely limited by noise. We have developed a real-time, analog approach to simulate vibronic chemical dynamics with existing quantum technology. Our approach uses an intuitive mapping of molecular electronic and vibrational degrees of freedom onto quantum resonators and qudit (d-level system) states, with controllable couplings between degrees of freedom. The measurement output can be mapped onto different time-dependent observables, including the time-domain simulation of vibronic spectra. Our approach can also incorporate controlled sources of noise to simulate system-bath interactions and dissipative dynamics at a minimal cost. We present experimental results using a trapped-ion device, thus showing the potential for near-term simulation of chemical dynamics in complex environments beyond the abilities of classical computers.
The generation and control of entanglement in a quantum mechanical system are critical elements of nearly all quantum applications. Molecular systems are promising candidates, with numerous degrees of freedom able to be targeted. However, knowledge of intersystem entanglement mechanisms in such systems is limited. In this work, we demonstrate the generation of entanglement between vibrational degrees of freedom in molecules via strong coupling to a cavity mode driven by a weak coherent field. In a bimolecular system, we show that entanglement can be generated not only between the cavity and molecular system but also between molecules. This process also results in the generation of nonclassical states of light, providing potential pathways for harnessing entanglement in molecular systems.
We propose and analyze a new approach to the coherent control and manipulation of quantum degrees of freedom in disordered, interacting systems in the many-body localized phase. Our approach leverages a number of unique features of many-body localization: a lack of thermalization, a locally gapped spectrum, and slow dephasing. Using the technique of quantum phase estimation, we demonstrate a protocol that enables the local preparation of a many-body system into an effective eigenstate. This leads to the ability to encode information and control interactions without full microscopic knowledge of the underlying Hamiltonian. Finally, we analyze the effects of weak coupling to an external bath and provide an estimate for the fidelity of our protocol.