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Quantum Electronics and Laser Science Conference

Generation and measurement of nonclassical states of molecules

Ian A. Walmsley, Leon J. Waxer, M. Anderson, Luı́s E. E. de Araujo, Czesław Radzewicz

Published Jan 20, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qels.1999.807490

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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.
Summary form only given. The development of methods to manipulate and measure the quantum mechanical state of a physical system represents one of the great challenges of modern science. Examples of systems in which quantum control is sought or has been accomplished include trapped atomic ions, the electromagnetic field, Rydberg electrons, nuclear spins and vibrations in molecules, and chemical reactions. For many years a paradigm for quantum coherent evolution has been the occurrence of tunneling in macroscopic and mesoscopic double-well potentials. Much theoretical work has been done on this model system, but a series of fundamental questions remain to be addressed in well-controlled experiments, notably whether coherent evolution can be enforced in the presence of a noisy environment, by suitable perturbations of the state of the tunneling particle. The challenge is to find simple physical systems, which can be made to interact with a well characterized environment in a controlled manner.
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.
Rydberg atoms held in optical tweezer arrays combine vibrational and electronic degrees of freedom that can be coupled and manipulated at a microscopic level. This opens opportunities for the quantum simulation of artificial molecular systems and offers in particular a platform for probing complex vibronic dynamics in controlled settings with increasing complexity. Tailored interatomic interactions and electron-phonon couplings yield handles for designing electronic state manifolds, for studying structural transitions, and for exploring nonclassical vibrational states near molecular instabilities. Furthermore, this quantum simulator opens opportunities for testing and quantifying the validity of fundamental concepts, such as the Born-Oppenheimer approximation and quantum corrections to it.
We have numerically examined optimization of the experimentally achievable shapes of mid-infrared femtosecond laser pulses to construct elementary quantum gates using molecular rovibrational states of a single molecule. Instead of optimizing the electric field by optimal control theory, the method generally used in theoretical studies of coherent control, the transmittance and the phase shift of conventional pulse shapers were optimized in the frequency domain by a genetic algorithm. The target molecular system we examined was the rotation-vibration states of CO in the $X({^{1}\ensuremath{\Sigma}}^{+})$ ground electronic state. Although the existence of the rotational degrees of freedom makes the quantum gate operation complicated, high fidelity of over 0.95 was achieved for one-rovibrational-qubit systems, which indicates that a molecular quantum computer may be feasible for at least one-qubit calculations on a diatomic molecule. On the other hand, two-qubit calculations are more difficult to achieve in a single CO molecule using rotational and vibrational degrees of freedom as different qubits. The importance of the control of the rotational in addition to the vibrational wave packet in order to realize a molecular quantum computer is discussed.
It was first realized by Purcell (1) that the spontaneous emission rate of a quantum system can be enhanced or suppressed by placing it in a resonant radiofrequency cavity. Spontaneous emission as it was first theoretically described by Einstein (2) is not a pure property of matter. It is described by matter coupled to quantized radiation field modes, which can be manipulated in an artificial structure such as a cavity. Cavity quantum electrodynamics (QED) is used to describe such effects that intimately depend on the fact that light is made of photons. Cavity QED has been extensively studied in atoms and the experimental proof was awarded with the Nobel Prize in 2012 (3). It has been applied to cooling of single atoms and for the detection of single atoms and creating and studying states with few photons and few atoms (4). In more recent developments these ideas have been extended to manipulate electronic states (5) and vibrations in molecules (6, 7). In PNAS, Flick et al. (8) introduce recent theoretical developments for the application of cavity QED to molecules and suggest possible novel applications to photochemistry. These include nonadiabatic dynamics of molecules in cavities, the modification of molecular properties, and the integration of QED with density functional theory. A quantized electromagnetic field mode can be described as a harmonic oscillator whose coordinate is the electric field displacement (Fig. 1 A ). The zero point energy translates into a nonvanishing field intensity ⟨ e 2 ⟩ in the ground state | 0 ⟩ (vacuum fluctuations). The electric vacuum field increases for a small cavity volume e c = ℏ ω c V ϵ 0 , [1] Fig. 1. ( A ) Illustration of the standing wave cavity mode and the resulting field quantization (Fock states). ( B ) Combined matter-field states (dressed states, | ± , n ⟩ … [↵][1]1To whom correspondence should be addressed. Email: smukamel{at}uci.edu. [1]: #xref-corresp-1-1